id
stringlengths 25
25
| question
stringlengths 45
1.01k
| chain
stringlengths 75
4.11k
| result
stringclasses 5
values | result_float
float64 -4,212
100B
| question_without_options
stringlengths 6
962
| options
dict | annotated_formula
stringlengths 7
6.48k
| linear_formula
stringlengths 8
925
| rationale
stringlengths 1
2.74k
| category
stringclasses 6
values |
|---|---|---|---|---|---|---|---|---|---|---|
math_qa__V6wRgcS4hPF1RHUU
|
In a hostel, the number of students decreased by 8% and the price of food increased by 20% over the previous year. If each student consumes the same amount of food then By how much should the consumption of food be cut short by every student, so that the total cost of the food remains the same as that of the previous year?
Choose the correct choice:
A) 19 % B) 15 % C) 25 % D) 40 % E) 9.4 %
|
<gadget id="calculator">100 * 100</gadget>
<output>10_000</output>
<gadget id="calculator">100 - 8</gadget>
<output>92</output>
<gadget id="calculator">100 + 20</gadget>
<output>120</output>
<gadget id="calculator">92 * 120</gadget>
<output>11_040</output>
<gadget id="calculator">10_000 / 11_040</gadget>
<output>125/138 = around 0.905797</output>
<gadget id="calculator">1 - (125/138)</gadget>
<output>13/138 = around 0.094203</output>
<gadget id="calculator">(13/138) * 100</gadget>
<output>650/69 = around 9.42029</output>
<result>E</result>
|
E
| 9.4 |
In a hostel, the number of students decreased by 8% and the price of food increased by 20% over the previous year. If each student consumes the same amount of food then By how much should the consumption of food be cut short by every student, so that the total cost of the food remains the same as that of the previous year?
|
{
"A": "19 %",
"B": "15 %",
"C": "25 %",
"D": "40 %",
"E": "9.4 %"
}
|
multiply(subtract(const_1, divide(multiply(const_100, const_100), multiply(subtract(const_100, 8), add(const_100, 20)))), const_100)
|
add(n1,const_100)|multiply(const_100,const_100)|subtract(const_100,n0)|multiply(#0,#2)|divide(#1,#3)|subtract(const_1,#4)|multiply(#5,const_100)|
|
"cost of food ( c ) = food consumed per student ( f ) * number of students ( n ) * price of food ( p ) originally , c = fnp when number of students decrease by 8 % , and the price of food increases by 20 % , c = f ( new ) * ( 0.92 n ) * ( 1.2 p ) = > f ( new ) = f / ( 0.92 * 1.2 ) = > f ( new ) = 0.906 f therefore the new cost of food must be 90.6 % of the old cost , or the cost of food must decrease by 9.4 % answer : e"
|
general
|
math_qa__TvWEF9fwlWfO1xjG
|
The total circumference of two circles is 88. If the first circle has a circumference that is exactly twice the circumference of the second circle, then what is the approximate sum of their two radii? Choose the correct choice from the following: A) 5.7 B) 6.0 C) 6.7 D) 9.7 E) 14.0
|
<gadget id="calculator">88 / 3</gadget>
<output>88/3 = around 29.333333</output>
<gadget id="calculator">(88/3) / 3</gadget>
<output>88/9 = around 9.777778</output>
<gadget id="calculator">(88/3) * 2</gadget>
<output>176/3 = around 58.666667</output>
<gadget id="calculator">(176/3) / 3</gadget>
<output>176/9 = around 19.555556</output>
<gadget id="calculator">(88/9) + (176/9)</gadget>
<output>88/3 = around 29.333333</output>
<gadget id="calculator">(88/3) / 2</gadget>
<output>44/3 = around 14.666667</output>
<result>E</result>
|
E
| 14 |
The total circumference of two circles is 88. If the first circle has a circumference that is exactly twice the circumference of the second circle, then what is the approximate sum of their two radii?
|
{
"A": "5.7",
"B": "6.0",
"C": "6.7",
"D": "9.7",
"E": "14.0"
}
|
divide(add(divide(divide(88, const_3), const_3), divide(multiply(divide(88, const_3), const_2), const_3)), const_2)
|
divide(n0,const_3)|divide(#0,const_3)|multiply(#0,const_2)|divide(#2,const_3)|add(#1,#3)|divide(#4,const_2)|
|
"let r = radius of smaller circle . let r = radius of larger circle therefore : 2 Ο r + 2 Ο r = 88 where 2 r = r thus : 2 Ο r + 4 Ο r = 88 6 Ο r = 88 r = approx 4.7 Ο r + 2 r Ο = 88 3 Ο r = 88 r = approx 9.3 r + r = approx 14.0 answer : e"
|
general
|
math_qa__ssRpNS2MNR2G3sHJ
|
How many multiples of 2 are there between 101 and 999 ? Choose the correct choice from the following answers.
A) 250 B) 440 C) 510 D) 575 E) 449
|
<gadget id="calculator">999 - 101</gadget>
<output>898</output>
<gadget id="calculator">898 / 2</gadget>
<output>449</output>
<gadget id="calculator">449 + 1</gadget>
<output>450</output>
<result>E</result>
|
E
| 449 |
How many multiples of 2 are there between 101 and 999 ?
|
{
"A": "250",
"B": "440",
"C": "510",
"D": "575",
"E": "449"
}
|
add(divide(subtract(999, 101), 2), const_1)
|
subtract(n2,n1)|divide(#0,n0)|add(#1,const_1)|
|
"2 multiples are 102 , 104,106 , - - - - - - - - - , 994 , 996,998 it should be mentioned whether 1 and 89 are inclusive . the answer is ( 998 - 102 ) / 2 + 1 = 449 answer is e"
|
general
|
math_qa__93q4vIEGkJLI81Mz
|
Find the smallest number which when divided by 13 and 16 leaves respective remainders of 2 and 5. Choose the correct option.
A) 128
B) 197
C) 127
D) 182
E) 091
|
<gadget id="calculator">13 * 16</gadget>
<output>208</output>
<gadget id="calculator">10 + 1</gadget>
<output>11</output>
<gadget id="calculator">208 - 11</gadget>
<output>197</output>
<result>B</result>
|
B
| 197 |
Find the smallest number which when divided by 13 and 16 leaves respective remainders of 2 and 5.
|
{
"A": "128",
"B": "197",
"C": "127",
"D": "182",
"E": "091"
}
|
subtract(multiply(13, 16), add(const_10, const_1))
|
add(const_1,const_10)|multiply(n0,n1)|subtract(#1,#0)|
|
"explanation : let ' n ' is the smallest number which divided by 13 and 16 leaves respective remainders of 2 and 5 . required number = ( lcm of 13 and 16 ) - ( common difference of divisors and remainders ) = ( 208 ) - ( 11 ) = 197 . answer : b"
|
general
|
math_qa__DK32PYeWH4qe1ser
|
How much is 80% of 40 is greater than 4/5 of 20? Choose the correct choice from the following
A) 12 B) 27 C) 18 D) 16 E) 81
|
<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">40 * (4/5)</gadget>
<output>32</output>
<gadget id="calculator">4 / 5</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(4/5) * 20</gadget>
<output>16</output>
<gadget id="calculator">32 - 16</gadget>
<output>16</output>
<result>D</result>
|
D
| 16 |
How much is 80% of 40 is greater than 4/5 of 20?
|
{
"A": "12",
"B": "27",
"C": "18",
"D": "16",
"E": "81"
}
|
subtract(multiply(40, divide(80, const_100)), multiply(divide(4, 5), 20))
|
divide(n0,const_100)|divide(n2,n3)|multiply(n1,#0)|multiply(n4,#1)|subtract(#2,#3)|
|
"( 80 / 100 ) * 40 Γ’ β¬ β ( 4 / 5 ) * 20 32 - 16 = 16 answer : d"
|
general
|
math_qa__E1NXIV3TwgQT2ALy
|
If the price of sugar rises from Rs. 10 per kg to Rs. 13 per kg, a person, to have no increase in the expenditure on sugar, will have to reduce his consumption of sugar by
Choose the correct option
A) 15 % B) 20 % C) 23 % D) 30 % E) none
|
<gadget id="calculator">1 * 10</gadget>
<output>10</output>
<gadget id="calculator">10 / 13</gadget>
<output>10/13 = around 0.769231</output>
<gadget id="calculator">1 - (10/13)</gadget>
<output>3/13 = around 0.230769</output>
<gadget id="calculator">(3/13) * 100</gadget>
<output>300/13 = around 23.076923</output>
<result>C</result>
|
C
| 23 |
If the price of sugar rises from Rs. 10 per kg to Rs. 13 per kg, a person, to have no increase in the expenditure on sugar, will have to reduce his consumption of sugar by
|
{
"A": "15 %",
"B": "20 %",
"C": "23 %",
"D": "30 %",
"E": "none"
}
|
multiply(subtract(const_1, divide(multiply(const_1, 10), 13)), const_100)
|
multiply(n0,const_1)|divide(#0,n1)|subtract(const_1,#1)|multiply(#2,const_100)|
|
"sol . let the original consumption = 100 kg and new consumption = x kg . so , 100 x 10 = x Γ 13 = x = 77 kg . β΄ reduction in consumption = 23 % . answer c"
|
general
|
math_qa__iHbSXJxLIMZIL10p
|
A train crosses a bridge of length 800 m in 45 seconds and a lamp post on the bridge in 15 seconds. What is the length of the train in metres?
Choices
A) 375 m B) 750 m C) 400 m D) 800 m E) 300 m
|
<gadget id="calculator">45 - 15</gadget>
<output>30</output>
<gadget id="calculator">800 / 30</gadget>
<output>80/3 = around 26.666667</output>
<gadget id="calculator">(80/3) * 15</gadget>
<output>400</output>
<result>C</result>
|
C
| 400 |
A train crosses a bridge of length 800 m in 45 seconds and a lamp post on the bridge in 15 seconds. What is the length of the train in metres?
|
{
"A": "375 m",
"B": "750 m",
"C": "400 m",
"D": "800 m",
"E": "300 m"
}
|
multiply(divide(800, subtract(45, 15)), 15)
|
subtract(n1,n2)|divide(n0,#0)|multiply(n2,#1)|
|
"let length of train = l case - 1 : distance = 800 + l ( while crossing the bridge ) time = 45 seconds i . e . speed = distance / time = ( 800 + l ) / 45 case - 2 : distance = l ( while passing the lamp post ) time = 15 seconds i . e . speed = distance / time = ( l ) / 15 but since speed has to be same in both cases so ( 800 + l ) / 45 = ( l ) / 15 i . e . 800 + l = 3 l i . e . 2 l = 800 i . e . l = 400 answer : option c"
|
physics
|
math_qa__ieyc1uXXHYGb4rDt
|
A train travels 290 km in 4.5 hours and 400 km in 5.5 hours.find the average speed of train. Select.
A) 80 kmph B) 69 kmph C) 70 kmph D) 90 kmph E) none of these
|
<gadget id="calculator">290 + 400</gadget>
<output>690</output>
<gadget id="calculator">4.5 + 5.5</gadget>
<output>10</output>
<gadget id="calculator">690 / 10</gadget>
<output>69</output>
<result>B</result>
|
B
| 69 |
A train travels 290 km in 4.5 hours and 400 km in 5.5 hours.find the average speed of train.
|
{
"A": "80 kmph",
"B": "69 kmph",
"C": "70 kmph",
"D": "90 kmph",
"E": "none of these"
}
|
divide(add(290, 400), add(4.5, 5.5))
|
add(n0,n2)|add(n1,n3)|divide(#0,#1)|
|
"as we know that speed = distance / time for average speed = total distance / total time taken thus , total distance = 290 + 400 = 690 km thus , total speed = 10 hrs or , average speed = 690 / 10 or , 69 kmph . answer : b"
|
physics
|
math_qa__aJZ9w0GZkzXjvcUl
|
When a certain tree was first planted, it was 4 feet tall, and the height of the tree increased by a constant amount each year for the next 6 years. At the end of the 6th year, the tree was 1/3 taller than it was at the end of the 4th year. By how many feet did the height of the tree increase each year?
Choose one.
A) 3 / 10 B) 2 C) 1 / 2 D) 2 / 3 E) 6 / 5
|
<gadget id="calculator">6 - 4</gadget>
<output>2</output>
<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">4 / 2</gadget>
<output>2</output>
<result>B</result>
|
B
| 2 |
When a certain tree was first planted, it was 4 feet tall, and the height of the tree increased by a constant amount each year for the next 6 years. At the end of the 6th year, the tree was 1/3 taller than it was at the end of the 4th year. By how many feet did the height of the tree increase each year?
|
{
"A": "3 / 10",
"B": "2",
"C": "1 / 2",
"D": "2 / 3",
"E": "6 / 5"
}
|
divide(4, subtract(multiply(subtract(6, 4), 3), 4))
|
subtract(n1,n0)|multiply(n4,#0)|subtract(#1,n0)|divide(n0,#2)|
|
"say , the tree grows by x feet every year . then , 4 + 6 x = ( 1 + 1 / 3 ) ( 4 + 4 x ) or , x = 2 answer b"
|
general
|
math_qa__oUsbiQyqSwiclXRP
|
A 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2. 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more. At the end of the two removal and replacement, what is the ratio W of milk and water in the resultant mixture? Options:
A) 17 : 3 B) 9 : 1 C) 3 : 17 D) 5 : 3 E) 11 : 2
|
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">3 / 5</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">20 - 10</gadget>
<output>10</output>
<gadget id="calculator">(3/5) * 10</gadget>
<output>6</output>
<gadget id="calculator">6 + 10</gadget>
<output>16</output>
<gadget id="calculator">16 / 20</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(4/5) * 10</gadget>
<output>8</output>
<gadget id="calculator">8 + 10</gadget>
<output>18</output>
<gadget id="calculator">2 / 5</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) * 10</gadget>
<output>4</output>
<gadget id="calculator">4 / 20</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 10</gadget>
<output>2</output>
<gadget id="calculator">18 / 2</gadget>
<output>9</output>
<result>B</result>
|
B
| 9 |
A 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2. 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more. At the end of the two removal and replacement, what is the ratio W of milk and water in the resultant mixture?
|
{
"A": "17 : 3",
"B": "9 : 1",
"C": "3 : 17",
"D": "5 : 3",
"E": "11 : 2"
}
|
divide(add(multiply(divide(add(multiply(divide(3, add(3, 2)), subtract(20, 10)), 10), 20), subtract(20, 10)), 10), multiply(divide(multiply(divide(2, add(3, 2)), subtract(20, 10)), 20), subtract(20, 10)))
|
add(n1,n2)|subtract(n0,n3)|divide(n1,#0)|divide(n2,#0)|multiply(#2,#1)|multiply(#3,#1)|add(n3,#4)|divide(#5,n0)|divide(#6,n0)|multiply(#7,#1)|multiply(#8,#1)|add(n3,#10)|divide(#11,#9)|
|
"he 20 litre mixture contains milk and water in the ratio of 3 : 2 . therefore , there will be 12 litres of milk in the mixture and 8 litres of water in the mixture . step 1 . when 10 litres of the mixture is removed , 6 litres of milk is removed and 4 litres of water is removed . therefore , there will be 6 litres of milk and 4 litres of water left in the container . it is then replaced with pure milk of 10 litres . now the container will have 16 litres of milk and 4 litres of water . step 2 . when 10 litres of the new mixture is removed , 8 litres of milk and 2 litres of water is removed . the container will have 8 litres of milk and 2 litres of water in it . now 10 litres of pure milk is added . therefore , the container will have 18 litres of milk and 2 litres of water in it at the end of the second step . therefore , the ratio of milk and water is 18 : 2 or 9 : 1 . shortcut . we are essentially replacing water in the mixture with pure milk . let w _ o be the amount of water in the mixture originally = 8 litres . let w _ r be the amount of water in the mixture after the replacements have taken place . then , { w _ r } / { w _ o } = ( 1 - r / m ) ^ n where r is the amount of the mixture replaced by milk in each of the steps , m is the total volume of the mixture and n is the number of times the cycle is repeated . hence , { w _ r } / { w _ o } Β = ( 1 / 2 ) ^ 2 Β = 1 / 4 therefore w , w _ r Β = { w _ o } / 4 = 8 / 4 Β = 2 litres . b"
|
general
|
math_qa__z524oOJVzpzfegGB
|
Of the families in City X in 1992, 60 percent owned a personal computer. The number of families in City X owning a computer in 1993 was 50 percent greater than it was in 1992, and the total number of families in City X was 3 percent greater in 1993 than it was in 1992. what percent of the families in City X owned a personal computer in 1993? Choose the correct choice from the following choices
A) 68.99 % B) 66.55 % C) 91.23 % D) 77.77 % E) 87.37 %
|
<gadget id="calculator">50 + 100</gadget>
<output>150</output>
<gadget id="calculator">150 * 60</gadget>
<output>9_000</output>
<gadget id="calculator">9_000 / 100</gadget>
<output>90</output>
<gadget id="calculator">100 + 3</gadget>
<output>103</output>
<gadget id="calculator">90 / 103</gadget>
<output>90/103 = around 0.873786</output>
<gadget id="calculator">100 * (90/103)</gadget>
<output>9_000/103 = around 87.378641</output>
<result>E</result>
|
E
| 87.37 |
Of the families in City X in 1992, 60 percent owned a personal computer. The number of families in City X owning a computer in 1993 was 50 percent greater than it was in 1992, and the total number of families in City X was 3 percent greater in 1993 than it was in 1992. what percent of the families in City X owned a personal computer in 1993?
|
{
"A": "68.99 %",
"B": "66.55 %",
"C": "91.23 %",
"D": "77.77 %",
"E": "87.37 %"
}
|
multiply(const_100, divide(divide(multiply(add(50, const_100), 60), const_100), add(const_100, 3)))
|
add(n3,const_100)|add(n5,const_100)|multiply(n1,#0)|divide(#2,const_100)|divide(#3,#1)|multiply(#4,const_100)|
|
"say a 100 families existed in 1994 then the number of families owning a computer in 1994 - 60 number of families owning computer in 1998 = 60 * 150 / 100 = 90 number of families in 1998 = 103 the percentage = 90 / 103 * 100 = 87.37 % . answer : e"
|
general
|
math_qa__chbUdl7flJAvAeR8
|
Find the value of (β1.21)/(β0.81) + (β1.00)/(β0.49) is Choose the correct choice from the following answers
A) 2.65 B) 145 / 63 C) 155 / 63 D) 125 / 63 E) 185 / 63
|
<gadget id="calculator">1.21 ** (1/2)</gadget>
<output>1.1</output>
<gadget id="calculator">0.81 ** (1/2)</gadget>
<output>0.9</output>
<gadget id="calculator">1.1 / 0.9</gadget>
<output>1.222222</output>
<gadget id="calculator">1 ** (1/2)</gadget>
<output>1</output>
<gadget id="calculator">0.49 ** (1/2)</gadget>
<output>0.7</output>
<gadget id="calculator">1 / 0.7</gadget>
<output>1.428571</output>
<gadget id="calculator">1.222222 + 1.428571</gadget>
<output>2.650793</output>
<result>A</result>
|
A
| 2.65 |
Find the value of (β1.21)/(β0.81) + (β1.00)/(β0.49) is
|
{
"A": "2.65",
"B": "145 / 63",
"C": "155 / 63",
"D": "125 / 63",
"E": "185 / 63"
}
|
add(divide(sqrt(1.21), sqrt(0.81)), divide(sqrt(1), sqrt(0.49)))
|
sqrt(n0)|sqrt(n1)|sqrt(n2)|sqrt(n3)|divide(#0,#1)|divide(#2,#3)|add(#4,#5)
|
( β 1.21 ) / ( β 0.81 ) + ( β 1.00 ) / ( β 0.49 ) 11 / 9 + 10 / 7 = > 2.65 answer is a
|
general
|
math_qa__rBRHBbL05xEoeNAm
|
louie takes out a 3 - month loan of $ 1000 . the lender charges him 10 % interest per month compounded monthly . the terms of the loan state that louie must repay the loan in 3 equal monthly payments . to the nearest dollar , how much does louis have to pay each month ? Choose the correct option:
A) 333 B) 383 C) 402 D) 433 E) 483
|
<gadget id="calculator">1_000 * 3</gadget>
<output>3_000</output>
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">3_000 * (1/10)</gadget>
<output>300</output>
<gadget id="calculator">300 * (1/10)</gadget>
<output>30</output>
<gadget id="calculator">300 + 30</gadget>
<output>330</output>
<gadget id="calculator">330 + 1</gadget>
<output>331</output>
<gadget id="calculator">1_000 + 331</gadget>
<output>1_331</output>
<gadget id="calculator">331 / 100</gadget>
<output>331/100 = around 3.31</output>
<gadget id="calculator">1_331 / (331/100)</gadget>
<output>133_100/331 = around 402.114804</output>
<result>C</result>
|
C
| 402 |
louie takes out a 3 - month loan of $ 1000 . the lender charges him 10 % interest per month compounded monthly . the terms of the loan state that louie must repay the loan in 3 equal monthly payments . to the nearest dollar , how much does louis have to pay each month ?
|
{
"A": "333",
"B": "383",
"C": "402",
"D": "433",
"E": "483"
}
|
divide(add(1000, add(add(multiply(multiply(1000, 3), divide(10, const_100)), multiply(multiply(multiply(1000, 3), divide(10, const_100)), divide(10, const_100))), const_1)), divide(add(add(multiply(multiply(1000, 3), divide(10, const_100)), multiply(multiply(multiply(1000, 3), divide(10, const_100)), divide(10, const_100))), const_1), const_100))
|
divide(n2,const_100)|multiply(n0,n1)|multiply(#0,#1)|multiply(#0,#2)|add(#2,#3)|add(#4,const_1)|add(n1,#5)|divide(#5,const_100)|divide(#6,#7)
|
after 1 st month : ( 1000 ) ( 1.1 ) - x = 1100 - x after 2 nd month : ( 1100 - x ) ( 1.1 ) - x = 1210 - 2.21 x after 3 rd month : ( 1210 - 2.21 x ) ( 1.1 ) - x = 1331 - 3.31 x now , the amount after the last payment in 3 rd month must bring the total to 0 . hence : 1331 - 3.31 x = 0 x = 1331 / 3.31 = 402.11 the answer is c
|
general
|
math_qa__lGKqalICvurGal4i
|
If the perimeter of a rectangular garden is 600 m, its length when its breadth is 200 m is?
Choose the correct choice from the following answers
A) 299 m
B) 777 m
C) 200 m
D) 100 m
E) 128 m
|
<gadget id="calculator">600 / 2</gadget>
<output>300</output>
<gadget id="calculator">300 - 200</gadget>
<output>100</output>
<result>D</result>
|
D
| 100 |
If the perimeter of a rectangular garden is 600 m, its length when its breadth is 200 m is?
|
{
"A": "299 m",
"B": "777 m",
"C": "200 m",
"D": "100 m",
"E": "128 m"
}
|
subtract(divide(600, const_2), 200)
|
divide(n0,const_2)|subtract(#0,n1)|
|
"2 ( l + 200 ) = 600 = > l = 100 m answer : d"
|
physics
|
math_qa__YDsa0g2nYKFAkyOQ
|
Rs 3000 is divided into two parts such that one part is put out at 3% and the other at 5%. If the annual interest earned from both the investments be Rs 144, find the first part. Choose the correct choice: A) s 400 B) s 280 C) s 300 D) s 350 E) s 310
|
<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">3_000 * (1/20)</gadget>
<output>150</output>
<gadget id="calculator">150 - 144</gadget>
<output>6</output>
<gadget id="calculator">3 / 100</gadget>
<output>3/100 = around 0.03</output>
<gadget id="calculator">(1/20) - (3/100)</gadget>
<output>1/50 = around 0.02</output>
<gadget id="calculator">6 / (1/50)</gadget>
<output>300</output>
<result>C</result>
|
C
| 300 |
Rs 3000 is divided into two parts such that one part is put out at 3% and the other at 5%. If the annual interest earned from both the investments be Rs 144, find the first part.
|
{
"A": "s 400",
"B": "s 280",
"C": "s 300",
"D": "s 350",
"E": "s 310"
}
|
divide(subtract(multiply(3000, divide(5, const_100)), 144), subtract(divide(5, const_100), divide(3, const_100)))
|
divide(n2,const_100)|divide(n1,const_100)|multiply(n0,#0)|subtract(#0,#1)|subtract(#2,n3)|divide(#4,#3)
|
explanation : average rate = ( 144 / 3000 ) * 100 = 4.8 ratio = 2 : 18 so , first part = ( 2 / 20 ) * 3000 = rs 300 . answer : c
|
gain
|
math_qa__Li4nDoheLKILMwdK
|
A machine, working at a constant rate, manufactures 18 dies in 25 minutes. How many dies does it make in 1 hr 15 min? Choose the correct choice from the following: A) 55 B) 53 C) 54 D) 52 E) 50
|
<gadget id="calculator">1 * 60</gadget>
<output>60</output>
<gadget id="calculator">60 + 15</gadget>
<output>75</output>
<gadget id="calculator">75 / 25</gadget>
<output>3</output>
<gadget id="calculator">3 * 18</gadget>
<output>54</output>
<result>C</result>
|
C
| 54 |
A machine, working at a constant rate, manufactures 18 dies in 25 minutes. How many dies does it make in 1 hr 15 min?
|
{
"A": "55",
"B": "53",
"C": "54",
"D": "52",
"E": "50"
}
|
multiply(divide(add(multiply(1, const_60), 15), 25), 18)
|
multiply(n2,const_60)|add(n3,#0)|divide(#1,n1)|multiply(n0,#2)|
|
"change 1 hr 15 min to 75 min . for this , we need to set up a simple proportion of dies per time 18 / 25 = s / 75 the absolutely worst thing you could do at this point in the problem is to cross - multiply . that would be a supremely unstrategic move . we can cancel the common factor of 25 in the two denominators . 18 / 1 = s / 3 s = 3 * 18 s = 54 the machine would be 54 dies in 1 hr 15 min . answer : c"
|
physics
|
math_qa__fEUma0j4SCOxtQWT
|
A room 5.44m long and 3.74m broad is to be paved with square tiles. The least number of square tiles required to cover the floor is:
Choose the correct answer: A) 176 B) 192 C) 184 D) 162 E) 172
|
<gadget id="calculator">5.44 * 100</gadget>
<output>544</output>
<gadget id="calculator">3.74 * 100</gadget>
<output>374</output>
<gadget id="calculator">544 * 374</gadget>
<output>203_456</output>
<gadget id="calculator">10 + 10</gadget>
<output>20</output>
<gadget id="calculator">20 + 10</gadget>
<output>30</output>
<gadget id="calculator">30 + 4</gadget>
<output>34</output>
<gadget id="calculator">34 * 34</gadget>
<output>1_156</output>
<gadget id="calculator">203_456 / 1_156</gadget>
<output>176</output>
<result>A</result>
|
A
| 176 |
A room 5.44m long and 3.74m broad is to be paved with square tiles. The least number of square tiles required to cover the floor is:
|
{
"A": "176",
"B": "192",
"C": "184",
"D": "162",
"E": "172"
}
|
divide(multiply(multiply(5.44, const_100), multiply(3.74, const_100)), multiply(add(add(add(const_10, const_10), const_10), const_4), add(add(add(const_10, const_10), const_10), const_4)))
|
add(const_10,const_10)|multiply(n0,const_100)|multiply(n1,const_100)|add(#0,const_10)|multiply(#1,#2)|add(#3,const_4)|multiply(#5,#5)|divide(#4,#6)
|
area of the room = 544 * 374 sq . cm size of largest square tile = hcf of 544 cm & 374 cm area of 1 tile = 34 * 34 sq . cm therefore , number of tiles = ( 544 * 374 / 34 * 34 ) = 176 answer : a
|
physics
|
math_qa__EYqKCi4IgDD71e63
|
Find the maximum value of n such that 50! is perfectly divisible by 2520^n Choose the correct choice from the following options
A) 7
B) 8
C) 9
D) 6
E) 5
|
<gadget id="calculator">50 / 10</gadget>
<output>5</output>
<gadget id="calculator">5 + 3</gadget>
<output>8</output>
<result>B</result>
|
B
| 8 |
Find the maximum value of n such that 50! is perfectly divisible by 2520^n
|
{
"A": "7",
"B": "8",
"C": "9",
"D": "6",
"E": "5"
}
|
add(divide(50, const_10), const_3)
|
divide(n0,const_10)|add(#0,const_3)
|
2520 = 2 ^ 3 * 3 ^ 2 * 5 * 7 here , 7 is the highest prime , so find the no . of 7 ' s in 50 ! only no . of 7 ' s in 50 ! = [ 50 / 7 ] + [ 50 / 7 ^ 2 ] = 7 + 1 = 8 answer : b
|
general
|
math_qa__vwO68qN2SKbiMSL4
|
In two triangle, the ratio of the areas is 4:3 and that of their heights is 3:4 the ratio of their bases is Choices
A) 16 : 9 B) 9 : 16 C) 9 : 12 D) 16 : 12 E) 4 : 12
|
<gadget id="calculator">4 * 4</gadget>
<output>16</output>
<gadget id="calculator">3 * 3</gadget>
<output>9</output>
<gadget id="calculator">16 / 9</gadget>
<output>16/9 = around 1.777778</output>
<result>A</result>
|
A
| 1.777778 |
In two triangle, the ratio of the areas is 4:3 and that of their heights is 3:4 the ratio of their bases is
|
{
"A": "16 : 9",
"B": "9 : 16",
"C": "9 : 12",
"D": "16 : 12",
"E": "4 : 12"
}
|
divide(multiply(4, 4), multiply(3, 3))
|
multiply(n0,n0)|multiply(n1,n1)|divide(#0,#1)
|
explanation : given a 1 / a 2 = 4 / 3 , h 1 / h 2 = 3 / 4 also , we know that a 1 / a 2 = ( 1 / 2 Γ b 1 Γ h 1 ) / ( 1 / 2 Γ b 2 Γ h 2 ) on substituting in above equation , we get b 1 / b 2 = 16 / 9 therefore b 1 : b 2 = 16 : 9 answer : option a
|
geometry
|
math_qa__8yt302chqdsFm4Qs
|
A number exceeds by 30 from its 3/8 part. Then the number is? Choose the correct choice:
A) 32
B) 35
C) 39
D) 40
E) 48
|
<gadget id="calculator">30 * 8</gadget>
<output>240</output>
<gadget id="calculator">8 - 3</gadget>
<output>5</output>
<gadget id="calculator">240 / 5</gadget>
<output>48</output>
<result>E</result>
|
E
| 48 |
A number exceeds by 30 from its 3/8 part. Then the number is?
|
{
"A": "32",
"B": "35",
"C": "39",
"D": "40",
"E": "48"
}
|
divide(multiply(30, 8), subtract(8, 3))
|
multiply(n0,n2)|subtract(n2,n1)|divide(#0,#1)|
|
"x β 3 / 8 x = 30 x = 48 answer : e"
|
general
|
math_qa__CZjKAxtQLqrIE4sh
|
The radius of a cylinder is 12 m, height 21 m. the lateral surface area of the cylinder is:
Choose the correct choice from the following options:
A) 1584 B) 1854 C) 1458 D) 1485 E) none of them
|
<gadget id="calculator">2 * pi * 12</gadget>
<output>24*pi = around 75.398224</output>
<gadget id="calculator">(24*pi) * 21</gadget>
<output>504*pi = around 1_583.362697</output>
<result>A</result>
|
A
| 1,584 |
The radius of a cylinder is 12 m, height 21 m. the lateral surface area of the cylinder is:
|
{
"A": "1584",
"B": "1854",
"C": "1458",
"D": "1485",
"E": "none of them"
}
|
multiply(circumface(12), 21)
|
circumface(n0)|multiply(n1,#0)
|
lateral surface area = 2 Ο rh = 2 Γ 22 / 7 Γ 12 Γ 21 = 44 Γ 36 = 1584 m ( power 2 ) answer is a .
|
geometry
|
math_qa__OxwqQn7eIhog88Nf
|
In an election between two candidates, the first candidate got 80% of the votes and the second candidate got 240 votes. What was the total number of votes? Choose the most appropriate option:
A) 600
B) 900
C) 1200
D) 1500
E) 1800
|
<gadget id="calculator">240 * 100</gadget>
<output>24_000</output>
<gadget id="calculator">100 - 80</gadget>
<output>20</output>
<gadget id="calculator">24_000 / 20</gadget>
<output>1_200</output>
<result>C</result>
|
C
| 1,200 |
In an election between two candidates, the first candidate got 80% of the votes and the second candidate got 240 votes. What was the total number of votes?
|
{
"A": "600",
"B": "900",
"C": "1200",
"D": "1500",
"E": "1800"
}
|
divide(multiply(240, const_100), subtract(const_100, 80))
|
multiply(n1,const_100)|subtract(const_100,n0)|divide(#0,#1)|
|
"let v be the total number of votes . 0.2 v = 240 v = 1200 the answer is c ."
|
gain
|
math_qa__coazA3OETljCQDwu
|
A retailer buys a radio for Rs 225. His overhead expenses are Rs 30. He sellis the radio for Rs 300. The profit percent of the retailer is Choose the correct choice from the following options
A) 10 %
B) 50 %
C) 25 %
D) 17.6 %
E) none of these
|
<gadget id="calculator">225 + 30</gadget>
<output>255</output>
<gadget id="calculator">300 / 255</gadget>
<output>20/17 = around 1.176471</output>
<gadget id="calculator">(20/17) * 100</gadget>
<output>2_000/17 = around 117.647059</output>
<gadget id="calculator">(2_000/17) - 100</gadget>
<output>300/17 = around 17.647059</output>
<result>D</result>
|
D
| 17.6 |
A retailer buys a radio for Rs 225. His overhead expenses are Rs 30. He sellis the radio for Rs 300. The profit percent of the retailer is
|
{
"A": "10 %",
"B": "50 %",
"C": "25 %",
"D": "17.6 %",
"E": "none of these"
}
|
subtract(multiply(divide(300, add(225, 30)), const_100), const_100)
|
add(n0,n1)|divide(n2,#0)|multiply(#1,const_100)|subtract(#2,const_100)|
|
"explanation : cost price = ( 225 + 30 ) = 255 sell price = 300 gain = ( 45 / 255 ) * 100 = 17.6 % . answer : d"
|
gain
|
math_qa__LFOMFrfdE8OMBYBL
|
If it is assumed that 60 percent of those who receive a questionnaire by mail will respond and 210 responses are needed, what is the minimum number of questionnaires that should be mailed? Choose the correct option.
A) 290
B) 320
C) 350
D) 380
E) 410
|
<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">210 / (3/5)</gadget>
<output>350</output>
<result>C</result>
|
C
| 350 |
If it is assumed that 60 percent of those who receive a questionnaire by mail will respond and 210 responses are needed, what is the minimum number of questionnaires that should be mailed?
|
{
"A": "290",
"B": "320",
"C": "350",
"D": "380",
"E": "410"
}
|
divide(210, divide(60, const_100))
|
divide(n0,const_100)|divide(n1,#0)
|
let x be the minimum number of questionnaires to be mailed . 0.6 x = 210 x = 350 the answer is c .
|
gain
|
math_qa__DGKB7Eu08HnzHsJX
|
A lemonade stand sold only small and large cups of lemonade on Tuesday. 4/5 of the cups sold were small and the rest were large. If the large cups were sold for 7/6 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups? Choices: A) ( a ) 7 / 16 B) ( b ) 7 / 15 C) ( c ) 10 / 21 D) ( d ) 7 / 31 E) ( e ) 1 / 2
|
<gadget id="calculator">4 / 5</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(4/5) * 10</gadget>
<output>8</output>
<gadget id="calculator">10 - 8</gadget>
<output>2</output>
<gadget id="calculator">7 / 6</gadget>
<output>7/6 = around 1.166667</output>
<gadget id="calculator">(7/6) * 8</gadget>
<output>28/3 = around 9.333333</output>
<gadget id="calculator">2 * (28/3)</gadget>
<output>56/3 = around 18.666667</output>
<gadget id="calculator">8 * 8</gadget>
<output>64</output>
<gadget id="calculator">64 + (56/3)</gadget>
<output>248/3 = around 82.666667</output>
<gadget id="calculator">(56/3) / (248/3)</gadget>
<output>7/31 = around 0.225806</output>
<result>D</result>
|
D
| 0.225806 |
A lemonade stand sold only small and large cups of lemonade on Tuesday. 4/5 of the cups sold were small and the rest were large. If the large cups were sold for 7/6 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups?
|
{
"A": "( a ) 7 / 16",
"B": "( b ) 7 / 15",
"C": "( c ) 10 / 21",
"D": "( d ) 7 / 31",
"E": "( e ) 1 / 2"
}
|
divide(multiply(subtract(const_10, multiply(divide(4, 5), const_10)), multiply(divide(7, 6), multiply(divide(4, 5), const_10))), add(multiply(multiply(divide(4, 5), const_10), multiply(divide(4, 5), const_10)), multiply(subtract(const_10, multiply(divide(4, 5), const_10)), multiply(divide(7, 6), multiply(divide(4, 5), const_10)))))
|
divide(n2,n3)|divide(n0,n1)|multiply(#1,const_10)|multiply(#0,#2)|multiply(#2,#2)|subtract(const_10,#2)|multiply(#3,#5)|add(#4,#6)|divide(#6,#7)|
|
"a simpler way i guess would be to think that in total 5 cups were sold . out of which 4 are small and 1 is large . now let the small ones cost $ 6 . so the large ones would cost $ 7 . so , 4 * 6 = 24 and 1 * 7 = 7 . total revenue was 24 + 7 = 31 and large cup sales as found above is 7 therefore answer is 7 / 31 d"
|
general
|
math_qa__8yKiFq77wEsvXrEK
|
96% of the population of a city is 23040. Find the total population of the city? Choose one: A) 30000 B) 28000 C) 24000 D) 25000 E) 25500
|
<gadget id="calculator">100 / 96</gadget>
<output>25/24 = around 1.041667</output>
<gadget id="calculator">(25/24) * 23_040</gadget>
<output>24_000</output>
<result>C</result>
|
C
| 24,000 |
96% of the population of a city is 23040. Find the total population of the city?
|
{
"A": "30000",
"B": "28000",
"C": "24000",
"D": "25000",
"E": "25500"
}
|
multiply(divide(const_100, 96), 23040)
|
divide(const_100,n0)|multiply(n1,#0)|
|
"population consider as x x * ( 96 / 100 ) = 23040 x = 240 * 100 = = > 24000 answer c"
|
gain
|
math_qa__HJmi2Qe3SjScVuvE
|
The average weight of 10 men is increased by 2 Β½ kg when one of the men who weighs 58 kg is replaced by a new man. What is the weight of the new man? Choose the correct choice from the following answers:
A) 80 kg
B) 83 kg
C) 70 kg
D) 75 kg
E) 85 kg
|
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">2 + (1/2)</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">10 * (5/2)</gadget>
<output>25</output>
<gadget id="calculator">58 + 25</gadget>
<output>83</output>
<result>B</result>
|
B
| 83 |
The average weight of 10 men is increased by 2 Β½ kg when one of the men who weighs 58 kg is replaced by a new man. What is the weight of the new man?
|
{
"A": "80 kg",
"B": "83 kg",
"C": "70 kg",
"D": "75 kg",
"E": "85 kg"
}
|
add(58, multiply(10, add(2, divide(const_1, const_2))))
|
divide(const_1,const_2)|add(n1,#0)|multiply(n0,#1)|add(n2,#2)
|
since the average has increased by 2.5 kg , the weight of the man who stepped in must be equal to 58 + 10 x 2.5 58 + 25 = 83 kg ans : ' b '
|
general
|
math_qa__rHYxAAxNpHSGsbUi
|
In the rectangular coordinate system, what is the x-intercept of a line passing through (10, 3) and (β10, β7)? Choose the correct choice from the following answers
A) 4 B) 2 C) 0 D) β 2 E) β 4
|
<gadget id="calculator">-7</gadget>
<output>-7</output>
<gadget id="calculator">(-7) - 3</gadget>
<output>-10</output>
<gadget id="calculator">-10</gadget>
<output>-10</output>
<gadget id="calculator">(-10) - 10</gadget>
<output>-20</output>
<gadget id="calculator">(-10) / (-20)</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) * 10</gadget>
<output>5</output>
<gadget id="calculator">5 - 3</gadget>
<output>2</output>
<gadget id="calculator">2 / (1/2)</gadget>
<output>4</output>
<result>A</result>
|
A
| 4 |
In the rectangular coordinate system, what is the x-intercept of a line passing through (10, 3) and (β10, β7)?
|
{
"A": "4",
"B": "2",
"C": "0",
"D": "β 2",
"E": "β 4"
}
|
divide(subtract(multiply(divide(subtract(negate(7), 3), subtract(negate(10), 10)), 10), 3), divide(subtract(negate(7), 3), subtract(negate(10), 10)))
|
negate(n3)|negate(n2)|subtract(#0,n1)|subtract(#1,n0)|divide(#2,#3)|multiply(n0,#4)|subtract(#5,n1)|divide(#6,#4)|
|
"slope = rise / run = 10 / 20 = 1 / 2 the equation of the line is y = ( 1 / 2 ) x + b 3 = ( 1 / 2 ) ( 10 ) + b b = - 2 the equation of the line is y = ( 1 / 2 ) x - 2 to find the x - intercept , let y = 0 : 0 = ( 1 / 2 ) x - 2 x = 4 the answer is a ."
|
general
|
math_qa__EETx6CPzzqu0yZig
|
The price of a T.V. set worth Rs. 40000 is to be paid in 20 installments of Rs. 2500 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be?
Choose one:
A) 29997 B) 28088 C) 27098 D) 37500 E) 2799
|
<gadget id="calculator">40_000 - 2_500</gadget>
<output>37_500</output>
<result>D</result>
|
D
| 37,500 |
The price of a T.V. set worth Rs. 40000 is to be paid in 20 installments of Rs. 2500 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be?
|
{
"A": "29997",
"B": "28088",
"C": "27098",
"D": "37500",
"E": "2799"
}
|
subtract(40000, 2500)
|
subtract(n0,n2)|
|
"money paid in cash = rs . 2500 balance payment = ( 40000 - 2500 ) = rs . 37500 . answer : d"
|
gain
|
math_qa__OdqtAQ5nYDsJlhMv
|
When Greenville State University decided to move its fine arts collection to a new library, it had to package the collection in 20-inch by 20-inch by 12-inch boxes. If the university pays $0.50 for every box, and if the university needs 2.4 million cubic inches to package the collection, what is the minimum amount the university must spend on boxes? Select the correct option
A) $ 250 B) $ 275 C) $ 510 D) $ 1,250 E) $ 2,550
|
<gadget id="calculator">1_000 * 1_000</gadget>
<output>1_000_000</output>
<gadget id="calculator">2.4 * 1_000_000</gadget>
<output>2_400_000</output>
<gadget id="calculator">20 * 20</gadget>
<output>400</output>
<gadget id="calculator">400 * 12</gadget>
<output>4_800</output>
<gadget id="calculator">2_400_000 / 4_800</gadget>
<output>500</output>
<gadget id="calculator">500 * 0.5</gadget>
<output>250</output>
<result>A</result>
|
A
| 250 |
When Greenville State University decided to move its fine arts collection to a new library, it had to package the collection in 20-inch by 20-inch by 12-inch boxes. If the university pays $0.50 for every box, and if the university needs 2.4 million cubic inches to package the collection, what is the minimum amount the university must spend on boxes?
|
{
"A": "$ 250",
"B": "$ 275",
"C": "$ 510",
"D": "$ 1,250",
"E": "$ 2,550"
}
|
multiply(divide(multiply(2.4, multiply(const_1000, const_1000)), multiply(multiply(20, 20), 12)), 0.50)
|
multiply(const_1000,const_1000)|multiply(n0,n0)|multiply(n4,#0)|multiply(n2,#1)|divide(#2,#3)|multiply(n3,#4)|
|
"the volume of each box is 20 * 20 * 12 = 4800 cubic inches . number of boxes = 2 , 400,000 / 4800 = 500 boxes total cost = 500 Γ $ 0.5 = $ 250 the answer is a ."
|
general
|
math_qa__7FTuvmeX13Z9U4Xp
|
Boy sells a book for Rs. 450 he gets a loss of 10 %, To gain 10%, what should be the SP?
Choose the correct answer
A) rs . 320 B) rs . 450 C) rs . 550 D) rs . 640 E) rs . 680
|
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 - (1/10)</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">450 / (9/10)</gadget>
<output>500</output>
<gadget id="calculator">500 * (1/10)</gadget>
<output>50</output>
<gadget id="calculator">500 + 50</gadget>
<output>550</output>
<result>C</result>
|
C
| 550 |
Boy sells a book for Rs. 450 he gets a loss of 10 %, To gain 10%, what should be the SP?
|
{
"A": "rs . 320",
"B": "rs . 450",
"C": "rs . 550",
"D": "rs . 640",
"E": "rs . 680"
}
|
add(divide(450, subtract(const_1, divide(10, const_100))), multiply(divide(450, subtract(const_1, divide(10, const_100))), divide(10, const_100)))
|
divide(n1,const_100)|divide(n2,const_100)|subtract(const_1,#0)|divide(n0,#2)|multiply(#3,#1)|add(#3,#4)|
|
"find selling price to gain 10 % . now , we are asked to find selling price to gain 10 % profit . hint : selling price = ( 100 + gain % ) Γ c . p . 100 selling price = ( 100 + 10 ) Γ 500 100 selling price = ( 110 ) Γ 500 100 therefore , selling price = rs . 550 c"
|
gain
|
math_qa__tFzX9VUSYkH5XwPV
|
In country Z, 10% of the people do not have a university diploma but have the job of their choice, and 25% of the people who do not have the job of their choice have a university diploma. If 20% of the people have the job of their choice, what percent of the people have a university diploma? Options:
A) 30 % B) 45 % C) 55 % D) 65 % E) 75 %
|
<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">25 * 80</gadget>
<output>2_000</output>
<gadget id="calculator">2_000 / 100</gadget>
<output>20</output>
<gadget id="calculator">20 - 10</gadget>
<output>10</output>
<gadget id="calculator">20 + 10</gadget>
<output>30</output>
<result>A</result>
|
A
| 30 |
In country Z, 10% of the people do not have a university diploma but have the job of their choice, and 25% of the people who do not have the job of their choice have a university diploma. If 20% of the people have the job of their choice, what percent of the people have a university diploma?
|
{
"A": "30 %",
"B": "45 %",
"C": "55 %",
"D": "65 %",
"E": "75 %"
}
|
add(divide(multiply(25, subtract(const_100, 20)), const_100), subtract(20, 10))
|
subtract(const_100,n2)|subtract(n2,n0)|multiply(n1,#0)|divide(#2,const_100)|add(#3,#1)|
|
"setting up a matrix is how i solve this one . diploma no diploma totals job of choice w / diploma job of choice w / o diploma = 10 % job of choice total = 20 % not job of choice with diploma = . 25 x not job of choice w / o diploma = . 75 x total not job of choice = x total with diploma total without diploma total citizen = 100 if 20 % of people have their job of choice , then 80 % of people do not have their job of choice . 25 % of 80 % = 20 % . we can also see that 10 % of the people have their job of choice and a diploma ( 20 % - 10 % = 10 % ) . 10 % + 20 % = 30 % . therefore 30 % of the people in country z have a diploma . ans a"
|
gain
|
math_qa__oZ0b4eEz4vOFIrvs
|
A batsman makes a score of 84 runs in the 17th inning and thus increases his averages by 3.Find his average after 17th inning? Choose the correct choice from the following options:
A) 19
B) 29
C) 36
D) 49
E) 59
|
<gadget id="calculator">17 * 3</gadget>
<output>51</output>
<gadget id="calculator">84 - 51</gadget>
<output>33</output>
<gadget id="calculator">33 + 3</gadget>
<output>36</output>
<result>C</result>
|
C
| 36 |
A batsman makes a score of 84 runs in the 17th inning and thus increases his averages by 3.Find his average after 17th inning?
|
{
"A": "19",
"B": "29",
"C": "36",
"D": "49",
"E": "59"
}
|
add(subtract(84, multiply(17, 3)), 3)
|
multiply(n1,n2)|subtract(n0,#0)|add(n2,#1)|
|
"let the average after 17 th inning = x then average after 16 th inning = ( x - 3 ) therefore 16 ( x - 3 ) + 84 = 17 x therefore x = 36 answer : c"
|
general
|
math_qa__r3sBivjjOxA1SqS2
|
Of the 120 passengers on Flight 750, 40% are female. 10% of the passengers sit in first class, and the rest of the passengers sit in coach class. If 1/3 of the passengers in first class are male, how many females are there in coach class? Choose the correct option.
A) 40
B) 48
C) 50
D) 52
E) 56
|
<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">120 * (2/5)</gadget>
<output>48</output>
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">120 * (1/10)</gadget>
<output>12</output>
<gadget id="calculator">12 / 3</gadget>
<output>4</output>
<gadget id="calculator">12 - 4</gadget>
<output>8</output>
<gadget id="calculator">48 - 8</gadget>
<output>40</output>
<result>A</result>
|
A
| 40 |
Of the 120 passengers on Flight 750, 40% are female. 10% of the passengers sit in first class, and the rest of the passengers sit in coach class. If 1/3 of the passengers in first class are male, how many females are there in coach class?
|
{
"A": "40",
"B": "48",
"C": "50",
"D": "52",
"E": "56"
}
|
subtract(multiply(120, divide(40, const_100)), subtract(multiply(120, divide(10, const_100)), divide(multiply(120, divide(10, const_100)), 3)))
|
divide(n2,const_100)|divide(n3,const_100)|multiply(n0,#0)|multiply(n0,#1)|divide(#3,n5)|subtract(#3,#4)|subtract(#2,#5)|
|
"number of passengers on flight = 120 number of female passengers = . 4 * 120 = 48 number of passengers in first class = ( 10 / 100 ) * 120 = 12 number of passengers in coach class = ( 90 / 100 ) * 120 = 108 number of male passengers in first class = 1 / 3 * 12 = 4 number of female passengers in first class = 12 - 4 = 8 number of female passengers in coach class = 48 - 8 = 40 answer a"
|
gain
|
math_qa__c3nRUfG8baL6QsCK
|
The maximum numbers of students among them 451 pens and 410 toys can be distributed in such a way that each student gets the same number of pens and same number of toys is Choose the correct choice from the following answers
A) 41
B) 910
C) 1001
D) 1911
E) none
|
<gadget id="calculator">451 - 410</gadget>
<output>41</output>
<result>A</result>
|
A
| 41 |
The maximum numbers of students among them 451 pens and 410 toys can be distributed in such a way that each student gets the same number of pens and same number of toys is
|
{
"A": "41",
"B": "910",
"C": "1001",
"D": "1911",
"E": "none"
}
|
subtract(451, 410)
|
subtract(n0,n1)|
|
"olution required number of students . = h . c . f of 451 and 410 . Γ’ β¬ ΒΉ = Γ’ β¬ ΒΊ 41 . answer a"
|
general
|
math_qa__XaliiAfJ6sk0B340
|
Find the average of all the numbers between 4 and 32 which are divisible by 5.
Select.
A) 17.5 B) 20 C) 24 D) 30 E) 32
|
<gadget id="calculator">4 + 4</gadget>
<output>8</output>
<gadget id="calculator">32 - 4</gadget>
<output>28</output>
<gadget id="calculator">8 + 28</gadget>
<output>36</output>
<gadget id="calculator">36 / 2</gadget>
<output>18</output>
<result>A</result>
|
A
| 17.5 |
Find the average of all the numbers between 4 and 32 which are divisible by 5.
|
{
"A": "17.5",
"B": "20",
"C": "24",
"D": "30",
"E": "32"
}
|
divide(add(add(4, const_4), subtract(32, const_4)), const_2)
|
add(n0,const_4)|subtract(n1,const_4)|add(#0,#1)|divide(#2,const_2)|
|
"solution average = ( 5 + 10 + 15 + 20 + 25 + 30 ) / 6 ) = 105 / 6 = 17.5 . answer a"
|
general
|
math_qa__D6ye5leBpw6RybbR
|
A cylinder with base radius of 8 cm and height of 2 cm is melted to form a cone of height 6 cm. The radius of the cone will be :
Select:
A) 8 cm B) 9 cm C) 10 cm D) 11 cm E) none
|
<gadget id="calculator">pi * (8 ** 2) * 2</gadget>
<output>128*pi = around 402.12386</output>
<gadget id="calculator">(128*pi) * 3</gadget>
<output>384*pi = around 1_206.371579</output>
<gadget id="calculator">(384*pi) / 6</gadget>
<output>64*pi = around 201.06193</output>
<gadget id="calculator">(64*pi) / pi</gadget>
<output>64</output>
<gadget id="calculator">64 ** (1/2)</gadget>
<output>8</output>
<result>A</result>
|
A
| 8 |
A cylinder with base radius of 8 cm and height of 2 cm is melted to form a cone of height 6 cm. The radius of the cone will be :
|
{
"A": "8 cm",
"B": "9 cm",
"C": "10 cm",
"D": "11 cm",
"E": "none"
}
|
sqrt(divide(divide(multiply(volume_cylinder(8, 2), const_3), 6), const_pi))
|
volume_cylinder(n0,n1)|multiply(#0,const_3)|divide(#1,n2)|divide(#2,const_pi)|sqrt(#3)
|
sol . let the radius of the cone be r cm . then , 1 / 3 β * r Β² * 6 = β * 8 * 8 * 2 β r Β² = [ 8 * 8 * 2 * 3 / 6 ] = 64 β r = 8 cm . answer a
|
geometry
|
math_qa__PFPiMYldk9k6qfsh
|
If @ is a binary operation defined as the difference between an integer n and the product of n and 5, then what is the largest positive integer n such that the outcome of the binary operation of n is less than 18? Choose the correct choice from the following options.
A) 1 B) 2 C) 3 D) 4 E) 5
|
<gadget id="calculator">5 - 1</gadget>
<output>4</output>
<gadget id="calculator">18 / 4</gadget>
<output>9/2 = around 4.5</output>
<gadget id="calculator">floor(9/2)</gadget>
<output>4</output>
<result>D</result>
|
D
| 4 |
If @ is a binary operation defined as the difference between an integer n and the product of n and 5, then what is the largest positive integer n such that the outcome of the binary operation of n is less than 18?
|
{
"A": "1",
"B": "2",
"C": "3",
"D": "4",
"E": "5"
}
|
floor(divide(18, subtract(5, const_1)))
|
subtract(n0,const_1)|divide(n1,#0)|floor(#1)|
|
"@ ( n ) = 5 n - n we need to find the largest positive integer such that 5 n - n < 18 . then 4 n < 18 and n < 4.5 the largest possible integer is n = 4 . the answer is d ."
|
general
|
math_qa__3Je6w2GtMz6hfS57
|
A runs twice as fast as B and gives B a start of 60m.How long should the racecourse be so that A and B might reach in the same time?
Select the correct option:
A) 120 m . B) 80 m . C) 150 m . D) 100 m . E) none of the above
|
<gadget id="calculator">60 * 2</gadget>
<output>120</output>
<result>A</result>
|
A
| 120 |
A runs twice as fast as B and gives B a start of 60m.How long should the racecourse be so that A and B might reach in the same time?
|
{
"A": "120 m .",
"B": "80 m .",
"C": "150 m .",
"D": "100 m .",
"E": "none of the above"
}
|
multiply(60, const_2)
|
multiply(n0,const_2)
|
ratio of speeds of a and b is 2 : 1 b is 60 m away from a but we know that a covers 1 meter ( 2 - 1 ) more in every second than b the time taken for a to cover 60 m is 60 / 1 = 60 m so the total time taken by a and b to reach = 2 * 60 = 120 m answer : a
|
physics
|
math_qa__TO4L586vgTh5FpNL
|
How long does a train 100 m long running at the speed of 80 km/hr takes to cross a bridge 142 m length? Choose the correct answer: A) 10.7 sec B) 10.9 sec C) 10.1 sec D) 15.1 sec E) 12.7 sec
|
<gadget id="calculator">100 + 142</gadget>
<output>242</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">80 * (5/18)</gadget>
<output>200/9 = around 22.222222</output>
<gadget id="calculator">242 / (200/9)</gadget>
<output>1_089/100 = around 10.89</output>
<result>B</result>
|
B
| 10.9 |
How long does a train 100 m long running at the speed of 80 km/hr takes to cross a bridge 142 m length?
|
{
"A": "10.7 sec",
"B": "10.9 sec",
"C": "10.1 sec",
"D": "15.1 sec",
"E": "12.7 sec"
}
|
divide(add(100, 142), multiply(80, const_0_2778))
|
add(n0,n2)|multiply(n1,const_0_2778)|divide(#0,#1)|
|
"speed = 80 * 5 / 18 = 22.2 m / sec total distance covered = 100 + 142 = 242 m . required time = 242 / 22.2 ' = 10.9 sec . answer : b"
|
physics
|
math_qa__nt49h49lxfe9drvE
|
A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 5 days before the project is completed, in how many days total will the project be completed?
Options: A) 12 B) 15 C) 18 D) 21 E) 24
|
<gadget id="calculator">1 / 30</gadget>
<output>1/30 = around 0.033333</output>
<gadget id="calculator">(1/30) * 5</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">1 - (1/6)</gadget>
<output>5/6 = around 0.833333</output>
<gadget id="calculator">1 / 20</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/20) + (1/30)</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">(5/6) / (1/12)</gadget>
<output>10</output>
<gadget id="calculator">10 + 5</gadget>
<output>15</output>
<result>B</result>
|
B
| 15 |
A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 5 days before the project is completed, in how many days total will the project be completed?
|
{
"A": "12",
"B": "15",
"C": "18",
"D": "21",
"E": "24"
}
|
add(divide(subtract(const_1, multiply(divide(const_1, 30), 5)), add(divide(const_1, 20), divide(const_1, 30))), 5)
|
divide(const_1,n1)|divide(const_1,n0)|add(#1,#0)|multiply(n2,#0)|subtract(const_1,#3)|divide(#4,#2)|add(n2,#5)|
|
"a ' s rate is 1 / 20 of the project per day . b ' s rate is 1 / 30 of the project per day . the combined rate is 1 / 12 of the project per day . in the last 5 days , b can do 1 / 6 of the project . thus a and b must complete 5 / 6 of the project , which takes 10 days . the total number of days is 10 + 5 = 15 . the answer is b ."
|
physics
|
math_qa__etgbci0zzYXCrlm7
|
The price of commodity X increases by 45 cents every year, while the price of commodity Y increases by 20 cents every year. In 2001, the price of commodity X was $5.20 and the price of commodity Y was $7.30. In which year will the price of commodity X be 35 cents less than the price of commodity Y? Choose the correct option
A) 2006
B) 2007
C) 2008
D) 2009
E) 2010
|
<gadget id="calculator">35 / 100</gadget>
<output>7/20 = around 0.35</output>
<gadget id="calculator">7.3 - 5.2</gadget>
<output>2.1</output>
<gadget id="calculator">(7/20) + 2.1</gadget>
<output>2.45</output>
<gadget id="calculator">45 / 100</gadget>
<output>9/20 = around 0.45</output>
<gadget id="calculator">(9/20) - 2.1</gadget>
<output>-1.65</output>
<gadget id="calculator">2.45 / (-1.65)</gadget>
<output>-1.484848</output>
<gadget id="calculator">2_001 + (-1.484848)</gadget>
<output>1_999.515152</output>
<result>C</result>
|
C
| 2,008 |
The price of commodity X increases by 45 cents every year, while the price of commodity Y increases by 20 cents every year. In 2001, the price of commodity X was $5.20 and the price of commodity Y was $7.30. In which year will the price of commodity X be 35 cents less than the price of commodity Y?
|
{
"A": "2006",
"B": "2007",
"C": "2008",
"D": "2009",
"E": "2010"
}
|
add(2001, divide(add(divide(35, const_100), subtract(7.30, 5.20)), subtract(divide(45, const_100), subtract(7.30, 5.20))))
|
divide(n5,const_100)|divide(n0,const_100)|subtract(n4,n3)|add(#0,#2)|subtract(#1,#2)|divide(#3,#4)|add(n2,#5)|
|
"the price of commodity x increases 25 cents each year relative to commodity y . the price difference is $ 2.10 and commodity x needs to be 35 cents less than commodity y . $ 1.75 / 25 cents = 7 years the answer is 2001 + 7 years = 2008 . the answer is c ."
|
general
|
math_qa__v2OJ5tK94PUD2onC
|
A river 4m deep and 65 m wide is flowing at the rate of 6 kmph the amount of water that runs into the sea per minute is? Choose the correct choice from the following.
A) 25000
B) 26000
C) 27000
D) 28000
E) 29000
|
<gadget id="calculator">4 * 65</gadget>
<output>260</output>
<gadget id="calculator">6 * 1_000</gadget>
<output>6_000</output>
<gadget id="calculator">260 * 6_000</gadget>
<output>1_560_000</output>
<gadget id="calculator">1 * 60</gadget>
<output>60</output>
<gadget id="calculator">1_560_000 / 60</gadget>
<output>26_000</output>
<result>B</result>
|
B
| 26,000 |
A river 4m deep and 65 m wide is flowing at the rate of 6 kmph the amount of water that runs into the sea per minute is?
|
{
"A": "25000",
"B": "26000",
"C": "27000",
"D": "28000",
"E": "29000"
}
|
divide(multiply(multiply(4, 65), multiply(6, const_1000)), multiply(const_1, const_60))
|
multiply(n0,n1)|multiply(n2,const_1000)|multiply(const_1,const_60)|multiply(#0,#1)|divide(#3,#2)|
|
"rate of water flow - 6 kmph - - 6000 / 60 - - 100 m / min depth of river - - 4 m width of river - - 65 m vol of water per min - - 100 * 4 * 65 - - - 26000 answer b"
|
physics
|
math_qa__7wvz0fBEEczI8Jyg
|
A sum fetched a total simple interest of 4052.25 at the rate of 9 %.p.a. in 5 years. What is the sum?
Choose the correct answer:
A) 9005 B) 8925 C) 2345 D) 6474 E) 8723
|
<gadget id="calculator">4_052.25 * 100</gadget>
<output>405_225</output>
<gadget id="calculator">405_225 / 9</gadget>
<output>45_025</output>
<gadget id="calculator">45_025 / 5</gadget>
<output>9_005</output>
<result>A</result>
|
A
| 9,005 |
A sum fetched a total simple interest of 4052.25 at the rate of 9 %.p.a. in 5 years. What is the sum?
|
{
"A": "9005",
"B": "8925",
"C": "2345",
"D": "6474",
"E": "8723"
}
|
divide(divide(multiply(4052.25, const_100), 9), 5)
|
multiply(n0,const_100)|divide(#0,n1)|divide(#1,n2)
|
principal = ( 100 x 4052.25 ) / ( 9 x 5 ) = 405225 / 45 = 9005 . answer a
|
gain
|
math_qa__leMErRwHVwEfVXqU
|
A rotameter is a device that measures flow of liquid and gases. When measuring liquid phase flows, 2.5 inches represent 60 liters per minute of liquid. With gas measurements the rotameter moves 50% of the movement he moves with the liquid phase. How many liters of gas passed through the rotameter if it measured 4 inches? Select the correct option
A) 176 B) 192 C) 202 D) 218 E) 284
|
<gadget id="calculator">60 * 4</gadget>
<output>240</output>
<gadget id="calculator">240 / 2.5</gadget>
<output>96</output>
<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">96 / (1/2)</gadget>
<output>192</output>
<result>B</result>
|
B
| 192 |
A rotameter is a device that measures flow of liquid and gases. When measuring liquid phase flows, 2.5 inches represent 60 liters per minute of liquid. With gas measurements the rotameter moves 50% of the movement he moves with the liquid phase. How many liters of gas passed through the rotameter if it measured 4 inches?
|
{
"A": "176",
"B": "192",
"C": "202",
"D": "218",
"E": "284"
}
|
divide(divide(multiply(60, 4), 2.5), divide(50, const_100))
|
divide(n2,const_100)|multiply(n1,n3)|divide(#1,n0)|divide(#2,#0)
|
in case of liquid - 2.5 inches represents 60 lit / min . in case of gas - 50 % of 2.5 inches represents 60 lit / min 1.25 inches represents 60 lit / min 4 inches will represent 60 * 4 / 1.25 = 192 b is the answer
|
physics
|
math_qa__Q0dl2x43wX8tKF9A
|
If a trader sold two cars each at Rs. 325475 and gains 10% on the first and loses 10% on the second, then his profit or loss percent on the whole is? Select:
A) 1.44 % B) 1.74 % C) 1.84 % D) 1.47 % E) 1.00 %
|
<gadget id="calculator">10 * 10</gadget>
<output>100</output>
<gadget id="calculator">100 / 100</gadget>
<output>1</output>
<result>E</result>
|
E
| 1 |
If a trader sold two cars each at Rs. 325475 and gains 10% on the first and loses 10% on the second, then his profit or loss percent on the whole is?
|
{
"A": "1.44 %",
"B": "1.74 %",
"C": "1.84 %",
"D": "1.47 %",
"E": "1.00 %"
}
|
divide(multiply(10, 10), const_100)
|
multiply(n1,n1)|divide(#0,const_100)|
|
"sp of each car is rs . 325475 , he gains 10 % on first car and losses 10 % on second car . in this case , there will be loss and percentage of loss is given by = [ ( profit % ) ( loss % ) ] / 100 = ( 10 ) ( 10 ) / 100 % = 1.00 % answer : e"
|
gain
|
math_qa__j4Es0vLkvD1xNiOS
|
The marks obtained by Polly and Sandy are in the ratio 5:6 and those obtained by Sandy and Willy are in the ratio of 3:2. The marks obtained by Polly and Willy are in the ratio of...? Choices
A) 3 : 2
B) 5 : 4
C) 7 : 6
D) 9 : 8
E) 11 : 10
|
<gadget id="calculator">5 * 3</gadget>
<output>15</output>
<gadget id="calculator">6 * 2</gadget>
<output>12</output>
<gadget id="calculator">15 / 12</gadget>
<output>5/4 = around 1.25</output>
<result>B</result>
|
B
| 1.25 |
The marks obtained by Polly and Sandy are in the ratio 5:6 and those obtained by Sandy and Willy are in the ratio of 3:2. The marks obtained by Polly and Willy are in the ratio of...?
|
{
"A": "3 : 2",
"B": "5 : 4",
"C": "7 : 6",
"D": "9 : 8",
"E": "11 : 10"
}
|
divide(multiply(5, 3), multiply(6, 2))
|
multiply(n0,n2)|multiply(n1,n3)|divide(#0,#1)|
|
"polly : sandy = 5 : 6 sandy : willy = 3 : 2 = 6 : 4 polly : sandy : willy = 5 : 6 : 4 polly : willy = 5 : 4 the answer is b ."
|
other
|
math_qa__Pi9gwmy2czCzLv5g
|
What is the greatest positive integer x such that 3^x is a factor of 9^7? Choose one:
A) 5
B) 14
C) 10
D) 20
E) 30
|
<gadget id="calculator">9 - 7</gadget>
<output>2</output>
<gadget id="calculator">2 * 7</gadget>
<output>14</output>
<result>B</result>
|
B
| 14 |
What is the greatest positive integer x such that 3^x is a factor of 9^7?
|
{
"A": "5",
"B": "14",
"C": "10",
"D": "20",
"E": "30"
}
|
multiply(subtract(9, 7), 7)
|
subtract(n1,n2)|multiply(n2,#0)
|
what is the greatest positive integer x such that 3 ^ x is a factor of 9 ^ 7 ? 9 ^ 7 = ( 3 ^ 2 ) ^ 7 = 3 ^ 14 b . 14
|
general
|
math_qa__jPG4D0dod0pkbWYW
|
If 70 percent of a class answered the first question on a certain test correctly, 55 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percent answered both correctly?
Choose the correct option
A) 45 % B) 40 % C) 35 % D) 30 % E) 25 %
|
<gadget id="calculator">70 + 55</gadget>
<output>125</output>
<gadget id="calculator">125 + 20</gadget>
<output>145</output>
<gadget id="calculator">145 - 100</gadget>
<output>45</output>
<result>A</result>
|
A
| 45 |
If 70 percent of a class answered the first question on a certain test correctly, 55 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percent answered both correctly?
|
{
"A": "45 %",
"B": "40 %",
"C": "35 %",
"D": "30 %",
"E": "25 %"
}
|
subtract(add(add(70, 55), 20), const_100)
|
add(n0,n1)|add(n2,#0)|subtract(#1,const_100)|
|
"70 % answered the first question correctly and 20 % answered neither correctly . then 10 % missed the first question but answered the second question correctly . then the percent who answered both correctly is 55 % - 10 % = 45 % . the answer is a ."
|
other
|
math_qa__FOJq4ZwtMQS3Vg93
|
Each Machine of type A has 3 steel parts and 2 chrome parts. Each machine of type B has 2 steel parts and 4 chrome parts. If a certain group of type A and type B machines has a total of 50 steel parts and 66 chrome parts, how many machines are in the group Options:
A) 11
B) 21
C) 31
D) 61
E) 51
|
<gadget id="calculator">4 + 2</gadget>
<output>6</output>
<gadget id="calculator">66 / 6</gadget>
<output>11</output>
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">50 / 5</gadget>
<output>10</output>
<gadget id="calculator">11 + 10</gadget>
<output>21</output>
<result>B</result>
|
B
| 21 |
Each Machine of type A has 3 steel parts and 2 chrome parts. Each machine of type B has 2 steel parts and 4 chrome parts. If a certain group of type A and type B machines has a total of 50 steel parts and 66 chrome parts, how many machines are in the group
|
{
"A": "11",
"B": "21",
"C": "31",
"D": "61",
"E": "51"
}
|
add(divide(66, add(4, 2)), divide(50, add(3, 2)))
|
add(n1,n3)|add(n0,n1)|divide(n5,#0)|divide(n4,#1)|add(#2,#3)|
|
"look at the below representation of the problem : steel chrome total a 3 2 50 > > no . of type a machines = 50 / 5 = 10 b 2 4 66 > > no . of type b machines = 66 / 6 = 11 so the answer is 21 i . e b . hope its clear ."
|
general
|
math_qa__P36GbT393CsZbrkH
|
A batsman in his 12th innings makes a score of 75 and thereby increases his average by 1 runs. What is his average after the 12th innings if he had never been βnot outβ? Choose the correct choice from the following options.
A) 42
B) 43
C) 44
D) 64
E) 46
|
<gadget id="calculator">12 * 1</gadget>
<output>12</output>
<gadget id="calculator">75 - 12</gadget>
<output>63</output>
<gadget id="calculator">63 + 1</gadget>
<output>64</output>
<result>D</result>
|
D
| 64 |
A batsman in his 12th innings makes a score of 75 and thereby increases his average by 1 runs. What is his average after the 12th innings if he had never been βnot outβ?
|
{
"A": "42",
"B": "43",
"C": "44",
"D": "64",
"E": "46"
}
|
add(subtract(75, multiply(12, 1)), 1)
|
multiply(n0,n2)|subtract(n1,#0)|add(n2,#1)|
|
"let β x β be the average score after 12 th innings β 12 x = 11 Γ ( x β 1 ) + 75 β΄ x = 64 answer d"
|
general
|
math_qa__KEBkIyWlSkGFW7eU
|
Students at a school were on average 180 cm tall. The average female height was 170 cm, and the average male height was 188 cms. What was the ratio of men to women? Choose the correct choice from the following answers
A) 5 : 2 B) 5 : 1 C) 4 : 3 D) 5 : 4 E) 3 : 1
|
<gadget id="calculator">180 - 170</gadget>
<output>10</output>
<gadget id="calculator">188 - 180</gadget>
<output>8</output>
<gadget id="calculator">10 / 8</gadget>
<output>5/4 = around 1.25</output>
<result>D</result>
|
D
| 1.25 |
Students at a school were on average 180 cm tall. The average female height was 170 cm, and the average male height was 188 cms. What was the ratio of men to women?
|
{
"A": "5 : 2",
"B": "5 : 1",
"C": "4 : 3",
"D": "5 : 4",
"E": "3 : 1"
}
|
divide(subtract(180, 170), subtract(188, 180))
|
subtract(n0,n1)|subtract(n2,n0)|divide(#0,#1)|
|
"we ' re given a few facts to work with : 1 ) the average height of the females is 170 cm 2 ) the average height of the males is 188 cm 3 ) the average of the group is 180 cm we ' re asked for the ratio of men to women . w = number of women m = number of men ( 170 w + 188 m ) / ( w + m ) = 180 170 w + 188 m = 180 w + 180 m 8 m = 10 w 4 m = 5 w m / w = 5 / 4 the ratio of men to women is 5 t α» 4 . d"
|
general
|
math_qa__IC8bcBogeD4xnV0u
|
A car traveling at a certain constant speed takes 5 seconds longer to travel 1 km than it would take to travel 1 km at 90 km/hour. At what speed, in km/hr, is the car traveling? Choose the correct choice from the following.
A) 70 B) 80 C) 74 D) 75 E) 78
|
<gadget id="calculator">1 / 90</gadget>
<output>1/90 = around 0.011111</output>
<gadget id="calculator">3_600 * (1/90)</gadget>
<output>40</output>
<gadget id="calculator">40 + 5</gadget>
<output>45</output>
<gadget id="calculator">45 / 3_600</gadget>
<output>1/80 = around 0.0125</output>
<gadget id="calculator">1 / (1/80)</gadget>
<output>80</output>
<result>B</result>
|
B
| 80 |
A car traveling at a certain constant speed takes 5 seconds longer to travel 1 km than it would take to travel 1 km at 90 km/hour. At what speed, in km/hr, is the car traveling?
|
{
"A": "70",
"B": "80",
"C": "74",
"D": "75",
"E": "78"
}
|
divide(1, divide(add(multiply(const_3600, divide(1, 90)), 5), const_3600))
|
divide(n1,n3)|multiply(#0,const_3600)|add(n0,#1)|divide(#2,const_3600)|divide(n1,#3)|
|
"time to cover 1 kilometer at 80 kilometers per hour is 1 / 90 hours = 3,600 / 90 seconds = 40 seconds ; time to cover 1 kilometer at regular speed is 40 + 5 = 45 seconds = 45 / 3,600 hours = 1 / 80 hours ; so , we get that to cover 1 kilometer 1 / 80 hours is needed - - > regular speed 80 kilometers per hour ( rate is a reciprocal of time or rate = distance / time ) . answer : b ."
|
physics
|
math_qa__rjOzIgL5XOOkm3sI
|
If the price of gasoline increases by 25% and Ron intends to spend only 15% more on gasoline, by how much percent should he reduce the quantity of gasoline that he buys? Pick.
A) 6.66 %
B) 8 %
C) 10 %
D) 12 %
E) 12.5 %
|
<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">1 + (3/20)</gadget>
<output>23/20 = around 1.15</output>
<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 + (1/4)</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">(23/20) / (5/4)</gadget>
<output>23/25 = around 0.92</output>
<gadget id="calculator">1 - (23/25)</gadget>
<output>2/25 = around 0.08</output>
<gadget id="calculator">(2/25) * 100</gadget>
<output>8</output>
<result>B</result>
|
B
| 8 |
If the price of gasoline increases by 25% and Ron intends to spend only 15% more on gasoline, by how much percent should he reduce the quantity of gasoline that he buys?
|
{
"A": "6.66 %",
"B": "8 %",
"C": "10 %",
"D": "12 %",
"E": "12.5 %"
}
|
multiply(subtract(const_1, divide(add(const_1, divide(15, const_100)), add(const_1, divide(25, const_100)))), const_100)
|
divide(n1,const_100)|divide(n0,const_100)|add(#0,const_1)|add(#1,const_1)|divide(#2,#3)|subtract(const_1,#4)|multiply(#5,const_100)|
|
"let price of original price of gasoline = 10 $ and let original consumption of gasoline = 10 amount spend on gasoline originally = 10 * 10 = 100 $ the price of gasoline increases by 25 % and ron intends to spend only 15 % more on gasoline increased price of gasoline = 12.5 $ now ron intends to spend on gasoline = 1.15 * 100 = 115 $ consumption of gasoline needs to be = 115 / 12.5 = 1150 / 125 = 46 / 5 = 9.2 reduction in consumption of gasoline = 10 - 9.2 = . 8 % reduction in consumption of gasoline = . 8 / 10 * 100 % = 8 % answer b"
|
general
|
math_qa__NT8wug1HyD8l3M1X
|
A rower can row 7 km/h in still water. When the river is running at 1 km/h, it takes the rower 1 hour to row to Big Rock and back. How many kilometers is it to Big Rock? Select
A) 3.19 B) 3.28 C) 3.35 D) 3.43 E) 3.56
|
<gadget id="calculator">7 - 1</gadget>
<output>6</output>
<gadget id="calculator">7 + 1</gadget>
<output>8</output>
<gadget id="calculator">8 + 6</gadget>
<output>14</output>
<gadget id="calculator">6 / 14</gadget>
<output>3/7 = around 0.428571</output>
<gadget id="calculator">(3/7) * 8</gadget>
<output>24/7 = around 3.428571</output>
<result>D</result>
|
D
| 3.43 |
A rower can row 7 km/h in still water. When the river is running at 1 km/h, it takes the rower 1 hour to row to Big Rock and back. How many kilometers is it to Big Rock?
|
{
"A": "3.19",
"B": "3.28",
"C": "3.35",
"D": "3.43",
"E": "3.56"
}
|
multiply(divide(subtract(7, 1), add(add(7, 1), subtract(7, 1))), add(7, 1))
|
add(n0,n1)|subtract(n0,n1)|add(#0,#1)|divide(#1,#2)|multiply(#0,#3)|
|
"let x be the distance to big rock . time = x / 6 + x / 8 = 1 x = 48 / 14 = 3.43 km the answer is d ."
|
physics
|
math_qa__Fc4vJLkz9kSHOMMm
|
A cistern is normally filled in 4 hours but takes two hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in? Choose the correct choice
A) 33
B) 88
C) 40
D) 99
E) 12
|
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">4 + 2</gadget>
<output>6</output>
<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(1/4) - (1/6)</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">1 / (1/12)</gadget>
<output>12</output>
<result>E</result>
|
E
| 12 |
A cistern is normally filled in 4 hours but takes two hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in?
|
{
"A": "33",
"B": "88",
"C": "40",
"D": "99",
"E": "12"
}
|
inverse(subtract(divide(const_1, 4), divide(const_1, add(4, const_2))))
|
add(n0,const_2)|divide(const_1,n0)|divide(const_1,#0)|subtract(#1,#2)|inverse(#3)|
|
"1 / 4 - 1 / x = 1 / 6 x = 12 answer : e"
|
physics
|
math_qa__LnLp9KyXjHm8PKbn
|
25.25/1500 is equal to:
Choose the correct answer.
A) 1.012526333
B) 0.012625333
C) 0.125263333
D) 0.126253333
E) 0.016833333
|
<gadget id="calculator">25.25 / 1_500</gadget>
<output>0.016833</output>
<result>E</result>
|
E
| 0.016833 |
25.25/1500 is equal to:
|
{
"A": "1.012526333",
"B": "0.012625333",
"C": "0.125263333",
"D": "0.126253333",
"E": "0.016833333"
}
|
divide(25.25, 1500)
|
divide(n0,n1)|
|
"25.25 / 2000 = 2525 / 200000 = 0.016833333 answer : e"
|
general
|
math_qa__hFuWEkoG9RhV1Zn1
|
If Jake loses 20 pounds, he will weigh twice as much as his sister. Together they now weigh 224 pounds. What is Jakeβs present weight, in pounds? Choose the correct choice from the following choices: A) 131 B) 135 C) 156 D) 177 E) 188
|
<gadget id="calculator">224 - 20</gadget>
<output>204</output>
<gadget id="calculator">204 / 3</gadget>
<output>68</output>
<gadget id="calculator">68 * 2</gadget>
<output>136</output>
<gadget id="calculator">136 + 20</gadget>
<output>156</output>
<result>C</result>
|
C
| 156 |
If Jake loses 20 pounds, he will weigh twice as much as his sister. Together they now weigh 224 pounds. What is Jakeβs present weight, in pounds?
|
{
"A": "131",
"B": "135",
"C": "156",
"D": "177",
"E": "188"
}
|
add(multiply(divide(subtract(224, 20), const_3), const_2), 20)
|
subtract(n1,n0)|divide(#0,const_3)|multiply(#1,const_2)|add(n0,#2)|
|
"lets say j is the weight of jack and s is the wt of his sister . if he loses 20 pounds , he s twice as heavy as his sister . j - 20 = 2 * s also , together they weight 224 pounds j + s = 224 solvong the 2 equation , we get j = 156 pounds ! c"
|
general
|
math_qa__ML0xxI0iPdJXy8dD
|
If the sides of a rectangle are increased by 15%, what is the percentage increase in the area? Choose the correct choice from the following answers:
A) 32.25 % B) 40 % C) 37.50 % D) 36.75 % E) 32 %
|
<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">(3/20) + 1</gadget>
<output>23/20 = around 1.15</output>
<gadget id="calculator">(23/20) ** 2</gadget>
<output>529/400 = around 1.3225</output>
<gadget id="calculator">(529/400) - 1</gadget>
<output>129/400 = around 0.3225</output>
<gadget id="calculator">(129/400) * 100</gadget>
<output>129/4 = around 32.25</output>
<result>A</result>
|
A
| 32.25 |
If the sides of a rectangle are increased by 15%, what is the percentage increase in the area?
|
{
"A": "32.25 %",
"B": "40 %",
"C": "37.50 %",
"D": "36.75 %",
"E": "32 %"
}
|
multiply(subtract(power(add(divide(15, const_100), const_1), const_2), const_1), const_100)
|
divide(n0,const_100)|add(#0,const_1)|power(#1,const_2)|subtract(#2,const_1)|multiply(#3,const_100)|
|
"say both sides of the rectangle are equal to 100 ( so consider that we have a square ) . in this case the area is 100 * 100 = 10,000 . the area of new rectangle would be 115 * 115 = 13,225 , which is 32.25 % greater than the old area . answer : a ."
|
geometry
|
math_qa__rr9S9OpPj1WEzVPD
|
A fashion designer sold a pair of jeans to a retail store for 40 percent more than it cost to manufacture the pair of jeans. A customer bought the pair of jeans for 40 percent more than the retailer paid for them. The price the customer paid was what percent greater than the cost of manufacturing the jeans? Select
A) 65 %
B) 70 %
C) 75 %
D) 85 %
E) 96 %
|
<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">1 + (2/5)</gadget>
<output>7/5 = around 1.4</output>
<gadget id="calculator">100 * (7/5)</gadget>
<output>140</output>
<gadget id="calculator">140 * (7/5)</gadget>
<output>196</output>
<gadget id="calculator">196 / 100</gadget>
<output>49/25 = around 1.96</output>
<gadget id="calculator">(49/25) - 1</gadget>
<output>24/25 = around 0.96</output>
<gadget id="calculator">(24/25) * 100</gadget>
<output>96</output>
<result>E</result>
|
E
| 96 |
A fashion designer sold a pair of jeans to a retail store for 40 percent more than it cost to manufacture the pair of jeans. A customer bought the pair of jeans for 40 percent more than the retailer paid for them. The price the customer paid was what percent greater than the cost of manufacturing the jeans?
|
{
"A": "65 %",
"B": "70 %",
"C": "75 %",
"D": "85 %",
"E": "96 %"
}
|
multiply(subtract(divide(multiply(multiply(const_100, add(const_1, divide(40, const_100))), add(const_1, divide(40, const_100))), const_100), const_1), const_100)
|
divide(n1,const_100)|divide(n0,const_100)|add(#0,const_1)|add(#1,const_1)|multiply(#3,const_100)|multiply(#2,#4)|divide(#5,const_100)|subtract(#6,const_1)|multiply(#7,const_100)|
|
"find the product of the two increases : ( 14 / 10 ) * ( 14 / 10 ) which is 1.96 and a 96 % increase . e"
|
gain
|
math_qa__Y3aPT37uLheMrAUC
|
There were 35 students in a hostel. Due to the admission of 7 new students, ;he expenses of the mess were increased by Rs. 42 per day while the average expenditure per head diminished by Rs 1. Wbat was the original expenditure of the mess?
Options
A) 520 B) 720 C) 425 D) 625 E) 420
|
<gadget id="calculator">42 + 42</gadget>
<output>84</output>
<gadget id="calculator">42 - 35</gadget>
<output>7</output>
<gadget id="calculator">84 / 7</gadget>
<output>12</output>
<gadget id="calculator">12 * 35</gadget>
<output>420</output>
<gadget id="calculator">42 - 12</gadget>
<output>30</output>
<gadget id="calculator">30 - 12</gadget>
<output>18</output>
<gadget id="calculator">18 + 2</gadget>
<output>20</output>
<gadget id="calculator">420 - 20</gadget>
<output>400</output>
<result>E</result>
|
E
| 420 |
There were 35 students in a hostel. Due to the admission of 7 new students, ;he expenses of the mess were increased by Rs. 42 per day while the average expenditure per head diminished by Rs 1. Wbat was the original expenditure of the mess?
|
{
"A": "520",
"B": "720",
"C": "425",
"D": "625",
"E": "420"
}
|
subtract(multiply(divide(add(42, 42), subtract(42, 35)), 35), add(subtract(subtract(42, divide(add(42, 42), subtract(42, 35))), divide(add(42, 42), subtract(42, 35))), const_2))
|
add(n2,n2)|subtract(n2,n0)|divide(#0,#1)|multiply(n0,#2)|subtract(n2,#2)|subtract(#4,#2)|add(#5,const_2)|subtract(#3,#6)|
|
"let the original average expenditure be rs . x . then , 42 ( x - 1 ) - 35 x = 42 7 x = 84 x = 12 . original expenditure = rs . ( 35 x 12 ) = rs . 420 . answer is e ."
|
general
|
math_qa__eYNiMafvfKS58N5G
|
Evaluate: |7 - 8(3 - 12)| - |5 - 11| = ? Pick one
A) 40 B) 50 C) 73 D) 70 E) 80
|
<gadget id="calculator">3 - 12</gadget>
<output>-9</output>
<gadget id="calculator">8 * (-9)</gadget>
<output>-72</output>
<gadget id="calculator">7 - (-72)</gadget>
<output>79</output>
<gadget id="calculator">5 - 11</gadget>
<output>-6</output>
<gadget id="calculator">-(-6)</gadget>
<output>6</output>
<gadget id="calculator">79 - 6</gadget>
<output>73</output>
<result>C</result>
|
C
| 73 |
Evaluate: |7 - 8(3 - 12)| - |5 - 11| = ?
|
{
"A": "40",
"B": "50",
"C": "73",
"D": "70",
"E": "80"
}
|
subtract(subtract(7, multiply(8, subtract(3, 12))), negate(subtract(5, 11)))
|
subtract(n2,n3)|subtract(n4,n5)|multiply(n1,#0)|negate(#1)|subtract(n0,#2)|subtract(#4,#3)|
|
"according to order of operations , inner brackets first . hence | 7 - 8 ( 3 - 12 ) | - | 5 - 11 | = | 7 - 8 * ( - 9 ) | - | 5 - 11 | according to order of operations , multiplication within absolute value signs ( which may be considered as brackets when it comes to order of operations ) next . hence = | 7 + 72 | - | 5 - 11 | = | 79 | - | - 6 | = 79 - 6 = 73 correct answer c ) 73"
|
general
|
math_qa__75CUe729pwCf7mWk
|
If 14 lions can kill 14 deers in 14 minutes how long will it take 100 lions to kill 100 deers? Choose the correct choice from the following options.
A) 1 minutes B) 14 minute C) 100 minutes D) 10000 minutes E) 1000 minutes
|
<gadget id="calculator">14 / 14</gadget>
<output>1</output>
<gadget id="calculator">1 * 14</gadget>
<output>14</output>
<result>B</result>
|
B
| 14 |
If 14 lions can kill 14 deers in 14 minutes how long will it take 100 lions to kill 100 deers?
|
{
"A": "1 minutes",
"B": "14 minute",
"C": "100 minutes",
"D": "10000 minutes",
"E": "1000 minutes"
}
|
multiply(divide(14, 14), 14)
|
divide(n0,n0)|multiply(n0,#0)|
|
"we can try the logic of time and work , our work is to kill the deers so 14 ( lions ) * 14 ( min ) / 14 ( deers ) = 100 ( lions ) * x ( min ) / 100 ( deers ) hence answer is x = 14 answer : b"
|
physics
|
math_qa__bkpF05DmDE5s8faB
|
In a 100m race, Sam beats John by 3 seconds. On the contrary, if Sam allowed John to start 24m ahead of Sam, then Sam and John reach the finishing point at the same time. How long does Sam take to run the 100m race? Select the correct option
A) 4 seconds B) 25.33 seconds C) 29 seconds D) 21 seconds E) 6.25 seconds
|
<gadget id="calculator">100 - 24</gadget>
<output>76</output>
<gadget id="calculator">76 / 3</gadget>
<output>76/3 = around 25.333333</output>
<result>B</result>
|
B
| 25.33 |
In a 100m race, Sam beats John by 3 seconds. On the contrary, if Sam allowed John to start 24m ahead of Sam, then Sam and John reach the finishing point at the same time. How long does Sam take to run the 100m race?
|
{
"A": "4 seconds",
"B": "25.33 seconds",
"C": "29 seconds",
"D": "21 seconds",
"E": "6.25 seconds"
}
|
divide(subtract(100, 24), const_3)
|
subtract(n0,n2)|divide(#0,const_3)
|
their difference is 3 second but this difference is 0 if john allows sam to start the race from 24 m ahead . that means jhon was 24 m away from finishing line when they started together . so he will cover 24 m in 3 seconds . so his speed = 24 / 3 = 8 metre / second . so time taken = 100 / 3 = 33.33 seconds . so sam took = 25.33 seconds . correct answer = b
|
physics
|
math_qa__uAm3ol2ooNsZdgCw
|
If |x - 25| = 50 what is the sum of all the values of x. Choose the correct answer: A) 0 B) - 100 C) - 50 D) 50 E) 100
|
<gadget id="calculator">50 + 25</gadget>
<output>75</output>
<gadget id="calculator">50 - 25</gadget>
<output>25</output>
<gadget id="calculator">75 - 25</gadget>
<output>50</output>
<result>D</result>
|
D
| 50 |
If |x - 25| = 50 what is the sum of all the values of x.
|
{
"A": "0",
"B": "- 100",
"C": "- 50",
"D": "50",
"E": "100"
}
|
subtract(add(50, 25), subtract(50, 25))
|
add(n0,n1)|subtract(n1,n0)|subtract(#0,#1)
|
there will be two cases x - 25 = 50 and x - 25 = - 50 solve for x = > x = 50 + 25 = > x = 75 or x = - 50 + 25 = > x = - 25 the sum of both values will be 75 + - 25 = 50 answer is d
|
general
|
math_qa__yEvwLF0i1HY94qjz
|
Product of two co-prime numbers is 117. Their L.C.M should be:
Choose one.
A) 1 B) 117 C) 116 D) equal to their h . c . f E) can not be calculated
|
<gadget id="calculator">117 * 1</gadget>
<output>117</output>
<result>B</result>
|
B
| 117 |
Product of two co-prime numbers is 117. Their L.C.M should be:
|
{
"A": "1",
"B": "117",
"C": "116",
"D": "equal to their h . c . f",
"E": "can not be calculated"
}
|
multiply(117, const_1)
|
multiply(n0,const_1)|
|
"h . c . f of co - prime numbers is 1 . so , l . c . m = 117 / 1 = 117 . answer : b"
|
general
|
math_qa__odL9L6OFrh8zu9gD
|
The price of a TV was increased by 30 percent. The new price was then increased by 40 percent. A single increase of what percent is equivalent to these two successive increases? Choose the correct choice from the following choices: A) 82 % B) 75 % C) 65 % D) 50 % E) 45 %
|
<gadget id="calculator">100 + 30</gadget>
<output>130</output>
<gadget id="calculator">130 / 100</gadget>
<output>13/10 = around 1.3</output>
<gadget id="calculator">40 + 100</gadget>
<output>140</output>
<gadget id="calculator">140 / 100</gadget>
<output>7/5 = around 1.4</output>
<gadget id="calculator">(13/10) * (7/5)</gadget>
<output>91/50 = around 1.82</output>
<gadget id="calculator">(91/50) - 1</gadget>
<output>41/50 = around 0.82</output>
<gadget id="calculator">(41/50) * 100</gadget>
<output>82</output>
<result>A</result>
|
A
| 82 |
The price of a TV was increased by 30 percent. The new price was then increased by 40 percent. A single increase of what percent is equivalent to these two successive increases?
|
{
"A": "82 %",
"B": "75 %",
"C": "65 %",
"D": "50 %",
"E": "45 %"
}
|
multiply(subtract(multiply(divide(add(const_100, 30), const_100), divide(add(40, const_100), const_100)), const_1), const_100)
|
add(n0,const_100)|add(n1,const_100)|divide(#0,const_100)|divide(#1,const_100)|multiply(#2,#3)|subtract(#4,const_1)|multiply(#5,const_100)|
|
"consider base price - $ 100 30 % increase = 1.30 * 100 = $ 130 another 40 % increase on new price = 1.4 * 130 = $ 182 so final price of radio - $ 182 therefore a 82 % increase correct option - a"
|
gain
|
math_qa__IsJLGByVE2rzvNdD
|
terry is having lunch at a salad bar . there are two types of lettuce to choose from , as well as 3 types of tomatoes , and 4 types of olives . he must also choose whether or not to have one of the two types of soup on the side . if terry has decided to have the salad and soup combo and he picks one type of lettuce , one type of tomato , and one type of olive for his salad , how many total options does he have for his lunch combo ? Choose the correct choice: A) 9 B) 11 C) 24 D) 48 E) 54
|
<gadget id="calculator">2 * 4</gadget>
<output>8</output>
<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">8 * 6</gadget>
<output>48</output>
<result>D</result>
|
D
| 48 |
terry is having lunch at a salad bar . there are two types of lettuce to choose from , as well as 3 types of tomatoes , and 4 types of olives . he must also choose whether or not to have one of the two types of soup on the side . if terry has decided to have the salad and soup combo and he picks one type of lettuce , one type of tomato , and one type of olive for his salad , how many total options does he have for his lunch combo ?
|
{
"A": "9",
"B": "11",
"C": "24",
"D": "48",
"E": "54"
}
|
multiply(multiply(const_2, 4), multiply(const_2, 3))
|
multiply(n1,const_2)|multiply(n0,const_2)|multiply(#0,#1)
|
terry can pick one lunch salad bar . . . . we can choose lettuce 2 c 1 , tomatoes - 3 c 1 and olives - 4 c 1 . . . two types of soups , if he picks one then 2 c 1 ways . terry decided to have the combo : soup + salad . . . hmmm . . . using the above information , we get ( 2 c 1 * 2 c 1 * 3 c 1 * 4 c 1 ) = 48 . . ans option d is correct answer . .
|
general
|
math_qa__tCMw2lZL5P8Uok6P
|
What will be the reminder when (31^31+31) is divided by 32?
Pick:
A) 72
B) 43
C) 91
D) 40
E) 30
|
<gadget id="calculator">31 ** 31</gadget>
<output>17_069_174_130_723_235_958_610_643_029_059_314_756_044_734_431</output>
<gadget id="calculator">17_069_174_130_723_235_958_610_643_029_059_314_756_044_734_431 + 31</gadget>
<output>17_069_174_130_723_235_958_610_643_029_059_314_756_044_734_462</output>
<gadget id="calculator">17_069_174_130_723_235_958_610_643_029_059_314_756_044_734_462 / 32</gadget>
<output>8_534_587_065_361_617_979_305_321_514_529_657_378_022_367_231/16 = around 533_411_691_585_101_154_829_130_050_730_846_835_315_834_880</output>
<gadget id="calculator">floor(8_534_587_065_361_617_979_305_321_514_529_657_378_022_367_231/16)</gadget>
<output>533_411_691_585_101_123_706_582_594_658_103_586_126_397_951</output>
<gadget id="calculator">32 * 533_411_691_585_101_123_706_582_594_658_103_586_126_397_951</gadget>
<output>17_069_174_130_723_235_958_610_643_029_059_314_756_044_734_432</output>
<gadget id="calculator">17_069_174_130_723_235_958_610_643_029_059_314_756_044_734_462 - 17_069_174_130_723_235_958_610_643_029_059_314_756_044_734_432</gadget>
<output>30</output>
<result>E</result>
|
E
| 30 |
What will be the reminder when (31^31+31) is divided by 32?
|
{
"A": "72",
"B": "43",
"C": "91",
"D": "40",
"E": "30"
}
|
subtract(add(power(31, 31), 31), multiply(32, floor(divide(add(power(31, 31), 31), 32))))
|
power(n0,n0)|add(n0,#0)|divide(#1,n3)|floor(#2)|multiply(n3,#3)|subtract(#1,#4)|
|
"( x ^ n + 1 ) will be divisible by ( x + 1 ) only when n is odd ; ( 31 ^ 31 + 1 ) will be divisible by ( 31 + 1 ) ; ( 31 ^ 31 + 1 ) + 30 when divided by will give 30 as remainder . correct option : e"
|
general
|
math_qa__Ib5dSSnVVUO0Jjno
|
If M equals the sum of the odd integers from 1 to 111, inclusive, and T equals the sum of the even integers from 2 to 50, inclusive, what is the value of M + T? Choose one: A) 400 B) 5550 C) 6922 D) 3786 E) 5553
|
<gadget id="calculator">111 + 1</gadget>
<output>112</output>
<gadget id="calculator">112 / 2</gadget>
<output>56</output>
<gadget id="calculator">56 ** 2</gadget>
<output>3_136</output>
<gadget id="calculator">50 / 2</gadget>
<output>25</output>
<gadget id="calculator">25 + 1</gadget>
<output>26</output>
<gadget id="calculator">25 * 26</gadget>
<output>650</output>
<gadget id="calculator">3_136 + 650</gadget>
<output>3_786</output>
<result>D</result>
|
D
| 3,786 |
If M equals the sum of the odd integers from 1 to 111, inclusive, and T equals the sum of the even integers from 2 to 50, inclusive, what is the value of M + T?
|
{
"A": "400",
"B": "5550",
"C": "6922",
"D": "3786",
"E": "5553"
}
|
add(power(divide(add(111, 1), 2), const_2), multiply(divide(50, 2), add(divide(50, 2), const_1)))
|
add(n0,n1)|divide(n3,n2)|add(#1,const_1)|divide(#0,n2)|multiply(#2,#1)|power(#3,const_2)|add(#4,#5)
|
use following formulae for such problems : sum of evenly spaced integers = ( # of integers ) * ( mean of integers ) # of integers = [ ( last - first ) / 2 ] + 1 mean of integers = ( last + first ) / 2 in above problem : # of integers = [ ( 111 - 1 ) / 2 ] + 1 = 56 and [ ( 50 - 2 ) / 2 ] + 1 = 25 mean of integers = ( 111 + 1 ) / 2 = 56 and ( 50 + 2 ) / 2 = 26 sum of integers = ( 56 * 56 ) = 3136 and ( 25 * 26 ) = 650 thus their sum ( m + t ) = 3786 answer : d
|
general
|
math_qa__pQ8nccQBPFAffc6v
|
A train ,125 meters long travels at a speed of 45 km/hr crosses a bridge in 30 seconds. The length of the bridge is Choose the correct choice from the following answers
A) 250 m B) 245 m C) 235 m D) 220 m E) 240 m
|
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">45 * (5/18)</gadget>
<output>25/2 = around 12.5</output>
<gadget id="calculator">(25/2) * 30</gadget>
<output>375</output>
<gadget id="calculator">375 - 125</gadget>
<output>250</output>
<result>A</result>
|
A
| 250 |
A train ,125 meters long travels at a speed of 45 km/hr crosses a bridge in 30 seconds. The length of the bridge is
|
{
"A": "250 m",
"B": "245 m",
"C": "235 m",
"D": "220 m",
"E": "240 m"
}
|
subtract(multiply(multiply(45, const_0_2778), 30), 125)
|
multiply(n1,const_0_2778)|multiply(n2,#0)|subtract(#1,n0)|
|
"explanation : assume the length of the bridge = x meter total distance covered = 125 + x meter total time taken = 30 s speed = total distance covered / total time taken = ( 125 + x ) / 30 m / s = > 45 Γ£ β ( 10 / 36 ) = ( 125 + x ) / 30 = > 45 Γ£ β 10 Γ£ β 30 / 36 = 125 + x = > 45 Γ£ β 10 Γ£ β 10 / 12 = 125 + x = > 15 Γ£ β 10 Γ£ β 10 / 4 = 125 + x = > 15 Γ£ β 25 = 125 + x = 375 = > x = 375 - 125 = 250 answer : option a"
|
physics
|
math_qa__Ld9wrZIyBvEhYQkl
|
In a division sum, the quotient is 36, the divisor 85 and the remainder 26, find the dividend? Select.
A) 3066
B) 3586
C) 3086
D) 3968
E) 3286
|
<gadget id="calculator">36 * 85</gadget>
<output>3_060</output>
<gadget id="calculator">3_060 + 26</gadget>
<output>3_086</output>
<result>C</result>
|
C
| 3,086 |
In a division sum, the quotient is 36, the divisor 85 and the remainder 26, find the dividend?
|
{
"A": "3066",
"B": "3586",
"C": "3086",
"D": "3968",
"E": "3286"
}
|
add(multiply(36, 85), 26)
|
multiply(n0,n1)|add(n2,#0)|
|
"explanation : 36 * 85 + 26 = 3086 answer : c"
|
general
|
math_qa__CIgfTyZPElkCfMSy
|
A company conducted a survey about its two brands, A and B. x percent of respondents liked product A, (x β 20) percent liked product B, 23 percent liked both products, and 23 percent liked neither product. What is the minimum number Q of people surveyed by the company? Select
A) 46 B) q . 80 C) q . 90 D) q . 100 E) 200
|
<gadget id="calculator">100 - 23</gadget>
<output>77</output>
<gadget id="calculator">77 + 23</gadget>
<output>100</output>
<gadget id="calculator">100 + 20</gadget>
<output>120</output>
<gadget id="calculator">120 / 2</gadget>
<output>60</output>
<gadget id="calculator">60 - 20</gadget>
<output>40</output>
<gadget id="calculator">40 + 60</gadget>
<output>100</output>
<result>D</result>
|
D
| 100 |
A company conducted a survey about its two brands, A and B. x percent of respondents liked product A, (x β 20) percent liked product B, 23 percent liked both products, and 23 percent liked neither product. What is the minimum number Q of people surveyed by the company?
|
{
"A": "46",
"B": "q . 80",
"C": "q . 90",
"D": "q . 100",
"E": "200"
}
|
add(subtract(divide(add(add(subtract(const_100, 23), 23), 20), const_2), 20), divide(add(add(subtract(const_100, 23), 23), 20), const_2))
|
subtract(const_100,n1)|add(n1,#0)|add(n0,#1)|divide(#2,const_2)|subtract(#3,n0)|add(#3,#4)|
|
"100 = x + x - 20 + 23 - 23 x = 60 , so , product a = 60 % , product b = 40 % , both = 23 % , neither = 23 % 23 % of the total no . of people should be an integer . so , a , bc are out . 60 % of d and 40 % of d are both integers . so , d satisfies all conditions . so , answer is d ."
|
other
|
math_qa__aJMDnJCRmTHXomfS
|
Two trains 141 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet? Options
A) 7.16 B) 7.59 C) 7.12 D) 7.15 E) 7.11
|
<gadget id="calculator">141 + 165</gadget>
<output>306</output>
<gadget id="calculator">80 + 65</gadget>
<output>145</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">145 * (5/18)</gadget>
<output>725/18 = around 40.277778</output>
<gadget id="calculator">306 / (725/18)</gadget>
<output>5_508/725 = around 7.597241</output>
<result>B</result>
|
B
| 7.59 |
Two trains 141 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?
|
{
"A": "7.16",
"B": "7.59",
"C": "7.12",
"D": "7.15",
"E": "7.11"
}
|
divide(add(141, 165), multiply(add(80, 65), const_0_2778))
|
add(n0,n1)|add(n2,n3)|multiply(#1,const_0_2778)|divide(#0,#2)|
|
"t = ( 141 + 165 ) / ( 80 + 65 ) * 18 / 5 t = 7.59 answer : b"
|
physics
|
math_qa__XihhXvhlEHvPZtqb
|
A pharmaceutical company received $6 million in royalties on the first $20 million in sales of the generic equivalent of one of its products and then $9 million in royalties on the next $108 million in sales. By approximately what percent did the ratio of royalties to sales decrease from the first $20 million in sales to the next $108 million in sales? Choose the correct choice from the following
A) 8 %
B) 15 %
C) 45 %
D) 52 %
E) 72 %
|
<gadget id="calculator">6 / 20</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(3/10) * 100</gadget>
<output>30</output>
<gadget id="calculator">9 / 108</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">(1/12) * 100</gadget>
<output>25/3 = around 8.333333</output>
<gadget id="calculator">30 - (25/3)</gadget>
<output>65/3 = around 21.666667</output>
<gadget id="calculator">(65/3) / 30</gadget>
<output>13/18 = around 0.722222</output>
<gadget id="calculator">(13/18) * 100</gadget>
<output>650/9 = around 72.222222</output>
<result>E</result>
|
E
| 72 |
A pharmaceutical company received $6 million in royalties on the first $20 million in sales of the generic equivalent of one of its products and then $9 million in royalties on the next $108 million in sales. By approximately what percent did the ratio of royalties to sales decrease from the first $20 million in sales to the next $108 million in sales?
|
{
"A": "8 %",
"B": "15 %",
"C": "45 %",
"D": "52 %",
"E": "72 %"
}
|
multiply(divide(subtract(multiply(divide(6, 20), const_100), multiply(divide(9, 108), const_100)), multiply(divide(6, 20), const_100)), const_100)
|
divide(n0,n1)|divide(n2,n3)|multiply(#0,const_100)|multiply(#1,const_100)|subtract(#2,#3)|divide(#4,#2)|multiply(#5,const_100)|
|
"solution : this is a percent decrease problem . we will use the formula : percent change = ( new β old ) / old x 100 to calculate the final answer . we first set up the ratios of royalties to sales . the first ratio will be for the first 20 million in sales , and the second ratio will be for the next 108 million in sales . because all of the sales are in millions , we do not have to express all the trailing zeros in our ratios . first 20 million royalties / sales = 6 / 20 = 3 / 10 next 108 million royalties / sales = 9 / 108 = 1 / 12 because each ratio is not an easy number to use , we can simplify each one by multiplying each by the lcm of the two denominators , which is 60 . keep in mind that we are able to do this only because our answer choices are expressed in percents . first 20 million royalties / sales = ( 6 / 20 ) x 60 = 18 next 108 million royalties / sales = 9 / 108 = ( 1 / 12 ) x 60 = 5 we can plug 18 and 5 into our percent change formula : ( new β old ) / old x 100 [ ( 5 β 18 ) / 18 ] x 100 - 650 / 9 x 100 at this point we can stop and consider the answer choices . since we know that 650 / 9 is just a bit less than Β½ , we know that - 650 / 9 x 100 is about a 72 % decrease . answer e ."
|
general
|
math_qa__KPBtQapdnYyXU3Lr
|
One train is travelling 45 kmph and other is at 10 meters a second. Ratio of the speed of the two trains is? Pick one
A) 3 : 3 B) 5 : 7 C) 5 : 4 D) 7 : 2 E) 8 : 5
|
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">45 * (5/18)</gadget>
<output>25/2 = around 12.5</output>
<gadget id="calculator">(25/2) / 10</gadget>
<output>5/4 = around 1.25</output>
<result>C</result>
|
C
| 1.25 |
One train is travelling 45 kmph and other is at 10 meters a second. Ratio of the speed of the two trains is?
|
{
"A": "3 : 3",
"B": "5 : 7",
"C": "5 : 4",
"D": "7 : 2",
"E": "8 : 5"
}
|
divide(multiply(45, const_0_2778), 10)
|
multiply(n0,const_0_2778)|divide(#0,n1)
|
c 5 : 4 45 * 5 / 18 = 10 25 : 20 = > 5 : 4
|
physics
|
math_qa__1Kmf8yggNcDM1HT0
|
in the xy - plane , a triangle has vertices ( 00 ) , ( 40 ) and ( 410 ) . if a point ( a , b ) is selected at random from the triangular region , what is the probability that a - b > 0 ?
Choices
A) 1 / 5 B) 1 / 3 C) 1 / 2 D) 2 / 3 E) 2 / 5
|
<gadget id="calculator">40 / 10</gadget>
<output>4</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">2 / 5</gadget>
<output>2/5 = around 0.4</output>
<result>E</result>
|
E
| 0.4 |
in the xy - plane , a triangle has vertices ( 00 ) , ( 40 ) and ( 410 ) . if a point ( a , b ) is selected at random from the triangular region , what is the probability that a - b > 0 ?
|
{
"A": "1 / 5",
"B": "1 / 3",
"C": "1 / 2",
"D": "2 / 3",
"E": "2 / 5"
}
|
divide(const_2, add(divide(40, const_10), const_1))
|
divide(n1,const_10)|add(#0,const_1)|divide(const_2,#1)
|
the area of the right triangle is ( 1 / 2 ) * 4 * 10 = 20 . only the points ( a , b ) below the line y = x satisfy a - b > 0 . the part of the triangle which is below the line y = x has an area of ( 1 / 2 ) ( 4 ) ( 4 ) = 8 . p ( a - b > 0 ) = 8 / 20 = 2 / 5 the answer is e .
|
geometry
|
math_qa__7U0KGLKMihX0ySnU
|
A train 150m long takes 6 sec to cross a man walking at 5kmph in a direction opposite to that of the train. Find the speed of the train? Choose the correct choice
A) 75 kmph B) 85 kmph C) 95 kmph D) 105 kmph E) 115 kmph
|
<gadget id="calculator">150 / 6</gadget>
<output>25</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">25 / (5/18)</gadget>
<output>90</output>
<gadget id="calculator">90 - 5</gadget>
<output>85</output>
<result>B</result>
|
B
| 85 |
A train 150m long takes 6 sec to cross a man walking at 5kmph in a direction opposite to that of the train. Find the speed of the train?
|
{
"A": "75 kmph",
"B": "85 kmph",
"C": "95 kmph",
"D": "105 kmph",
"E": "115 kmph"
}
|
subtract(divide(divide(150, 6), const_0_2778), 5)
|
divide(n0,n1)|divide(#0,const_0_2778)|subtract(#1,n2)
|
let the speed of the train be x kmph speed of the train relative to man = x + 5 = ( x + 5 ) * 5 / 18 m / sec 150 / [ ( x + 5 ) * 5 / 18 ] = 6 30 ( x + 5 ) = 2700 x = 85 kmph answer is b
|
physics
|
math_qa__h6lSKdwoTdGjIF34
|
working together , wayne and his son can shovel the entire driveway in 3 hours . if wayne can shovel 6 times as fast as his son can , how many hours would it take for his son to shovel the entire driveway on his own ? Pick one:
A) 4
B) 6
C) 8
D) 7
E) 12
|
<gadget id="calculator">6 + 1</gadget>
<output>7</output>
<gadget id="calculator">3 * 7</gadget>
<output>21</output>
<gadget id="calculator">21 / 3</gadget>
<output>7</output>
<result>D</result>
|
D
| 7 |
working together , wayne and his son can shovel the entire driveway in 3 hours . if wayne can shovel 6 times as fast as his son can , how many hours would it take for his son to shovel the entire driveway on his own ?
|
{
"A": "4",
"B": "6",
"C": "8",
"D": "7",
"E": "12"
}
|
divide(multiply(3, add(6, const_1)), 3)
|
add(n1,const_1)|multiply(n0,#0)|divide(#1,n0)
|
w : the time for wyane to do the job s : the time for his son to do the job we have 1 / w + 1 / s = 1 / 6 and w = 6 s then we have 1 / ( 6 * s ) + 1 / s = 1 / 6 < = > 7 / ( 6 * s ) = 1 / 6 < = > s = 7 ans : d
|
physics
|
math_qa__7zV4Wk02L0qJWTP5
|
The cost of 10 kg of mangos is equal to the cost of 24 kg of rice. The cost of 6 kg of flour equals the cost of 2 kg of rice. The cost of each kg of flour is $21. Find the total cost of 4 kg of mangos, 3 kg of rice and 5 kg of flour? Pick one:
A) 347.8 B) 987.8 C) 877.8 D) 898.8 E) 667.4
|
<gadget id="calculator">24 / 10</gadget>
<output>12/5 = around 2.4</output>
<gadget id="calculator">21 * 6</gadget>
<output>126</output>
<gadget id="calculator">126 / 2</gadget>
<output>63</output>
<gadget id="calculator">(12/5) * 63</gadget>
<output>756/5 = around 151.2</output>
<gadget id="calculator">4 * (756/5)</gadget>
<output>3_024/5 = around 604.8</output>
<gadget id="calculator">3 * 63</gadget>
<output>189</output>
<gadget id="calculator">(3_024/5) + 189</gadget>
<output>3_969/5 = around 793.8</output>
<gadget id="calculator">5 * 21</gadget>
<output>105</output>
<gadget id="calculator">(3_969/5) + 105</gadget>
<output>4_494/5 = around 898.8</output>
<result>D</result>
|
D
| 898.8 |
The cost of 10 kg of mangos is equal to the cost of 24 kg of rice. The cost of 6 kg of flour equals the cost of 2 kg of rice. The cost of each kg of flour is $21. Find the total cost of 4 kg of mangos, 3 kg of rice and 5 kg of flour?
|
{
"A": "347.8",
"B": "987.8",
"C": "877.8",
"D": "898.8",
"E": "667.4"
}
|
add(add(multiply(4, multiply(divide(24, 10), divide(multiply(21, 6), 2))), multiply(3, divide(multiply(21, 6), 2))), multiply(5, 21))
|
divide(n1,n0)|multiply(n2,n4)|multiply(n4,n7)|divide(#1,n3)|multiply(#0,#3)|multiply(n6,#3)|multiply(n5,#4)|add(#6,#5)|add(#7,#2)|
|
"let the costs of each kg of mangos and each kg of rice be $ a and $ r respectively . 10 a = 24 r and 6 * 21 = 2 r a = 12 / 5 r and r = 63 a = 151.2 required total cost = 4 * 151.2 + 3 * 63 + 5 * 21 = 604.8 + 189 + 105 = $ 898.80 d"
|
general
|
math_qa__sycNhhoMAAUIKIyj
|
How many pieces of 85 cm length can be cut from a rod of 25.5 meters long? Choose the correct answer: A) 50 B) 40 C) 30 D) 20 E) 10
|
<gadget id="calculator">25.5 * 100</gadget>
<output>2_550</output>
<gadget id="calculator">2_550 / 85</gadget>
<output>30</output>
<result>C</result>
|
C
| 30 |
How many pieces of 85 cm length can be cut from a rod of 25.5 meters long?
|
{
"A": "50",
"B": "40",
"C": "30",
"D": "20",
"E": "10"
}
|
divide(multiply(25.5, const_100), 85)
|
multiply(n1,const_100)|divide(#0,n0)|
|
"number of pieces = 2550 / 85 = 30 the answer is c ."
|
physics
|
math_qa__PBuQIZpkQyKazfgo
|
a father is 4 times as old as his son . in 20 years , he ' ll be twice as old . how old are they now ?
Pick.
A) 540
B) 1040
C) 2040
D) 1030
E) 15,30
|
<gadget id="calculator">20 / 2</gadget>
<output>10</output>
<gadget id="calculator">10 * 4</gadget>
<output>40</output>
<gadget id="calculator">1_000 + 40</gadget>
<output>1_040</output>
<result>B</result>
|
B
| 1,040 |
a father is 4 times as old as his son . in 20 years , he ' ll be twice as old . how old are they now ?
|
{
"A": "540",
"B": "1040",
"C": "2040",
"D": "1030",
"E": "15,30"
}
|
add(const_1000, multiply(divide(20, const_2), 4))
|
divide(n1,const_2)|multiply(n0,#0)|add(#1,const_1000)
|
if f is age of father and s is age of son f = 4 s f + 20 = 2 * ( s + 20 ) 4 s + 20 = 2 s + 40 2 s = 20 s = 10 f = 40 answer : b
|
general
|
math_qa__tmeWedWBlRl5MfHd
|
how many positive integers h less than 10000 are such that the product of their digits is 210 ? Choose one
A) 24 B) 30 C) 48 D) 54 E) 72
|
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">210 / 5</gadget>
<output>42</output>
<gadget id="calculator">42 / 3</gadget>
<output>14</output>
<gadget id="calculator">14 / 2</gadget>
<output>7</output>
<gadget id="calculator">7 - 3</gadget>
<output>4</output>
<gadget id="calculator">factorial(4)</gadget>
<output>24</output>
<gadget id="calculator">24 + 24</gadget>
<output>48</output>
<gadget id="calculator">7 - 4</gadget>
<output>3</output>
<gadget id="calculator">factorial(3)</gadget>
<output>6</output>
<gadget id="calculator">48 + 6</gadget>
<output>54</output>
<result>D</result>
|
D
| 54 |
how many positive integers h less than 10000 are such that the product of their digits is 210 ?
|
{
"A": "24",
"B": "30",
"C": "48",
"D": "54",
"E": "72"
}
|
add(add(factorial(subtract(divide(divide(divide(210, add(const_4, const_1)), const_3), const_2), const_3)), factorial(subtract(divide(divide(divide(210, add(const_4, const_1)), const_3), const_2), const_3))), factorial(subtract(divide(divide(divide(210, add(const_4, const_1)), const_3), const_2), subtract(divide(divide(divide(210, add(const_4, const_1)), const_3), const_2), const_3))))
|
add(const_1,const_4)|divide(n1,#0)|divide(#1,const_3)|divide(#2,const_2)|subtract(#3,const_3)|factorial(#4)|subtract(#3,#4)|add(#5,#5)|factorial(#6)|add(#7,#8)
|
210 is the answer when 2 , 3 , 5 and 7 are multiplied . 210 can also be arrive using 56 and 7 and 1 , 5 , 6 and 7 . so sum of arrangements of 2357 , 567 and 1567 . this translates to 4 ! + 3 ! + 4 ! , this equals to 24 + 6 + 24 = 54 , d is the answer .
|
general
|
math_qa__cLczpa1KRrLemVlT
|
Two trains of lengths 156.62 and 100 meters are running on parallel lines with respective speeds of 30 km/hr and 36 km/hr. The time of crossing each other, if they run in the opposite direction is
Choose the most appropriate option:
A) 322 sec B) 14 sec C) 11 sec D) 13 sec E) 34 sec
|
<gadget id="calculator">156.62 + 100</gadget>
<output>256.62</output>
<gadget id="calculator">30 + 36</gadget>
<output>66</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">66 * (5/18)</gadget>
<output>55/3 = around 18.333333</output>
<gadget id="calculator">256.62 / (55/3)</gadget>
<output>13.997455</output>
<result>B</result>
|
B
| 14 |
Two trains of lengths 156.62 and 100 meters are running on parallel lines with respective speeds of 30 km/hr and 36 km/hr. The time of crossing each other, if they run in the opposite direction is
|
{
"A": "322 sec",
"B": "14 sec",
"C": "11 sec",
"D": "13 sec",
"E": "34 sec"
}
|
divide(add(156.62, 100), multiply(add(30, 36), const_0_2778))
|
add(n0,n1)|add(n2,n3)|multiply(#1,const_0_2778)|divide(#0,#2)
|
explanation : total distance to be covered = 156.62 + 100 = 256.62 m trains are running in opposite directions , hence relative speed = 30 + 36 = 66 km / hr = 18.33 m / sec time = distance / relative speed = 256.62 / 18.33 sec = 14 sec therefore , the time of crossing each other in the opposite direction is 14 seconds . answer : b
|
physics
|
math_qa__ddP5suBQuJ7w7YuQ
|
The length of the bridge, which a train 170 meters long and travelling at 45 km/hr can cross in 30 seconds, is? Choose the correct answer:
A) 388
B) 267
C) 205
D) 288
E) 261
|
<gadget id="calculator">1_000 / 1</gadget>
<output>1_000</output>
<gadget id="calculator">45 * 1_000</gadget>
<output>45_000</output>
<gadget id="calculator">3_600 / 1</gadget>
<output>3_600</output>
<gadget id="calculator">45_000 / 3_600</gadget>
<output>25/2 = around 12.5</output>
<gadget id="calculator">(25/2) * 30</gadget>
<output>375</output>
<gadget id="calculator">375 - 170</gadget>
<output>205</output>
<result>C</result>
|
C
| 205 |
The length of the bridge, which a train 170 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
|
{
"A": "388",
"B": "267",
"C": "205",
"D": "288",
"E": "261"
}
|
subtract(multiply(divide(multiply(45, speed(const_1000, const_1)), speed(const_3600, const_1)), 30), 170)
|
speed(const_1000,const_1)|speed(const_3600,const_1)|multiply(n1,#0)|divide(#2,#1)|multiply(n2,#3)|subtract(#4,n0)|
|
"speed = ( 45 * 5 / 18 ) m / sec = ( 25 / 2 ) m / sec . time = 30 sec . let the length of bridge be x meters . then , ( 170 + x ) / 30 = 25 / 2 = = > 2 ( 170 + x ) = 750 = = > x = 205 m . answer : c"
|
physics
|
math_qa__slXFS8mWY7PUw5fb
|
On multiplying a number A by 153, the result obtained was 102325. However, it is found that both the 2's are wrong. Find the correct result. Choices:
A) 104345
B) 107375
C) 108385
D) 109395
E) 105355
|
<gadget id="calculator">4 + 3</gadget>
<output>7</output>
<gadget id="calculator">7 * 10</gadget>
<output>70</output>
<gadget id="calculator">100 * 10</gadget>
<output>1_000</output>
<gadget id="calculator">7 * 1_000</gadget>
<output>7_000</output>
<gadget id="calculator">70 + 7_000</gadget>
<output>7_070</output>
<gadget id="calculator">7_070 + 102_325</gadget>
<output>109_395</output>
<result>D</result>
|
D
| 109,395 |
On multiplying a number A by 153, the result obtained was 102325. However, it is found that both the 2's are wrong. Find the correct result.
|
{
"A": "104345",
"B": "107375",
"C": "108385",
"D": "109395",
"E": "105355"
}
|
add(add(multiply(add(const_4, const_3), const_10), multiply(add(const_4, const_3), multiply(const_100, const_10))), 102325)
|
add(const_3,const_4)|multiply(const_10,const_100)|multiply(#0,const_10)|multiply(#0,#1)|add(#2,#3)|add(n1,#4)
|
the only thing you actually know about the correct number a is that it is divisible by 153 and has 5 as a factor . you should immediately try to find the factors of 153 and look for them in the options . 153 = 9 * 17 divisibility by 9 is easy to check . only ( d ) satisfies .
|
other
|
math_qa__31vShs7O0Y7qk6Oz
|
Andrew purchased 11kg of grapes at the rate of 98 per kg and 7 kg of mangoes at the rate of 50 per kg. How much amount did he pay to the shopkeeper? Options:
A) 1000
B) 1055
C) 1428
D) 1500
E) 1080
|
<gadget id="calculator">11 * 98</gadget>
<output>1_078</output>
<gadget id="calculator">7 * 50</gadget>
<output>350</output>
<gadget id="calculator">1_078 + 350</gadget>
<output>1_428</output>
<result>C</result>
|
C
| 1,428 |
Andrew purchased 11kg of grapes at the rate of 98 per kg and 7 kg of mangoes at the rate of 50 per kg. How much amount did he pay to the shopkeeper?
|
{
"A": "1000",
"B": "1055",
"C": "1428",
"D": "1500",
"E": "1080"
}
|
add(multiply(11, 98), multiply(7, 50))
|
multiply(n0,n1)|multiply(n2,n3)|add(#0,#1)|
|
"cost of 11 kg grapes = 98 Γ 11 = 1078 . cost of 7 kg of mangoes = 50 Γ 7 = 350 . total cost he has to pay = 1078 + 350 = 1428 c"
|
gain
|
math_qa__RkCOG6GTBqmzrlvF
|
In an election a candidate who gets 60% of the votes is elected by a majority of 1380 votes. What is the total number of votes polled?
Choose the correct option:
A) 4500
B) 5200
C) 6900
D) 7520
E) 6000
|
<gadget id="calculator">100 - 60</gadget>
<output>40</output>
<gadget id="calculator">60 - 40</gadget>
<output>20</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1_380 / (1/5)</gadget>
<output>6_900</output>
<result>C</result>
|
C
| 6,900 |
In an election a candidate who gets 60% of the votes is elected by a majority of 1380 votes. What is the total number of votes polled?
|
{
"A": "4500",
"B": "5200",
"C": "6900",
"D": "7520",
"E": "6000"
}
|
divide(1380, divide(subtract(60, subtract(const_100, 60)), const_100))
|
subtract(const_100,n0)|subtract(n0,#0)|divide(#1,const_100)|divide(n1,#2)|
|
"let the total number of votes polled be x then , votes polled by other candidate = ( 100 - 60 ) % of x = 40 % of x 60 % of x - 40 % of x = 1380 20 x / 100 = 1380 x = 1380 * 100 / 20 = 6900 answer is c"
|
gain
|
math_qa__PaquOMk0RI5ihTNd
|
rounded to 3 decimal places , 1.003 ^ 4 = Choose the correct choice from the following answers:
A) 1.004 B) 1.006 C) 1.008 D) 1.012 E) 1.016
|
<gadget id="calculator">3 / 1_000</gadget>
<output>3/1_000 = around 0.003</output>
<gadget id="calculator">(3/1_000) * 3</gadget>
<output>9/1_000 = around 0.009</output>
<gadget id="calculator">1.003 + (9/1_000)</gadget>
<output>1.012</output>
<result>D</result>
|
D
| 1.012 |
rounded to 3 decimal places , 1.003 ^ 4 =
|
{
"A": "1.004",
"B": "1.006",
"C": "1.008",
"D": "1.012",
"E": "1.016"
}
|
add(1.003, multiply(divide(3, const_1000), 3))
|
divide(n0,const_1000)|multiply(n0,#0)|add(n1,#1)
|
as compared to 1 , 0.003 is a very small quantity . thus , we can write ( 1 + 0.003 ) ^ 4 is nearly equal to ( 1 + 4 * 0.003 ) = 1.012 . as the question asks for approximation to three decimal places , the further terms will anyways not come into picture . d .
|
general
|
math_qa__yoUePhYVskd4w3Jp
|
The banker's gain of a certain sum due 2 years hence at 10% per annum is Rs. 24. What is the present worth? Select the correct option:
A) rs . 600 B) rs . 500 C) rs . 400 D) rs . 300 E) none of these
|
<gadget id="calculator">24 * 100</gadget>
<output>2_400</output>
<gadget id="calculator">2 * 10</gadget>
<output>20</output>
<gadget id="calculator">2_400 / 20</gadget>
<output>120</output>
<gadget id="calculator">100 * 120</gadget>
<output>12_000</output>
<gadget id="calculator">12_000 / 20</gadget>
<output>600</output>
<result>A</result>
|
A
| 600 |
The banker's gain of a certain sum due 2 years hence at 10% per annum is Rs. 24. What is the present worth?
|
{
"A": "rs . 600",
"B": "rs . 500",
"C": "rs . 400",
"D": "rs . 300",
"E": "none of these"
}
|
divide(multiply(const_100, divide(multiply(24, const_100), multiply(2, 10))), multiply(2, 10))
|
multiply(n2,const_100)|multiply(n0,n1)|divide(#0,#1)|multiply(#2,const_100)|divide(#3,#1)|
|
"explanation : t = 2 years r = 10 % td = ( bg Γ 100 ) / tr = ( 24 Γ 100 ) / ( 2 Γ 10 ) = 12 Γ 10 = rs . 120 td = ( pw Γ tr ) / 100 β 120 = ( pw Γ 2 Γ 10 ) / 100 β 1200 = pw Γ 2 pw = 1200 / 2 = rs . 600 answer : option a"
|
gain
|
math_qa__54OvOYHHM4AZwsEF
|
In a certain pond, 50 fish were caught, tagged, and returned to the pond. A few days later, 50 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what is the approximate number of fish in the pond? Choose the most appropriate option.
A) 400 B) 625 C) 1,250 D) 2,500 E) 10,000
|
<gadget id="calculator">2 / 50</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">50 / (1/25)</gadget>
<output>1_250</output>
<result>C</result>
|
C
| 1,250 |
In a certain pond, 50 fish were caught, tagged, and returned to the pond. A few days later, 50 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what is the approximate number of fish in the pond?
|
{
"A": "400",
"B": "625",
"C": "1,250",
"D": "2,500",
"E": "10,000"
}
|
divide(50, divide(2, 50))
|
divide(n2,n1)|divide(n0,#0)|
|
"total fish = x percentage of second catch = ( 2 / 50 ) * 100 = 4 % so , x * 4 % = 50 x = 1250 answer : c"
|
gain
|
math_qa__wjOF6bzLoMB6NQHL
|
The profit earned by selling an article for 912 is equal to the loss incurred when the same article is sold for 448. What should be the sale price of the article for making 50 per cent profit? Choose the correct option.
A) 960
B) 1060
C) 1,200
D) 1020
E) none of these
|
<gadget id="calculator">912 + 448</gadget>
<output>1_360</output>
<gadget id="calculator">1_360 / 2</gadget>
<output>680</output>
<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 + (1/2)</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">680 * (3/2)</gadget>
<output>1_020</output>
<result>D</result>
|
D
| 1,020 |
The profit earned by selling an article for 912 is equal to the loss incurred when the same article is sold for 448. What should be the sale price of the article for making 50 per cent profit?
|
{
"A": "960",
"B": "1060",
"C": "1,200",
"D": "1020",
"E": "none of these"
}
|
multiply(divide(add(912, 448), const_2), add(const_1, divide(50, const_100)))
|
add(n0,n1)|divide(n2,const_100)|add(#1,const_1)|divide(#0,const_2)|multiply(#2,#3)|
|
"let the profit or loss be x and 912 β x = 448 + x or , x = 464 β 2 = 232 \ cost price of the article = 912 β x = 448 + x = 680 \ sp of the article = 680 Γ 150 β 100 = 1020 answer d"
|
gain
|
math_qa__hBSxWEalZY83SMu0
|
Working individually, Julie can peel potatoes in 10 hours and Ted can peel potatoes in 8 hours. If Julie and Ted work together but independently at the task for 4 hours, at which point Ted leaves, how many remaining hours will it take Julie to complete the task alone? Choose the correct choice
A) 3 / 15 B) 2 / 11 C) 1 / 4 D) 1 / 3 E) 1
|
<gadget id="calculator">1 / 10</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 / 8</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">(1/10) + (1/8)</gadget>
<output>9/40 = around 0.225</output>
<gadget id="calculator">4 * (9/40)</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">1 - (9/10)</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/10) / (1/10)</gadget>
<output>1</output>
<result>E</result>
|
E
| 1 |
Working individually, Julie can peel potatoes in 10 hours and Ted can peel potatoes in 8 hours. If Julie and Ted work together but independently at the task for 4 hours, at which point Ted leaves, how many remaining hours will it take Julie to complete the task alone?
|
{
"A": "3 / 15",
"B": "2 / 11",
"C": "1 / 4",
"D": "1 / 3",
"E": "1"
}
|
divide(subtract(const_1, multiply(4, add(divide(const_1, 10), divide(const_1, 8)))), divide(const_1, 10))
|
divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|multiply(n2,#2)|subtract(const_1,#3)|divide(#4,#0)
|
in first 4 hrs ted will finish 4 / 8 = 1 / 2 of work and julie will finish 4 / 10 work so total 1 / 2 + 2 / 5 = 9 / 10 work is finished and 1 - 9 / 10 = 1 / 10 work remaining . now julie will take ( 1 / 10 ) * 10 = 1 hrs to finish it . so answer is e .
|
physics
|
math_qa__qwSWFNlAzBdFHLIw
|
X is able to do a piece of work in 8 days and Y can do the same work in 12 days. If they can work together for 3 days, what is the fraction of work left? Choose the correct choice:
A) 8 / 5
B) 6 / 5
C) 7 / 5
D) 3 / 5
E) 4 / 5
|
<gadget id="calculator">8 * 12</gadget>
<output>96</output>
<gadget id="calculator">8 + 12</gadget>
<output>20</output>
<gadget id="calculator">96 / 20</gadget>
<output>24/5 = around 4.8</output>
<gadget id="calculator">3 / (24/5)</gadget>
<output>5/8 = around 0.625</output>
<result>D</result>
|
D
| 0.6 |
X is able to do a piece of work in 8 days and Y can do the same work in 12 days. If they can work together for 3 days, what is the fraction of work left?
|
{
"A": "8 / 5",
"B": "6 / 5",
"C": "7 / 5",
"D": "3 / 5",
"E": "4 / 5"
}
|
divide(3, divide(multiply(8, 12), add(8, 12)))
|
add(n0,n1)|multiply(n0,n1)|divide(#1,#0)|divide(n2,#2)|
|
"explanation : amount of work x can do in 1 day = 1 / 8 amount of work y can do in 1 day = 1 / 12 amount of work x and y can do in 1 day = 1 / 8 + 1 / 12 = 5 / 24 amount of work x and y can together do in 3 days = 3 Γ ( 5 / 24 ) = 5 / 8 fraction of work left = 1 β 5 / 8 = 3 / 5 answer : option d"
|
physics
|
math_qa__MDJaS2F4eAOScH2Q
|
An article is bought for Rs.1450 and sold for Rs.1420, find the loss percent? Choose the correct choice from the following: A) 2 % B) 4 % C) 6 % D) 8 % E) 12 %
|
<gadget id="calculator">1_420 * 100</gadget>
<output>142_000</output>
<gadget id="calculator">142_000 / 1_450</gadget>
<output>2_840/29 = around 97.931034</output>
<gadget id="calculator">100 - (2_840/29)</gadget>
<output>60/29 = around 2.068966</output>
<result>A</result>
|
A
| 2 |
An article is bought for Rs.1450 and sold for Rs.1420, find the loss percent?
|
{
"A": "2 %",
"B": "4 %",
"C": "6 %",
"D": "8 %",
"E": "12 %"
}
|
subtract(const_100, divide(multiply(1420, const_100), 1450))
|
multiply(n1,const_100)|divide(#0,n0)|subtract(const_100,#1)|
|
"1450 - - - - 30 100 - - - - ? = > 2 % answer : a"
|
gain
|
math_qa__eogxF2CIKqAiH9sF
|
If 36 men can do a piece of work in 15 hours, in how many hours will 15 men do it? Select
A) 22 B) 36 C) 60 D) 88 E) 72
|
<gadget id="calculator">36 * 15</gadget>
<output>540</output>
<gadget id="calculator">540 / 15</gadget>
<output>36</output>
<result>B</result>
|
B
| 36 |
If 36 men can do a piece of work in 15 hours, in how many hours will 15 men do it?
|
{
"A": "22",
"B": "36",
"C": "60",
"D": "88",
"E": "72"
}
|
divide(multiply(36, 15), 15)
|
multiply(n0,n1)|divide(#0,n2)|
|
"explanation : let the required no of hours be x . then less men , more hours ( indirect proportion ) \ inline \ fn _ jvn \ therefore 15 : 36 : : 15 : x \ inline \ fn _ jvn \ leftrightarrow ( 15 x x ) = ( 36 x 15 ) \ inline \ fn _ jvn \ leftrightarrow \ inline \ fn _ jvn x = \ frac { 36 \ times 15 } { 15 } = 36 hence , 15 men can do it in 36 hours . answer : b ) 36"
|
physics
|
math_qa__aPJpBwr1eTqTPklU
|
Dawson is going with 14 friends on a trip to Washington D.C for spring break. Airfare and hotel costs a total of $13500.00 for the group of 15 friends. How much does each person have to pay for their hotel and airfare?
Choose one:
A) $ 900
B) $ 800
C) $ 850
D) $ 950
E) $ 920
|
<gadget id="calculator">13_500 / 15</gadget>
<output>900</output>
<result>A</result>
|
A
| 900 |
Dawson is going with 14 friends on a trip to Washington D.C for spring break. Airfare and hotel costs a total of $13500.00 for the group of 15 friends. How much does each person have to pay for their hotel and airfare?
|
{
"A": "$ 900",
"B": "$ 800",
"C": "$ 850",
"D": "$ 950",
"E": "$ 920"
}
|
divide(13500, 15)
|
divide(n1,n2)
|
answer = a the total cost of the trip ( $ 13500.00 ) divided by 15 equals $ 900.00 .
|
general
|
math_qa__A9bTGNyBQmfyiGQE
|
The batting average of a particular batsman is 60 runs in 46 innings. If the difference in his highest and lowest score is 190 runs and his average excluding these two innings is 58 runs, find his highest score. Pick:
A) 179
B) 367
C) 269
D) 177
E) 199
|
<gadget id="calculator">60 * 46</gadget>
<output>2_760</output>
<gadget id="calculator">46 - 2</gadget>
<output>44</output>
<gadget id="calculator">58 * 44</gadget>
<output>2_552</output>
<gadget id="calculator">2_760 - 2_552</gadget>
<output>208</output>
<gadget id="calculator">190 + 208</gadget>
<output>398</output>
<gadget id="calculator">398 / 2</gadget>
<output>199</output>
<result>E</result>
|
E
| 199 |
The batting average of a particular batsman is 60 runs in 46 innings. If the difference in his highest and lowest score is 190 runs and his average excluding these two innings is 58 runs, find his highest score.
|
{
"A": "179",
"B": "367",
"C": "269",
"D": "177",
"E": "199"
}
|
divide(add(190, subtract(multiply(60, 46), multiply(58, subtract(46, const_2)))), const_2)
|
multiply(n0,n1)|subtract(n1,const_2)|multiply(n3,#1)|subtract(#0,#2)|add(n2,#3)|divide(#4,const_2)|
|
"explanation : total runs scored by the batsman = 60 * 46 = 2760 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2760 Γ’ β¬ β 2552 = 208 runs . let the highest score be x , hence the lowest score = x Γ’ β¬ β 190 x + ( x - 190 ) = 208 2 x = 398 x = 199 runs answer : e"
|
general
|
math_qa__0AKAr5SSX7eKP1gc
|
The point A and point B is 30 miles apart, the point B and point C is 25 miles apart. A car travels from point A to point B in 30 min and point B to point C in 40 min. What is the average speed of the car? Pick one:
A) 34.15 B) 40.35 C) 47.14 D) 50.12 E) 56.66
|
<gadget id="calculator">30 / 30</gadget>
<output>1</output>
<gadget id="calculator">25 / 40</gadget>
<output>5/8 = around 0.625</output>
<gadget id="calculator">1 + (5/8)</gadget>
<output>13/8 = around 1.625</output>
<gadget id="calculator">(13/8) / 2</gadget>
<output>13/16 = around 0.8125</output>
<gadget id="calculator">(13/16) * 60</gadget>
<output>195/4 = around 48.75</output>
<result>C</result>
|
C
| 47.14 |
The point A and point B is 30 miles apart, the point B and point C is 25 miles apart. A car travels from point A to point B in 30 min and point B to point C in 40 min. What is the average speed of the car?
|
{
"A": "34.15",
"B": "40.35",
"C": "47.14",
"D": "50.12",
"E": "56.66"
}
|
multiply(divide(add(divide(30, 30), divide(25, 40)), const_2), const_60)
|
divide(n0,n0)|divide(n1,n3)|add(#0,#1)|divide(#2,const_2)|multiply(#3,const_60)
|
average speed = total distance covered / total time taken = 55 miles / 70 min = 0.79 miles / min = 47.14 miles / hour answer : c
|
physics
|
math_qa__Shx7OjPCBBkUwFSV
|
at the moment there are 54210 tagged birds in a certain wildlife refuge . if exactly 30 percent of all birds in the refuge are tagged , what percent of the untagged birds must be tagged so that half of all birds in the refuge are tagged ? Choose the correct choice from the following answers: A) 66.67 B) 66 C) 67 D) 65.99 E) 67.26
|
<gadget id="calculator">100 - 30</gadget>
<output>70</output>
<result>A</result>
|
A
| 66.67 |
at the moment there are 54210 tagged birds in a certain wildlife refuge . if exactly 30 percent of all birds in the refuge are tagged , what percent of the untagged birds must be tagged so that half of all birds in the refuge are tagged ?
|
{
"A": "66.67",
"B": "66",
"C": "67",
"D": "65.99",
"E": "67.26"
}
|
subtract(const_100, 30)
|
subtract(const_100,n1)
|
all birds = 54210 currently tagged = 54210 * 30 / 100 = 16263 so untagged birds = 54210 - 16263 = 37947 half of all birds = 27105 the number of birds to be tagged to make half of all birds tagged = 27105 - 16263 = 10842 so now the question remains - 10842 is how much percentage of untagged birds ( 16263 ) = 10842 * 100 / 16263 = 66.67 answer ( a )
|
gain
|
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