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__QByjrc0EaxNZof9t
|
At the end of year X, automobile installment credit accounted for 20% of all outstanding consumer installment credit. At that time automobile finance companies extended $57 billion of credit, or 1/3 of the automobile installment credit. How many billion dollars of consumer installment credit was outstanding at that time? Choices
A) 171 B) 855 C) 870 D) 788 E) 684
|
<gadget id="calculator">57 * 3</gadget>
<output>171</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">171 / (1/5)</gadget>
<output>855</output>
<result>B</result>
|
B
| 855 |
At the end of year X, automobile installment credit accounted for 20% of all outstanding consumer installment credit. At that time automobile finance companies extended $57 billion of credit, or 1/3 of the automobile installment credit. How many billion dollars of consumer installment credit was outstanding at that time?
|
{
"A": "171",
"B": "855",
"C": "870",
"D": "788",
"E": "684"
}
|
divide(multiply(57, 3), divide(20, const_100))
|
divide(n0,const_100)|multiply(n1,n3)|divide(#1,#0)|
|
"system of equations a = ( 20 / 100 ) c ( 1 / 3 ) a = 57 - - > a = 171 substitution 171 = ( 20100 ) c c = ( 100 / 20 ) 171 - calculate 171 / 20 * 100 the correct answer b . the answer is 855 ."
|
general
|
math_qa__kFAFnpOr8WdQEvC2
|
A man can row upstream at 32 kmph and downstream at 48 kmph, and then find the speed of the man in still water? Choose the correct choice from the following: A) 22 B) 37 C) 30 D) 27 E) 40
|
<gadget id="calculator">32 + 48</gadget>
<output>80</output>
<gadget id="calculator">80 / 2</gadget>
<output>40</output>
<result>E</result>
|
E
| 40 |
A man can row upstream at 32 kmph and downstream at 48 kmph, and then find the speed of the man in still water?
|
{
"A": "22",
"B": "37",
"C": "30",
"D": "27",
"E": "40"
}
|
divide(add(32, 48), const_2)
|
add(n0,n1)|divide(#0,const_2)|
|
"us = 32 ds = 48 m = ( 48 + 32 ) / 2 = 40 answer : e"
|
physics
|
math_qa__qmf9yPGHhrijHr4U
|
The radius of the two circular fields is in the ratio 3: 10 the area of the first field is what percent less than the area of the second? Choose the correct choice: A) 71 % B) 51 % C) 91 % D) 81 % E) 61 %
|
<gadget id="calculator">10 ** 2</gadget>
<output>100</output>
<gadget id="calculator">3 ** 2</gadget>
<output>9</output>
<gadget id="calculator">100 - 9</gadget>
<output>91</output>
<result>C</result>
|
C
| 91 |
The radius of the two circular fields is in the ratio 3: 10 the area of the first field is what percent less than the area of the second?
|
{
"A": "71 %",
"B": "51 %",
"C": "91 %",
"D": "81 %",
"E": "61 %"
}
|
subtract(power(10, const_2), power(3, const_2))
|
power(n1,const_2)|power(n0,const_2)|subtract(#0,#1)|
|
"r = 3 ï € r 2 = 9 r = 10 ï € r 2 = 100 100 ï € â € “ 9 ï € = 91 100 - - - - ? = > 91 % . answer : c"
|
geometry
|
math_qa__ICgsvNx4TR8L9yGc
|
3 buffaloes eat as much as 4 cows or 2 oxen. At a farm, there are 15 buffaloes, 8 oxen, and 24 cows. The fodder for these cattle is available for 24 days. If 60 more cows and 30 more buffaloes are brought in, how many days will the fodder last? Options:
A) 6
B) 9
C) 12
D) 15
E) 18
|
<gadget id="calculator">24 / 4</gadget>
<output>6</output>
<gadget id="calculator">6 * 3</gadget>
<output>18</output>
<gadget id="calculator">15 + 18</gadget>
<output>33</output>
<gadget id="calculator">8 / 2</gadget>
<output>4</output>
<gadget id="calculator">4 * 3</gadget>
<output>12</output>
<gadget id="calculator">33 + 12</gadget>
<output>45</output>
<gadget id="calculator">24 * 45</gadget>
<output>1_080</output>
<gadget id="calculator">15 + 30</gadget>
<output>45</output>
<gadget id="calculator">24 + 60</gadget>
<output>84</output>
<gadget id="calculator">84 / 4</gadget>
<output>21</output>
<gadget id="calculator">21 * 3</gadget>
<output>63</output>
<gadget id="calculator">45 + 63</gadget>
<output>108</output>
<gadget id="calculator">108 + 12</gadget>
<output>120</output>
<gadget id="calculator">1_080 / 120</gadget>
<output>9</output>
<result>B</result>
|
B
| 9 |
3 buffaloes eat as much as 4 cows or 2 oxen. At a farm, there are 15 buffaloes, 8 oxen, and 24 cows. The fodder for these cattle is available for 24 days. If 60 more cows and 30 more buffaloes are brought in, how many days will the fodder last?
|
{
"A": "6",
"B": "9",
"C": "12",
"D": "15",
"E": "18"
}
|
divide(multiply(24, add(add(15, multiply(divide(24, 4), 3)), multiply(divide(8, 2), 3))), add(add(add(15, 30), multiply(divide(add(24, 60), 4), 3)), multiply(divide(8, 2), 3)))
|
add(n3,n8)|add(n5,n7)|divide(n5,n1)|divide(n4,n2)|divide(#1,n1)|multiply(n0,#2)|multiply(n0,#3)|add(n3,#5)|multiply(n0,#4)|add(#7,#6)|add(#0,#8)|add(#10,#6)|multiply(n6,#9)|divide(#12,#11)|
|
"2 oxen = 3 buffaloes = 4 cows also : 15 buffaloes + 8 oxen + 24 cows = 10 oxen + 8 oxen + 12 oxen = 30 oxen there is enough fodder for 1 oxen for 30 * 24 days . 60 cows + 30 buffaloes = 30 oxen + 20 oxen = 50 oxen the new total is equal to 80 oxen instead of 30 oxen . 30 * 24 / 80 oxen = 9 days the answer is b ."
|
general
|
math_qa__wnKeWmn95zzpoZdp
|
An woman swims downstream 64 km and upstream 24 km taking 8 hours each time; what is the speed of the current?
Choose one.
A) 1.6 B) 1.8 C) 3.5 D) 1.5 E) 2.5
|
<gadget id="calculator">64 / 8</gadget>
<output>8</output>
<gadget id="calculator">24 / 8</gadget>
<output>3</output>
<gadget id="calculator">8 - 3</gadget>
<output>5</output>
<gadget id="calculator">5 / 2</gadget>
<output>5/2 = around 2.5</output>
<result>E</result>
|
E
| 2.5 |
An woman swims downstream 64 km and upstream 24 km taking 8 hours each time; what is the speed of the current?
|
{
"A": "1.6",
"B": "1.8",
"C": "3.5",
"D": "1.5",
"E": "2.5"
}
|
divide(subtract(divide(64, 8), divide(24, 8)), const_2)
|
divide(n0,n2)|divide(n1,n2)|subtract(#0,#1)|divide(#2,const_2)|
|
"64 - - - 8 ds = 8 ? - - - - 1 24 - - - - 8 us = 3 ? - - - - 1 s = ? s = ( 8 - 3 ) / 2 = 2.5 answer : e"
|
physics
|
math_qa__pYl0VvYhT1DeLRm3
|
The average age of students of a class is 15.8 years. The average age of boys in the class is 16.4 years and that of the girls is 15.3 years, The ratio of the number of boys to the number of girls in the class is
Select the correct option
A) 7 : 3 B) 2 : 3 C) 9 : 3 D) 6 : 3 E) 5 : 6
|
<gadget id="calculator">15.8 - 15.3</gadget>
<output>0.5</output>
<gadget id="calculator">16.4 - 15.8</gadget>
<output>0.6</output>
<gadget id="calculator">0.5 / 0.6</gadget>
<output>0.833333</output>
<result>E</result>
|
E
| 0.833333 |
The average age of students of a class is 15.8 years. The average age of boys in the class is 16.4 years and that of the girls is 15.3 years, The ratio of the number of boys to the number of girls in the class is
|
{
"A": "7 : 3",
"B": "2 : 3",
"C": "9 : 3",
"D": "6 : 3",
"E": "5 : 6"
}
|
divide(subtract(15.8, 15.3), subtract(16.4, 15.8))
|
subtract(n0,n2)|subtract(n1,n0)|divide(#0,#1)|
|
"explanation : let the ratio be k : 1 . then , k * 16.4 + 1 * 15.3 = ( k + 1 ) * 15.8 < = > ( 16.4 - 15.8 ) k = ( 15.8 - 15.3 ) < = > k = 0.5 / 0.6 = 5 / 6 . required ratio = 5 / 6 : 1 = 5 : 6 . answer : e"
|
general
|
math_qa__11uOE7pkzdRWiNLN
|
A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. What is the speed of the car? Pick one:
A) 22
B) 28
C) 120
D) 287
E) 278
|
<gadget id="calculator">12.5 * 2</gadget>
<output>25</output>
<gadget id="calculator">25 - 1</gadget>
<output>24</output>
<gadget id="calculator">24 * 25</gadget>
<output>600</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">600 / 5</gadget>
<output>120</output>
<result>C</result>
|
C
| 120 |
A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. What is the speed of the car?
|
{
"A": "22",
"B": "28",
"C": "120",
"D": "287",
"E": "278"
}
|
divide(multiply(subtract(multiply(12.5, const_2), const_1), multiply(12.5, const_2)), add(const_4, const_1))
|
add(const_1,const_4)|multiply(n2,const_2)|subtract(#1,const_1)|multiply(#1,#2)|divide(#3,#0)
|
let speed of the car = x kmphthen speed of the train = ( 100 + 50 ) 100 x = 150100 x = 32 x kmphtime taken by the car to travel from a to b = 75 x hourstime taken by the train to travel from a to b = 75 ( 32 x ) + 12.560 hourssince both start from a at the same time and reach point b at the same time 75 x = 75 ( 32 x ) + 12.56025 x = 12.560 x = 25 × 6012.5 = 2 × 60 = 120 answer : c
|
physics
|
math_qa__aPxWoF2MRYwtwM9D
|
If the sides of a triangle are 39 cm, 32 cm and 10 cm, what is its area?
Choose one
A) 120 B) 772 C) 288 D) 160 E) 2848
|
<gadget id="calculator">32 * 10</gadget>
<output>320</output>
<gadget id="calculator">320 / 2</gadget>
<output>160</output>
<result>D</result>
|
D
| 160 |
If the sides of a triangle are 39 cm, 32 cm and 10 cm, what is its area?
|
{
"A": "120",
"B": "772",
"C": "288",
"D": "160",
"E": "2848"
}
|
divide(multiply(32, 10), const_2)
|
multiply(n1,n2)|divide(#0,const_2)|
|
"the triangle with sides 39 cm , 32 cm and 10 cm is right angled , where the hypotenuse is 39 cm . area of the triangle = 1 / 2 * 32 * 10 = 160 cm 2 answer : d"
|
geometry
|
math_qa__t35ej0lWlu8yqea5
|
A car gets 20 kilometers per gallon of gasoline. How many gallons of gasoline would the car need to travel 120 kilometers? Choose the correct choice from the following options:
A) 8.5 gallons
B) 5 gallons
C) 7 gallons
D) 5.5 gallons
E) 6 gallons
|
<gadget id="calculator">120 / 20</gadget>
<output>6</output>
<result>E</result>
|
E
| 6 |
A car gets 20 kilometers per gallon of gasoline. How many gallons of gasoline would the car need to travel 120 kilometers?
|
{
"A": "8.5 gallons",
"B": "5 gallons",
"C": "7 gallons",
"D": "5.5 gallons",
"E": "6 gallons"
}
|
divide(120, 20)
|
divide(n1,n0)|
|
"each 20 kilometers , 1 gallon is needed . we need to know how many 20 kilometers are there in 120 kilometers ? 120 / 20 = 4.5 * 1 gallon = 6 gallons correct answer e"
|
physics
|
math_qa__VgKspb9QPbyFQAMq
|
A cuboidal block 6cm x 9cm x 12cm is cut up into an exact number of equal cubes.The least possible number of equal cubes will be
Pick.
A) 6 B) 9 C) 24 D) 30 E) 35
|
<gadget id="calculator">6 * 9</gadget>
<output>54</output>
<gadget id="calculator">54 * 12</gadget>
<output>648</output>
<gadget id="calculator">6 / 2</gadget>
<output>3</output>
<gadget id="calculator">3 * 3</gadget>
<output>9</output>
<gadget id="calculator">9 * 3</gadget>
<output>27</output>
<gadget id="calculator">648 / 27</gadget>
<output>24</output>
<result>C</result>
|
C
| 24 |
A cuboidal block 6cm x 9cm x 12cm is cut up into an exact number of equal cubes.The least possible number of equal cubes will be
|
{
"A": "6",
"B": "9",
"C": "24",
"D": "30",
"E": "35"
}
|
divide(multiply(multiply(6, 9), 12), multiply(multiply(divide(6, const_2), divide(6, const_2)), divide(6, const_2)))
|
divide(n0,const_2)|multiply(n0,n1)|multiply(n2,#1)|multiply(#0,#0)|multiply(#0,#3)|divide(#2,#4)
|
explanation : volume of block = ( 6 x 9 x 12 ) cm 3 = 648 cm 3 side of largest cube = h . c . f of 6 , 912 = 3 cm volume of the cube = ( 3 x 3 x 3 ) = 27 cm 3 number of cubes = ( 648 / 27 ) = 24 answer : c
|
general
|
math_qa__06cQCtXeBFdIYqc9
|
In a class of 25 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 4 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed? Choose the correct answer.
A) 8 B) 9 C) 10 D) 11 E) 12
|
<gadget id="calculator">25 * 2</gadget>
<output>50</output>
<gadget id="calculator">12 * 1</gadget>
<output>12</output>
<gadget id="calculator">12 + 4</gadget>
<output>16</output>
<gadget id="calculator">16 + 2</gadget>
<output>18</output>
<gadget id="calculator">25 - 18</gadget>
<output>7</output>
<gadget id="calculator">7 - 1</gadget>
<output>6</output>
<gadget id="calculator">6 * 3</gadget>
<output>18</output>
<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">12 + 8</gadget>
<output>20</output>
<gadget id="calculator">18 + 20</gadget>
<output>38</output>
<gadget id="calculator">50 - 38</gadget>
<output>12</output>
<result>E</result>
|
E
| 12 |
In a class of 25 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 4 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed?
|
{
"A": "8",
"B": "9",
"C": "10",
"D": "11",
"E": "12"
}
|
subtract(multiply(25, 2), add(multiply(subtract(subtract(25, add(add(multiply(12, 1), 4), 2)), 1), 3), add(multiply(12, 1), multiply(4, 2))))
|
multiply(n0,n1)|multiply(n2,n3)|multiply(n1,n4)|add(#1,#2)|add(n4,#1)|add(n1,#4)|subtract(n0,#5)|subtract(#6,n3)|multiply(n6,#7)|add(#3,#8)|subtract(#0,#9)|
|
"the total number of books the students borrowed is 25 * 2 = 50 . the students who borrowed zero , one , or two books borrowed 12 * 1 + 4 * 2 = 20 books . the 7 students who borrowed at least three books borrowed 50 - 20 = 30 books . if 6 of these students borrowed exactly 3 books , then the maximum that one student could have borrowed is 30 - 18 = 12 books . the answer is e ."
|
general
|
math_qa__siuOKKcPTAuzDdUK
|
Beginning in Town A, Biker Bob rides his bike 30 miles west, 6 miles north, 15 miles east, and then 18 miles north, to Town B. How far apart are Town A and Town B? (Ignore the curvature of the earth.)
Choose the correct option
A) 27 miles B) 25 miles C) 24 miles D) 28.3 miles E) 23 miles
|
<gadget id="calculator">6 + 18</gadget>
<output>24</output>
<gadget id="calculator">24 ** 2</gadget>
<output>576</output>
<gadget id="calculator">15 ** 2</gadget>
<output>225</output>
<gadget id="calculator">576 + 225</gadget>
<output>801</output>
<gadget id="calculator">801 ** (1/2)</gadget>
<output>3*sqrt(89) = around 28.301943</output>
<result>D</result>
|
D
| 28.3 |
Beginning in Town A, Biker Bob rides his bike 30 miles west, 6 miles north, 15 miles east, and then 18 miles north, to Town B. How far apart are Town A and Town B? (Ignore the curvature of the earth.)
|
{
"A": "27 miles",
"B": "25 miles",
"C": "24 miles",
"D": "28.3 miles",
"E": "23 miles"
}
|
sqrt(add(power(add(6, 18), const_2), power(15, const_2)))
|
add(n1,n3)|power(n2,const_2)|power(#0,const_2)|add(#2,#1)|sqrt(#3)|
|
"using pythagoras we have one side i , e total distance traveled in north direction = 18 + 6 = 24 m other being the base ie distance traveled west - distance traveled eat = 30 - 15 = 15 m now this third side or the distance between town a and town b = 24 ^ 2 + 15 ^ 2 = sq root 801 = 28.3 m answer : d"
|
physics
|
math_qa__KJ6acxpZzBAH3Nuw
|
A bowl of nuts is prepared for a party. Brand P mixed nuts are 20% almonds and Brand Q's Deluxe nuts are 25% almonds. If a bowl contains a total of 68 ounces of nuts, representing a mixture of both brands, and 15 ounces of the mixture are almonds, how many ounces of Brand Q's Deluxe mixed nuts are used? Choose the correct answer:
A) 16 B) 28 C) 32 D) 44 E) 48
|
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 68</gadget>
<output>68/5 = around 13.6</output>
<gadget id="calculator">15 - (68/5)</gadget>
<output>7/5 = around 1.4</output>
<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) - (1/5)</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(7/5) / (1/20)</gadget>
<output>28</output>
<result>B</result>
|
B
| 28 |
A bowl of nuts is prepared for a party. Brand P mixed nuts are 20% almonds and Brand Q's Deluxe nuts are 25% almonds. If a bowl contains a total of 68 ounces of nuts, representing a mixture of both brands, and 15 ounces of the mixture are almonds, how many ounces of Brand Q's Deluxe mixed nuts are used?
|
{
"A": "16",
"B": "28",
"C": "32",
"D": "44",
"E": "48"
}
|
divide(subtract(15, multiply(divide(20, const_100), 68)), subtract(divide(25, const_100), divide(20, const_100)))
|
divide(n0,const_100)|divide(n1,const_100)|multiply(n2,#0)|subtract(#1,#0)|subtract(n3,#2)|divide(#4,#3)|
|
"lets say x ounces of p is mixed with q . = > 68 - x ounces of q is present in the mixture ( as the total = 68 ounces ) given total almond weight = 15 ounces ( 20 x / 100 ) + ( 25 / 100 ) ( 68 - x ) = 15 = > x = 40 = > 68 - 40 = 28 ounces of q is present in the mixture . answer is b ."
|
general
|
math_qa__g65J4AtlCH8qJsdf
|
Two trains 200m and 300m long run at the speed of 70kmph and 50kmph in opposite directions in parallel tracks. The time which they take to cross each other is?
Choose one.
A) 10 sec B) 15 sec C) 18 sec D) 20 sec E) 22 sec
|
<gadget id="calculator">200 + 300</gadget>
<output>500</output>
<gadget id="calculator">70 + 50</gadget>
<output>120</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">120 * (5/18)</gadget>
<output>100/3 = around 33.333333</output>
<gadget id="calculator">500 / (100/3)</gadget>
<output>15</output>
<result>B</result>
|
B
| 15 |
Two trains 200m and 300m long run at the speed of 70kmph and 50kmph in opposite directions in parallel tracks. The time which they take to cross each other is?
|
{
"A": "10 sec",
"B": "15 sec",
"C": "18 sec",
"D": "20 sec",
"E": "22 sec"
}
|
divide(add(200, 300), multiply(add(70, 50), const_0_2778))
|
add(n0,n1)|add(n2,n3)|multiply(#1,const_0_2778)|divide(#0,#2)|
|
"relative speed = 70 + 50 = 120 kmph * 5 / 18 = 100 / 3 m / s distance covered in crossing each other = 200 + 300 = 500 m required time = 500 * 3 / 100 = 15 sec answer is b"
|
physics
|
math_qa__thL0ssmmWrpyZK7I
|
Find the area of a parallelogram with base 12 cm and height 10 cm? Options:
A) 297 cm 2 B) 384 cm 2 C) 120 cm 2 D) 267 cm 2 E) 186 cm 2
|
<gadget id="calculator">12 * 10</gadget>
<output>120</output>
<result>C</result>
|
C
| 120 |
Find the area of a parallelogram with base 12 cm and height 10 cm?
|
{
"A": "297 cm 2",
"B": "384 cm 2",
"C": "120 cm 2",
"D": "267 cm 2",
"E": "186 cm 2"
}
|
multiply(12, 10)
|
multiply(n0,n1)|
|
"area of a parallelogram = base * height = 12 * 10 = 120 cm 2 answer : c"
|
geometry
|
math_qa__WnViWl3e2ZPUnh8W
|
6 lights begin to flash together at 12 : 00 noon and flash respectively at intervals of 3 , 4 , 5 , 6 , 7 , and 8 seconds . not including the flash at 12 : 00 noon , how many more times will all 6 lights flash together before 1 : 00 pm ( i . e . one hour later ) ? Pick
A) 4 B) 6 C) 8 D) 10 E) 12
|
<gadget id="calculator">1 * 3_600</gadget>
<output>3_600</output>
<gadget id="calculator">lcm(7, 8)</gadget>
<output>56</output>
<gadget id="calculator">lcm(3, 4)</gadget>
<output>12</output>
<gadget id="calculator">lcm(5, 6)</gadget>
<output>30</output>
<gadget id="calculator">lcm(12, 30)</gadget>
<output>60</output>
<gadget id="calculator">lcm(56, 60)</gadget>
<output>840</output>
<gadget id="calculator">3_600 / 840</gadget>
<output>30/7 = around 4.285714</output>
<gadget id="calculator">floor(30/7)</gadget>
<output>4</output>
<result>A</result>
|
A
| 4 |
6 lights begin to flash together at 12 : 00 noon and flash respectively at intervals of 3 , 4 , 5 , 6 , 7 , and 8 seconds . not including the flash at 12 : 00 noon , how many more times will all 6 lights flash together before 1 : 00 pm ( i . e . one hour later ) ?
|
{
"A": "4",
"B": "6",
"C": "8",
"D": "10",
"E": "12"
}
|
floor(divide(multiply(const_1, const_3600), lcm(lcm(7, 8), lcm(lcm(3, 4), lcm(5, 6)))))
|
lcm(n7,n8)|lcm(n3,n4)|lcm(n0,n5)|multiply(const_1,const_3600)|lcm(#1,#2)|lcm(#0,#4)|divide(#3,#5)|floor(#6)
|
the least common multiple is 2 * 2 * 2 * 3 * 5 * 7 = 840 . 3600 seconds / 840 = 4 + remainder . the answer is a .
|
physics
|
math_qa__hUFXjFGR2DxOJAQz
|
a is the hundreds digit of the 3 digit integer x , b is the tens digit of x , and c is the units digit of x . 2 a = b = 4 c , and a > 0 . what is the difference between the two greatest possible values of x ? tip : dont stop till you have exhausted all answer choices to arrive at the correct one .
Choices
A) 124
B) 241
C) 394
D) 421
E) 842
|
<gadget id="calculator">4 * 1</gadget>
<output>4</output>
<gadget id="calculator">4 * 100</gadget>
<output>400</output>
<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">8 * 10</gadget>
<output>80</output>
<gadget id="calculator">400 + 80</gadget>
<output>480</output>
<gadget id="calculator">4 / 2</gadget>
<output>2</output>
<gadget id="calculator">480 + 2</gadget>
<output>482</output>
<gadget id="calculator">2 * 100</gadget>
<output>200</output>
<gadget id="calculator">4 * 10</gadget>
<output>40</output>
<gadget id="calculator">200 + 40</gadget>
<output>240</output>
<gadget id="calculator">240 + 1</gadget>
<output>241</output>
<gadget id="calculator">482 - 241</gadget>
<output>241</output>
<result>B</result>
|
B
| 241 |
a is the hundreds digit of the 3 digit integer x , b is the tens digit of x , and c is the units digit of x . 2 a = b = 4 c , and a > 0 . what is the difference between the two greatest possible values of x ? tip : dont stop till you have exhausted all answer choices to arrive at the correct one .
|
{
"A": "124",
"B": "241",
"C": "394",
"D": "421",
"E": "842"
}
|
subtract(add(add(multiply(multiply(4, const_1), const_100), multiply(multiply(4, 2), const_10)), divide(multiply(4, const_1), 2)), add(add(multiply(divide(multiply(4, const_1), 2), const_100), multiply(multiply(4, const_1), const_10)), const_1))
|
multiply(n2,const_1)|multiply(n1,n2)|divide(#0,n1)|multiply(#0,const_100)|multiply(#1,const_10)|multiply(#0,const_10)|add(#3,#4)|multiply(#2,const_100)|add(#6,#2)|add(#7,#5)|add(#9,const_1)|subtract(#8,#10)
|
ratio of a : b : c = 2 : 4 : 1 two possible greatest single digit values for b are 8 and 4 if b is 8 , then x = 482 if b is 4 , then x = 241 difference = 482 - 241 = 241 b is the answer
|
general
|
math_qa__5VYeF89GhtundD2T
|
A number with an interesting property:
When I divide it by 2, the remainder is 1.
When I divide it by 3, the remainder is 2.
When I divide it by 4, the remainder is 3.
When I divide it by 5, the remainder is 4.
When I divide it by 6, the remainder is 5.
When I divide it by 7, the remainder is 6.
When I divide it by 8, the remainder is 7.
When I divide it by 9, the remainder is 8.
When I divide it by 10, the remainder is 9.
It's not a small number, but it's not really big, either.
When I looked for a smaller number with this property I couldn't find one.
Can you find it? Choose the correct choice
A) 2588
B) 2474
C) 2254
D) 2519
E) 8725
|
<gadget id="calculator">lcm(9, 10)</gadget>
<output>90</output>
<gadget id="calculator">lcm(90, 7)</gadget>
<output>630</output>
<gadget id="calculator">630 * 2</gadget>
<output>1_260</output>
<gadget id="calculator">1_260 * 2</gadget>
<output>2_520</output>
<gadget id="calculator">2_520 - 1</gadget>
<output>2_519</output>
<result>D</result>
|
D
| 2,519 |
A number with an interesting property:
When I divide it by 2, the remainder is 1.
When I divide it by 3, the remainder is 2.
When I divide it by 4, the remainder is 3.
When I divide it by 5, the remainder is 4.
When I divide it by 6, the remainder is 5.
When I divide it by 7, the remainder is 6.
When I divide it by 8, the remainder is 7.
When I divide it by 9, the remainder is 8.
When I divide it by 10, the remainder is 9.
It's not a small number, but it's not really big, either.
When I looked for a smaller number with this property I couldn't find one.
Can you find it?
|
{
"A": "2588",
"B": "2474",
"C": "2254",
"D": "2519",
"E": "8725"
}
|
subtract(multiply(multiply(lcm(lcm(9, 10), 7), 2), 2), const_1)
|
lcm(n14,n16)|lcm(n10,#0)|multiply(n0,#1)|multiply(n0,#2)|subtract(#3,const_1)
|
d 2519 the number has to end in 9 . looked brute force for small numbers . 59 and 119 were promising , but no cigar . then looked for agreement among 39 + multiples of 40 , 69 + multiples of 70 and 89 + multiples of 90 smallest one was 2519 .
|
gain
|
math_qa__Kj5ObaQ5eGAICU0L
|
65% of a number is 21 less than 4/5th of that number. What is the number?
Select the correct option:
A) 100 B) 120 C) 140 D) 130 E) 115
|
<gadget id="calculator">21 * 5</gadget>
<output>105</output>
<gadget id="calculator">100 / 5</gadget>
<output>20</output>
<gadget id="calculator">105 * 20</gadget>
<output>2_100</output>
<gadget id="calculator">20 * 4</gadget>
<output>80</output>
<gadget id="calculator">80 - 65</gadget>
<output>15</output>
<gadget id="calculator">2_100 / 15</gadget>
<output>140</output>
<result>C</result>
|
C
| 140 |
65% of a number is 21 less than 4/5th of that number. What is the number?
|
{
"A": "100",
"B": "120",
"C": "140",
"D": "130",
"E": "115"
}
|
divide(multiply(multiply(21, 5), divide(const_100, 5)), subtract(multiply(divide(const_100, 5), 4), 65))
|
divide(const_100,n3)|multiply(n1,n3)|multiply(#0,#1)|multiply(n2,#0)|subtract(#3,n0)|divide(#2,#4)
|
let the number be x then , 4 x / 5 - ( 65 % of x ) = 21 4 x / 5 - 65 x / 100 = 21 x = 140 answer is c
|
general
|
math_qa__uX9zJrysObKZ3cUP
|
A vendor sells 60 percent of the apples he had and throws away 40 percent of the remainder. The next day, the vendor sells 50 percent of the remaining apples and throws away the rest. In total, what percent of his apples does the vendor throw away?
Choose the correct choice from the following answers:
A) 24 B) 26 C) 28 D) 30 E) 32
|
<gadget id="calculator">100 - 60</gadget>
<output>40</output>
<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) * 40</gadget>
<output>16</output>
<gadget id="calculator">40 - 16</gadget>
<output>24</output>
<gadget id="calculator">24 / 2</gadget>
<output>12</output>
<gadget id="calculator">12 + 16</gadget>
<output>28</output>
<result>C</result>
|
C
| 28 |
A vendor sells 60 percent of the apples he had and throws away 40 percent of the remainder. The next day, the vendor sells 50 percent of the remaining apples and throws away the rest. In total, what percent of his apples does the vendor throw away?
|
{
"A": "24",
"B": "26",
"C": "28",
"D": "30",
"E": "32"
}
|
add(divide(subtract(subtract(const_100, 60), multiply(divide(40, const_100), subtract(const_100, 60))), const_2), multiply(divide(40, const_100), subtract(const_100, 60)))
|
divide(n1,const_100)|subtract(const_100,n0)|multiply(#0,#1)|subtract(#1,#2)|divide(#3,const_2)|add(#4,#2)|
|
"let x be the original number of apples . on day one , the vendor throws away ( 0.4 ) ( 0.4 ) x = 0.16 x . the remaining apples are ( 0.6 ) ( 0.4 ) x = 0.24 x . on day two , the vendor throws away ( 0.5 ) ( 0.24 ) x = 0.12 x . the vendor throws away a total of 0.16 x + 0.12 x = 0.28 x . the vendor throws away 28 percent of the apples . the answer is c ."
|
general
|
math_qa__FBgJggNOHHexBHLL
|
A vendor sells 80 percent of the pears he had and throws away 50 percent of the remainder. The next day, the vendor sells 80 percent of the remaining pears and throws away the rest. In total, what percent of his pears does the vendor throw away? Choose the correct choice from the following answers:
A) 6 B) 8 C) 10 D) 12 E) 14
|
<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">1 - (4/5)</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) * (1/5)</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/5) - (1/10)</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/10) * (4/5)</gadget>
<output>2/25 = around 0.08</output>
<gadget id="calculator">(1/10) - (2/25)</gadget>
<output>1/50 = around 0.02</output>
<gadget id="calculator">(1/50) + (1/10)</gadget>
<output>3/25 = around 0.12</output>
<gadget id="calculator">100 * (3/25)</gadget>
<output>12</output>
<result>D</result>
|
D
| 12 |
A vendor sells 80 percent of the pears he had and throws away 50 percent of the remainder. The next day, the vendor sells 80 percent of the remaining pears and throws away the rest. In total, what percent of his pears does the vendor throw away?
|
{
"A": "6",
"B": "8",
"C": "10",
"D": "12",
"E": "14"
}
|
multiply(const_100, add(subtract(subtract(subtract(const_1, divide(80, const_100)), multiply(divide(50, const_100), subtract(const_1, divide(80, const_100)))), multiply(subtract(subtract(const_1, divide(80, const_100)), multiply(divide(50, const_100), subtract(const_1, divide(80, const_100)))), divide(80, const_100))), multiply(divide(50, const_100), subtract(const_1, divide(80, const_100)))))
|
divide(n1,const_100)|divide(n0,const_100)|subtract(const_1,#1)|multiply(#0,#2)|subtract(#2,#3)|multiply(#1,#4)|subtract(#4,#5)|add(#3,#6)|multiply(#7,const_100)|
|
"let x be the original number of pears . on day one , the vendor throws away ( 0.5 ) ( 0.2 ) x = 0.1 x . the remaining pears are ( 0.5 ) ( 0.2 ) x = 0.1 x . on day two , the vendor throws away ( 0.2 ) ( 0.1 ) x = 0.02 x . the vendor throws away a total of 0.1 x + 0.02 x = 0.12 x . the vendor throws away 12 percent of the pears . the answer is d ."
|
general
|
math_qa__08XdjEa455Jfhm7r
|
A train 700 m long can cross an electric pole in 20 sec and then find the speed of the train? Options.
A) 117 kmph B) 178 kmph C) 126 kmph D) 118 kmph E) 119 kmph
|
<gadget id="calculator">700 / 1_000</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">20 / 3_600</gadget>
<output>1/180 = around 0.005556</output>
<gadget id="calculator">(7/10) / (1/180)</gadget>
<output>126</output>
<result>C</result>
|
C
| 126 |
A train 700 m long can cross an electric pole in 20 sec and then find the speed of the train?
|
{
"A": "117 kmph",
"B": "178 kmph",
"C": "126 kmph",
"D": "118 kmph",
"E": "119 kmph"
}
|
divide(divide(700, const_1000), divide(20, const_3600))
|
divide(n0,const_1000)|divide(n1,const_3600)|divide(#0,#1)|
|
"length = speed * time speed = l / t s = 700 / 20 s = 35 m / sec speed = 35 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 126 kmph answer : c"
|
physics
|
math_qa__njwoFAi0mbnmnpFp
|
The average weight of 8 persons increases by 3.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person ? Choose one:
A) 75 kg B) 65 kg C) 55 kg D) 85 kg E) 93 kg
|
<gadget id="calculator">8 * 3.5</gadget>
<output>28</output>
<gadget id="calculator">65 + 28</gadget>
<output>93</output>
<result>E</result>
|
E
| 93 |
The average weight of 8 persons increases by 3.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person ?
|
{
"A": "75 kg",
"B": "65 kg",
"C": "55 kg",
"D": "85 kg",
"E": "93 kg"
}
|
add(65, multiply(8, 3.5))
|
multiply(n0,n1)|add(n2,#0)|
|
"total weight increased = ( 8 x 3.5 ) kg = 28 kg . weight of new person = ( 65 + 28 ) kg = 93 kg . answer : e"
|
general
|
math_qa__RjjhBCyPfQqdHYq4
|
An industrial loom weaves 1.14 meters of cloth every second. Approximately, how much time will it take to weave 52 meters of cloth ? Select the correct option.
A) 29.32 sec B) 42.51 sec C) 39.25 sec D) 45.61 sec E) none of these
|
<gadget id="calculator">52 / 1.14</gadget>
<output>45.614035</output>
<result>D</result>
|
D
| 45.61 |
An industrial loom weaves 1.14 meters of cloth every second. Approximately, how much time will it take to weave 52 meters of cloth ?
|
{
"A": "29.32 sec",
"B": "42.51 sec",
"C": "39.25 sec",
"D": "45.61 sec",
"E": "none of these"
}
|
divide(52, 1.14)
|
divide(n1,n0)
|
explanation : given loom weaves 1.14 mts of cloth in one second then 52 mts of cloth can be weaved by loom in , 1.14 - - - - - 1 52.0 - - - - - - ? = > 52 / 1.14 = 45.61 sec answer is d
|
physics
|
math_qa__CLJcbIzR834R2ksn
|
If M:N is 2:9 and N:P is 9:4 then M:P is equal to Options:
A) 1 : 4 B) 1 : 3 C) 5 : 2 D) 3 : 2 E) 1 : 2
|
<gadget id="calculator">2 / 4</gadget>
<output>1/2 = around 0.5</output>
<result>E</result>
|
E
| 0.5 |
If M:N is 2:9 and N:P is 9:4 then M:P is equal to
|
{
"A": "1 : 4",
"B": "1 : 3",
"C": "5 : 2",
"D": "3 : 2",
"E": "1 : 2"
}
|
divide(2, 4)
|
divide(n0,n3)
|
the two ratios given are having the same number 9 for n in both the ratios . hence - m : n = 2 : 9 n : p = 9 : 4 = > m : p = 2 : 4 = > 1 : 2 answer e
|
physics
|
math_qa__LzXufKnNo3e1Zgy7
|
A certain taxi company charges $2.80 for the first 1/5 of a mile plus $0.40 for each additional 1/5 of a mile. What would this company charge for a taxi ride that was 8 miles long? Select the correct option:
A) 15.6 B) 16.0 C) 18.4 D) 18.7 E) 19.1
|
<gadget id="calculator">1 / 5</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">8 / (1/5)</gadget>
<output>40</output>
<gadget id="calculator">40 - 1</gadget>
<output>39</output>
<gadget id="calculator">39 * 0.4</gadget>
<output>15.6</output>
<gadget id="calculator">2.8 + 15.6</gadget>
<output>18.4</output>
<result>C</result>
|
C
| 18.4 |
A certain taxi company charges $2.80 for the first 1/5 of a mile plus $0.40 for each additional 1/5 of a mile. What would this company charge for a taxi ride that was 8 miles long?
|
{
"A": "15.6",
"B": "16.0",
"C": "18.4",
"D": "18.7",
"E": "19.1"
}
|
add(2.80, multiply(subtract(divide(8, divide(1, 5)), 1), 0.40))
|
divide(n1,n2)|divide(n6,#0)|subtract(#1,n1)|multiply(n3,#2)|add(n0,#3)|
|
"a certain taxi company charges $ 2.80 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ? a . 15.60 b . 16.00 c . 17.50 d . 18.70 e . 19.10 1 / 5 miles = 0.2 miles . the cost of 8 miles long ride would be $ 2.80 for the first 0.2 miles plus ( 8 - 0.2 ) / 0.2 * 0.4 = $ 2.8 + $ 15.6 = $ 18.4 . answer : c ."
|
general
|
math_qa__f4C4qvtwDdXwLwJP
|
of the 3 - digit integers greater than 200 , how many have two digits that are equal to each other and the remaining digit different from the other two ? Pick one: A) 90 B) 82 C) 80 D) 45 E) 36
|
<gadget id="calculator">200 / 2</gadget>
<output>100</output>
<gadget id="calculator">100 - 1</gadget>
<output>99</output>
<gadget id="calculator">99 / 3</gadget>
<output>33</output>
<gadget id="calculator">33 + 3</gadget>
<output>36</output>
<result>E</result>
|
E
| 36 |
of the 3 - digit integers greater than 200 , how many have two digits that are equal to each other and the remaining digit different from the other two ?
|
{
"A": "90",
"B": "82",
"C": "80",
"D": "45",
"E": "36"
}
|
add(divide(subtract(divide(200, const_2), const_1), 3), 3)
|
divide(n1,const_2)|subtract(#0,const_1)|divide(#1,n0)|add(n0,#2)
|
let the three digit number be represented as x y z . there are 3 cases : case i . [ x = y ] z is not equal to xy : xxzoryyz x can be either 7 , 8 or 9 , so digit at x can be chosen in 3 ways after x is chosen , y can be chosen in 1 way after xy are chosen , z can be chosen in 9 ways thus , possible no of digits = ( 3 ways ) * ( 1 way ) * ( 9 ways ) = 27 . . . . ( 1 ) [ example numbers : 774,779 , 882,993 etc ] case ii . [ x = z ] y is not equal to xz : xyxorzyz x can be either 7 , 8 or 9 , so digit at x can be chosen in 3 ways after x is chosen , z can be chosen in 1 way after xz are chosen , z can be chosen in 9 ways thus , possible no of digits = ( 3 ways ) * ( 9 ways ) * ( 1 way ) = 27 . . . . ( 2 ) [ example numbers : 747,797 , 828,939 etc ] case iii . [ y = z ] x is not equal to yz : xyyorxzz x can be either 7 , 8 or 9 , so digit at x can be chosen in 3 ways after x is chosen , y can be chosen in 9 ways after y is chosen , z can have 1 way thus , possible no of digits = ( 3 ways ) * ( 1 way ) * ( 9 ways ) = 27 . . . . ( 3 ) [ example numbers : 744,799 , 822,933 etc ] therefore , total numbers of possible digits [ sum of case ( 1 ) , ( 2 ) ( 3 ) above ] = 27 + 27 + 27 - 1 = 80 one digit is subtracted from total number of possible digits to eliminate one possibility of xyz = 700 to satisfy the condition that digit > 200 . answer : ( e )
|
general
|
math_qa__tvP86xTG1qq5hJMA
|
A rectangular mat has an area of 120 sq.metres and perimeter of 46 m. The length of its diagonal is: Choose one.
A) 19 m B) 17 m C) 15 m D) 16 m E) 20 m
|
<gadget id="calculator">46 / 2</gadget>
<output>23</output>
<gadget id="calculator">23 ** 2</gadget>
<output>529</output>
<gadget id="calculator">120 * 2</gadget>
<output>240</output>
<gadget id="calculator">529 - 240</gadget>
<output>289</output>
<gadget id="calculator">289 ** (1/2)</gadget>
<output>17</output>
<result>B</result>
|
B
| 17 |
A rectangular mat has an area of 120 sq.metres and perimeter of 46 m. The length of its diagonal is:
|
{
"A": "19 m",
"B": "17 m",
"C": "15 m",
"D": "16 m",
"E": "20 m"
}
|
sqrt(subtract(power(divide(46, const_2), const_2), multiply(120, const_2)))
|
divide(n1,const_2)|multiply(n0,const_2)|power(#0,const_2)|subtract(#2,#1)|sqrt(#3)
|
rectangular area = l × b = 120 and perimeter = 2 ( l + b ) = 46 l + b = 23 ( l - b ) power 2 - 4 lb = ( 23 ) power 2 - 4 × 120 = ( 529 - 480 ) = 49 = l - b = 7 l + b = 23 , l - b = 7 , we get l = 15 , b = 8 diagonal = √ 152 + 82 √ 225 + 64 = > √ 289 = 17 m answer is b .
|
geometry
|
math_qa__t6Ec6HCJqfzBSYKH
|
A farmer used 1,034 acres of land for beans, wheat, and corn in the ratio of 5 : 2 : 4, respectively. How many R acres were used for corn? Options: A) 188 B) 258 C) 376 D) 470 E) 517
|
<gadget id="calculator">1_000 * 1</gadget>
<output>1_000</output>
<gadget id="calculator">10 * 3</gadget>
<output>30</output>
<gadget id="calculator">30 + 4</gadget>
<output>34</output>
<gadget id="calculator">1_000 + 34</gadget>
<output>1_034</output>
<gadget id="calculator">5 + 2</gadget>
<output>7</output>
<gadget id="calculator">7 + 4</gadget>
<output>11</output>
<gadget id="calculator">1_034 / 11</gadget>
<output>94</output>
<gadget id="calculator">94 * 4</gadget>
<output>376</output>
<result>C</result>
|
C
| 376 |
A farmer used 1,034 acres of land for beans, wheat, and corn in the ratio of 5 : 2 : 4, respectively. How many R acres were used for corn?
|
{
"A": "188",
"B": "258",
"C": "376",
"D": "470",
"E": "517"
}
|
multiply(divide(add(multiply(const_1000, const_1), add(multiply(const_10, const_3), 4)), add(add(5, 2), 4)), 4)
|
add(n1,n2)|multiply(const_10,const_3)|multiply(const_1,const_1000)|add(n3,#1)|add(n3,#0)|add(#3,#2)|divide(#5,#4)|multiply(n3,#6)|
|
"consider 5 x acres of land used for bean consider 2 x acres of land used for wheat consider 4 x acres of land used for corn total given is 1034 acres 11 x = 1034 x = 94 land used for corn r = 4 * 94 = 376 correct option - c"
|
other
|
math_qa__lmep3GAAdwoKWbEF
|
The tax on a commodity is diminished by 40% but its consumption is increased by 25%. Find the decrease percent in the revenue derived from it? Choices
A) 18 %
B) 72 %
C) 25 %
D) 12 %
E) 52 %
|
<gadget id="calculator">100 + 25</gadget>
<output>125</output>
<gadget id="calculator">100 - 40</gadget>
<output>60</output>
<gadget id="calculator">125 * 60</gadget>
<output>7_500</output>
<gadget id="calculator">7_500 / 100</gadget>
<output>75</output>
<gadget id="calculator">100 - 75</gadget>
<output>25</output>
<result>C</result>
|
C
| 25 |
The tax on a commodity is diminished by 40% but its consumption is increased by 25%. Find the decrease percent in the revenue derived from it?
|
{
"A": "18 %",
"B": "72 %",
"C": "25 %",
"D": "12 %",
"E": "52 %"
}
|
subtract(const_100, divide(multiply(add(const_100, 25), subtract(const_100, 40)), const_100))
|
add(n1,const_100)|subtract(const_100,n0)|multiply(#0,#1)|divide(#2,const_100)|subtract(const_100,#3)|
|
"100 * 100 = 10000 60 * 125 = 7500 10000 - - - - - - - 2500 100 - - - - - - - ? = 25 % answer : c"
|
general
|
math_qa__LlJLlK7ndzAxNHQo
|
A lady grows cabbage in her garden that is in the shape of a square. Each cabbage takes 1 square foot of area in her garden. This year, she has increased her output by 127 cabbages when compared to last year. The shape of the area used for growing the cabbage has remained a square in both these years. How many cabbages did she produce this year? Choose the correct choice from the following choices
A) 4096 B) 4098 C) 5000 D) 5096 E) can not be determined
|
<gadget id="calculator">127 - 1</gadget>
<output>126</output>
<gadget id="calculator">126 / 2</gadget>
<output>63</output>
<gadget id="calculator">63 + 1</gadget>
<output>64</output>
<gadget id="calculator">64 ** 2</gadget>
<output>4_096</output>
<result>A</result>
|
A
| 4,096 |
A lady grows cabbage in her garden that is in the shape of a square. Each cabbage takes 1 square foot of area in her garden. This year, she has increased her output by 127 cabbages when compared to last year. The shape of the area used for growing the cabbage has remained a square in both these years. How many cabbages did she produce this year?
|
{
"A": "4096",
"B": "4098",
"C": "5000",
"D": "5096",
"E": "can not be determined"
}
|
power(add(divide(subtract(127, 1), const_2), 1), const_2)
|
subtract(n1,n0)|divide(#0,const_2)|add(n0,#1)|power(#2,const_2)|
|
"explanatory answer the shape of the area used for growing cabbage has remained a square in both the years . let the side of the square area used for growing cabbage this year be x ft . therefore , the area of the ground used for cultivation this year = x 2 sq . ft . let the side of the square area used for growing cabbage last year be y ft . therefore , the area of the ground used for cultivation last year = y 2 sq . ft . as the number of cabbage grown has increased by 127 , the area would have increased by 127 sq ft because each cabbage takes 1 sq ft space . hence , x 2 - y 2 = 127 ( x + y ) ( x - y ) = 127 . 127 is a prime number and hence it will have only two factors . i . e . , 127 and 1 . therefore , 127 can be expressed as product of 2 numbers in only way = 127 * 1 i . e . , ( x + y ) ( x - y ) = 127 * 1 so , ( x + y ) should be 127 and ( x - y ) should be 1 . solving the two equations we get x = 64 and y = 63 . therefore , number of cabbage produced this year = x 2 = 642 = 4096 . alternative approach : use answer choices the area in both the years are squares of two numbers . that rules out choice b , c and d . as 4098,5000 and 5096 are not the square of any number . check choice a : if this year ' s produce is 4096 , last year ' s produce would have been 4096 - 127 = 3969 3969 is the square of 63 . so , 4096 is the answer . choice a"
|
geometry
|
math_qa__VehQQuC4z2T2Wqob
|
Out of 40 applicants to a law school, 15 majored in political science, 20 had a grade point average higher than 3.0, and 10 did not major in political science and had a GPA equal to or lower than 3.0. How many of Q applicants majored in political science and had a GPA higher than 3.0? Choose the correct choice from the following answers
A) 5
B) 10
C) 15
D) 25
E) 35
|
<gadget id="calculator">10 + 15</gadget>
<output>25</output>
<gadget id="calculator">40 - 25</gadget>
<output>15</output>
<gadget id="calculator">20 - 15</gadget>
<output>5</output>
<result>A</result>
|
A
| 5 |
Out of 40 applicants to a law school, 15 majored in political science, 20 had a grade point average higher than 3.0, and 10 did not major in political science and had a GPA equal to or lower than 3.0. How many of Q applicants majored in political science and had a GPA higher than 3.0?
|
{
"A": "5",
"B": "10",
"C": "15",
"D": "25",
"E": "35"
}
|
subtract(20, subtract(40, add(10, 15)))
|
add(n1,n4)|subtract(n0,#0)|subtract(n2,#1)
|
total applicants = 40 political science = 15 and non political science = 40 - 15 = 25 gpa > 3.0 = 20 and gpa < = 3.0 = 20 10 non political science students had gpa < = 3.0 - - > 15 non political science students had gpa > 3.0 gpa > 3.0 in political science = total - ( gpa > 3.0 in non political science ) q = 20 - 15 = 5 answer : a
|
general
|
math_qa__XWEsK4U5GFZ6Gf3g
|
The sum of the squares of the first 15 positive integers (1^2 + 2^2 + 3^2 + . . . + 15^2) is equal to 1270. What is the sum of the squares of the second 15 positive integers (16^2 + 17^2 + 18^2 + . . . + 30^2) ? Choices: A) 2480 B) 3490 C) 6785 D) 8245 E) 9255
|
<gadget id="calculator">30 + 1</gadget>
<output>31</output>
<gadget id="calculator">30 * 31</gadget>
<output>930</output>
<gadget id="calculator">2 * 30</gadget>
<output>60</output>
<gadget id="calculator">60 + 1</gadget>
<output>61</output>
<gadget id="calculator">930 * 61</gadget>
<output>56_730</output>
<gadget id="calculator">3 + 3</gadget>
<output>6</output>
<gadget id="calculator">56_730 / 6</gadget>
<output>9_455</output>
<gadget id="calculator">9_455 - 1_270</gadget>
<output>8_185</output>
<result>D</result>
|
D
| 8,245 |
The sum of the squares of the first 15 positive integers (1^2 + 2^2 + 3^2 + . . . + 15^2) is equal to 1270. What is the sum of the squares of the second 15 positive integers (16^2 + 17^2 + 18^2 + . . . + 30^2) ?
|
{
"A": "2480",
"B": "3490",
"C": "6785",
"D": "8245",
"E": "9255"
}
|
subtract(divide(multiply(multiply(30, add(30, 1)), add(multiply(2, 30), 1)), add(3, 3)), 1270)
|
add(n17,n1)|add(n5,n5)|multiply(n17,n2)|add(#2,n1)|multiply(n17,#0)|multiply(#3,#4)|divide(#5,#1)|subtract(#6,n9)|
|
"you ' ll never need a formula for the sums of squares on the actual gmat . you do n ' t need to use that formula here , though it ' s not all that straightforward to solve without one . two different approaches : 16 ^ 2 + 17 ^ 2 + 18 ^ 2 + . . . + 30 ^ 2 = ( 15 + 1 ) ^ 2 + ( 15 + 2 ) ^ 2 + ( 15 + 3 ) ^ 2 + . . . + ( 15 + 15 ) ^ 2 now we can expand each square ; they are all in the ( x + y ) ^ 2 = x ^ 2 + 2 xy + y ^ 2 pattern . = ( 15 ^ 2 + 2 * 15 + 1 ^ 2 ) + ( 15 ^ 2 + 4 * 15 + 2 ^ 2 ) + ( 15 ^ 2 + 6 * 15 + 3 ^ 2 ) + . . . + ( 15 ^ 2 + 30 * 15 + 15 ^ 2 ) now we have fifteen 15 ^ 2 terms , so adding these gives 15 * 15 ^ 2 = 15 ^ 3 = 3375 . we also have the entire sum 1 ^ 2 + 2 ^ 2 + . . . + 15 ^ 2 , which we know is equal to 1240 . finally adding the middle terms , we have : 2 * 15 + 4 * 15 + 6 * 15 + . . . + 30 * 15 = 15 ( 2 + 4 + 6 + . . . . + 30 ) = 15 * 2 * ( 1 + 2 + 3 + . . . + 15 ) = 15 * 2 * 8 * 15 = 3600 so the sum must be 3375 + 1240 + 3600 = 8215 alternatively , we can use a different factoring pattern . we want to find the value of 30 ^ 2 + 29 ^ 2 + . . . + 17 ^ 2 + 16 ^ 2 . well if we subtract 15 ^ 2 + 14 ^ 2 + . . . . + 2 ^ 2 + 1 ^ 2 from this , the answer will be 1240 less than what we want to find . so if we can find the value of 30 ^ 2 + 29 ^ 2 + . . . + 17 ^ 2 + 16 ^ 2 - ( 15 ^ 2 + 14 ^ 2 + . . . . + 2 ^ 2 + 1 ^ 2 ) then we can add 1240 to get the answer . now grouping the terms above to get differences of squares , we have = ( 30 ^ 2 - 15 ^ 2 ) + ( 29 ^ 2 - 14 ^ 2 ) + . . . + ( 16 ^ 2 - 1 ^ 2 ) and factoring each of these using x ^ 2 - y ^ 2 = ( x + y ) ( x - y ) , we have = 45 * 15 + 43 * 15 + 41 * 15 + . . . + 17 * 15 = 15 ( 45 + 43 + 41 + . . . + 17 ) in brackets we have an equally spaced sum with fifteen terms , which we can evaluate using the familiar formula . so the above equals 15 * 15 * 62 / 2 = 6975 and adding back the 1270 , we get the answer of 8245 . ( ans d )"
|
general
|
math_qa__87bZQH94CM1C2uCd
|
Last week Vartan spent 15 percent of his wages on recreation. This week, his wages are 10 percent less than last weekʼs wages and he spent 30 percent of his wages on recreation. The amount he spends on recreation this week is what percent of the amount he spent on recreation last week? Choose one:
A) 100 %
B) 160 %
C) 180 %
D) 200 %
E) 220 %
|
<gadget id="calculator">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">30 * 90</gadget>
<output>2_700</output>
<gadget id="calculator">2_700 / 15</gadget>
<output>180</output>
<result>C</result>
|
C
| 180 |
Last week Vartan spent 15 percent of his wages on recreation. This week, his wages are 10 percent less than last weekʼs wages and he spent 30 percent of his wages on recreation. The amount he spends on recreation this week is what percent of the amount he spent on recreation last week?
|
{
"A": "100 %",
"B": "160 %",
"C": "180 %",
"D": "200 %",
"E": "220 %"
}
|
divide(multiply(30, subtract(const_100, 10)), 15)
|
subtract(const_100,n1)|multiply(n2,#0)|divide(#1,n0)
|
say vartan ' s wages last week were $ 100 , so he spent 0.15 * 100 = $ 15 on recreation ; this week ' s wages is 0.9 * 100 = $ 90 , so he spends 0.3 * 90 = $ 27 on recreation ; 27 / 15 = 1.8 , hence the amount he spends on recreation this week is 180 % of the amount he spent on recreation last week : 15 * 1.8 = 27 . answer : c .
|
general
|
math_qa__nsWKx3aZVTr1Kdsf
|
The circumferences of two circles are 528 meters and 704 meters. Find the difference between the areas of the larger and the smaller circles? Select the correct option.
A) 29963 sq m B) 28937 sq m C) 43162 sq m D) 27688 sq m E) 17248 sq m
|
<gadget id="calculator">2 * pi</gadget>
<output>2*pi = around 6.283185</output>
<gadget id="calculator">704 / (2*pi)</gadget>
<output>352/pi = around 112.04508</output>
<gadget id="calculator">pi * ((352/pi) ** 2)</gadget>
<output>123904/pi = around 39_439.868138</output>
<gadget id="calculator">528 / (2*pi)</gadget>
<output>264/pi = around 84.03381</output>
<gadget id="calculator">pi * ((264/pi) ** 2)</gadget>
<output>69696/pi = around 22_184.925827</output>
<gadget id="calculator">(123904/pi) - (69696/pi)</gadget>
<output>54208/pi = around 17_254.94231</output>
<result>E</result>
|
E
| 17,248 |
The circumferences of two circles are 528 meters and 704 meters. Find the difference between the areas of the larger and the smaller circles?
|
{
"A": "29963 sq m",
"B": "28937 sq m",
"C": "43162 sq m",
"D": "27688 sq m",
"E": "17248 sq m"
}
|
subtract(circle_area(divide(704, multiply(const_2, const_pi))), circle_area(divide(528, multiply(const_2, const_pi))))
|
multiply(const_2,const_pi)|divide(n1,#0)|divide(n0,#0)|circle_area(#1)|circle_area(#2)|subtract(#3,#4)|
|
"let the radii of the smaller and the larger circles be s m and l m respectively . 2 ∏ s = 528 and 2 ∏ l = 704 s = 528 / 2 ∏ and l = 704 / 2 ∏ difference between the areas = ∏ l ^ 2 - ∏ s ^ 2 = ∏ { 264 ^ 2 / ∏ ^ 2 - 352 ^ 2 / ∏ ^ 2 } = 264 ^ 2 / ∏ - 352 ^ 2 / ∏ = ( 264 - 352 ) ( 264 + 352 ) / ∏ = ( 88 ) ( 616 ) / ( 22 / 7 ) = 17248 sq m answer : e"
|
geometry
|
math_qa__LU9uKbnpYv7EsVCf
|
If 15% of A is the same as 25% of B, then A : B is : Pick:
A) 5 : 3 B) 4 : 3 C) 7 : 16 D) 12 : 17 E) 11 : 13
|
<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">(1/4) / (3/20)</gadget>
<output>5/3 = around 1.666667</output>
<result>A</result>
|
A
| 1.666667 |
If 15% of A is the same as 25% of B, then A : B is :
|
{
"A": "5 : 3",
"B": "4 : 3",
"C": "7 : 16",
"D": "12 : 17",
"E": "11 : 13"
}
|
divide(divide(25, const_100), divide(15, const_100))
|
divide(n1,const_100)|divide(n0,const_100)|divide(#0,#1)|
|
"expl : 15 % of a i = 25 % of b = 15 a / 100 = 25 b / 100 = 5 / 3 = 5 : 3 answer : a"
|
gain
|
math_qa__Sfiu5bqiJf4AQrTZ
|
the ages of old and young total 48 . old is twice as old as young was when old was half as old as young will be when young is 3 times as old was when old was 3 times as old as young . how old is old ? Select:
A) 23 B) 27 C) 12 D) 43 E) 37
|
<gadget id="calculator">3 + 3</gadget>
<output>6</output>
<gadget id="calculator">6 * 2</gadget>
<output>12</output>
<result>C</result>
|
C
| 12 |
the ages of old and young total 48 . old is twice as old as young was when old was half as old as young will be when young is 3 times as old was when old was 3 times as old as young . how old is old ?
|
{
"A": "23",
"B": "27",
"C": "12",
"D": "43",
"E": "37"
}
|
multiply(add(3, 3), const_2)
|
add(n1,n1)|multiply(#0,const_2)
|
explanation : from the options itself , we can see that option c old = 30 young = 18 30 + 18 = 48 by reducing this years only by one before 6 years old = 24 ( half of young ) young = 12 ( twice of old ) answer : c
|
general
|
math_qa__yNLSONHn7fssNqiq
|
The percentage profit earned by selling an article for Rs. 1520 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?
Choose the correct choice from the following choices: A) 3000 B) 1230 C) 1750 D) 5600 E) 3400
|
<gadget id="calculator">100 + 25</gadget>
<output>125</output>
<gadget id="calculator">125 / 100</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">1_520 + 1_280</gadget>
<output>2_800</output>
<gadget id="calculator">2_800 / 2</gadget>
<output>1_400</output>
<gadget id="calculator">(5/4) * 1_400</gadget>
<output>1_750</output>
<result>C</result>
|
C
| 1,750 |
The percentage profit earned by selling an article for Rs. 1520 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?
|
{
"A": "3000",
"B": "1230",
"C": "1750",
"D": "5600",
"E": "3400"
}
|
multiply(divide(add(const_100, 25), const_100), divide(add(1520, 1280), const_2))
|
add(n2,const_100)|add(n0,n1)|divide(#0,const_100)|divide(#1,const_2)|multiply(#2,#3)|
|
"c . p . be rs . x . then , ( 1520 - x ) / x * 100 = ( x - 1280 ) / x * 100 1520 - x = x - 1280 2 x = 2800 = > x = 1400 required s . p . = 125 % of rs . 1400 = 125 / 100 * 1400 = rs . 1750 . answer c"
|
gain
|
math_qa__oAAoeMQKQ3oujHJD
|
Keats Library purchases a number of new books, all in the category of biography, and the library does not acquire any other books. With the addition of the new biographies, the biography collection of the library amounts to 32% of the total number of books in the library. If prior to the purchase, only 20% of the books in Keats Library were biographies, by what percent has the number of biographies in the library increased?
Choose the most appropriate option: A) 60 % B) 72 % C) 88 % D) 95 % E) 110 %
|
<gadget id="calculator">32 * 100</gadget>
<output>3_200</output>
<gadget id="calculator">20 * 100</gadget>
<output>2_000</output>
<gadget id="calculator">3_200 - 2_000</gadget>
<output>1_200</output>
<gadget id="calculator">100 - 32</gadget>
<output>68</output>
<gadget id="calculator">1_200 / 68</gadget>
<output>300/17 = around 17.647059</output>
<gadget id="calculator">(300/17) / 20</gadget>
<output>15/17 = around 0.882353</output>
<gadget id="calculator">(15/17) * 100</gadget>
<output>1_500/17 = around 88.235294</output>
<result>C</result>
|
C
| 88 |
Keats Library purchases a number of new books, all in the category of biography, and the library does not acquire any other books. With the addition of the new biographies, the biography collection of the library amounts to 32% of the total number of books in the library. If prior to the purchase, only 20% of the books in Keats Library were biographies, by what percent has the number of biographies in the library increased?
|
{
"A": "60 %",
"B": "72 %",
"C": "88 %",
"D": "95 %",
"E": "110 %"
}
|
multiply(divide(divide(subtract(multiply(32, const_100), multiply(20, const_100)), subtract(const_100, 32)), 20), const_100)
|
multiply(n0,const_100)|multiply(n1,const_100)|subtract(const_100,n0)|subtract(#0,#1)|divide(#3,#2)|divide(#4,n1)|multiply(#5,const_100)
|
let x be the number of new biographies added to the library . let b be the original number of biographies , so the original number of books was 5 b . 0.32 ( 5 b + x ) = b + x 0.6 b = 0.68 x x = 0.88 b the answer is c .
|
general
|
math_qa__bfybn6NxS1N9hDNE
|
If the volume of two cubes are in the ratio 125:1, the ratio of their edges is:
Choose the most appropriate option: A) 3 : 1 B) 5 : 1 C) 3 : 5 D) 3 : 7 E) none of these
|
<gadget id="calculator">125 ** (1/3)</gadget>
<output>5</output>
<result>B</result>
|
B
| 5 |
If the volume of two cubes are in the ratio 125:1, the ratio of their edges is:
|
{
"A": "3 : 1",
"B": "5 : 1",
"C": "3 : 5",
"D": "3 : 7",
"E": "none of these"
}
|
cube_edge_by_volume(125)
|
cube_edge_by_volume(n0)|
|
"explanation : let the edges be a and b of two cubes , then a 3 / b 3 = 125 / 1 = > ( a / b ) 3 = ( 5 / 1 ) 3 a / b = 5 / 1 = > a : b = 5 : 1 option b"
|
geometry
|
math_qa__2HKPwl5TGPfSKJEb
|
In a class of 20 students in an examination in Mathematics 2 students scored 100 Marks each, 3 get
zero each and the average of the rest was 40. What is the average Of the whole class? Choices
A) 46
B) 49
C) 40
D) 38
E) 35
|
<gadget id="calculator">20 - 2</gadget>
<output>18</output>
<gadget id="calculator">18 - 3</gadget>
<output>15</output>
<gadget id="calculator">40 * 15</gadget>
<output>600</output>
<gadget id="calculator">2 * 100</gadget>
<output>200</output>
<gadget id="calculator">600 + 200</gadget>
<output>800</output>
<gadget id="calculator">800 / 20</gadget>
<output>40</output>
<result>C</result>
|
C
| 40 |
In a class of 20 students in an examination in Mathematics 2 students scored 100 Marks each, 3 get
zero each and the average of the rest was 40. What is the average Of the whole class?
|
{
"A": "46",
"B": "49",
"C": "40",
"D": "38",
"E": "35"
}
|
divide(add(multiply(40, subtract(subtract(20, 2), 3)), multiply(2, 100)), 20)
|
multiply(n1,n2)|subtract(n0,n1)|subtract(#1,n3)|multiply(n4,#2)|add(#3,#0)|divide(#4,n0)
|
total marks obtained by a class of 20 students = 2 * 100 + 3 * 0 + 15 * 40 = 200 + 600 = 800 : average marks of whole class = 800 / 20 = 40 answer is c .
|
general
|
math_qa__Mh0jU4gKtDMUBvUJ
|
A can do a piece of work in 20days, and B can do it in 15days. How long will they take if both work together? Choices.
A) 7 days B) 8.6 days C) 13 days D) 5.6 days E) 10 days
|
<gadget id="calculator">1 / 15</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">1 / 20</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/15) + (1/20)</gadget>
<output>7/60 = around 0.116667</output>
<gadget id="calculator">1 / (7/60)</gadget>
<output>60/7 = around 8.571429</output>
<result>B</result>
|
B
| 8.6 |
A can do a piece of work in 20days, and B can do it in 15days. How long will they take if both work together?
|
{
"A": "7 days",
"B": "8.6 days",
"C": "13 days",
"D": "5.6 days",
"E": "10 days"
}
|
inverse(add(inverse(15), inverse(20)))
|
inverse(n1)|inverse(n0)|add(#0,#1)|inverse(#2)
|
a + b can do the work in 20 * 15 / 20 + 15 = 20 * 15 / 35 = 8.6 days answer is b
|
physics
|
math_qa__ZTykPhGhOhTl7JZO
|
If the sides of a triangle are 28 cm, 26 cm and 12 cm, what is its area? Options:
A) 120 cm 2
B) 156 cm 2
C) 178 cm 2
D) 189 cm 2
E) 176 cm 2
|
<gadget id="calculator">26 * 12</gadget>
<output>312</output>
<gadget id="calculator">312 / 2</gadget>
<output>156</output>
<result>B</result>
|
B
| 156 |
If the sides of a triangle are 28 cm, 26 cm and 12 cm, what is its area?
|
{
"A": "120 cm 2",
"B": "156 cm 2",
"C": "178 cm 2",
"D": "189 cm 2",
"E": "176 cm 2"
}
|
divide(multiply(26, 12), const_2)
|
multiply(n1,n2)|divide(#0,const_2)|
|
"the triangle with sides 28 cm , 26 cm and 12 cm is right angled , where the hypotenuse is 28 cm . area of the triangle = 1 / 2 * 26 * 12 = 156 cm 2 answer : b"
|
geometry
|
math_qa__snzmSEeyFmpxYGDU
|
The average weight of 29 students is 28 kg. By the admission of a new student, the average weight is reduced to 27.4 kg. The weight of the new student is
Choose one:
A) 22 kg B) 21.6 kg C) 22.4 kg D) 10 kg E) none of these
|
<gadget id="calculator">29 + 1</gadget>
<output>30</output>
<gadget id="calculator">30 * 27.4</gadget>
<output>822</output>
<gadget id="calculator">29 * 28</gadget>
<output>812</output>
<gadget id="calculator">822 - 812</gadget>
<output>10</output>
<result>D</result>
|
D
| 10 |
The average weight of 29 students is 28 kg. By the admission of a new student, the average weight is reduced to 27.4 kg. The weight of the new student is
|
{
"A": "22 kg",
"B": "21.6 kg",
"C": "22.4 kg",
"D": "10 kg",
"E": "none of these"
}
|
subtract(multiply(add(29, const_1), 27.4), multiply(29, 28))
|
add(n0,const_1)|multiply(n0,n1)|multiply(n2,#0)|subtract(#2,#1)|
|
"exp . the total weight of 29 students = 29 * 28 the total weight of 30 students = 30 * 27.4 weight of the new student = ( 30 * 27.4 – 29 * 28 ) = 822 - 812 = 10 answer : d"
|
general
|
math_qa__DSEn36EGivONXyJX
|
22 buckets of water fill a tank when the capacity of each bucket is 13.5 litres. How many buckets will be required to fill the same tank if the capacity of each bucket is 9 litres? Choose the correct choice:
A) 33 B) 32 C) 60 D) data inadequate E) none of these
|
<gadget id="calculator">13.5 * 22</gadget>
<output>297</output>
<gadget id="calculator">297 / 9</gadget>
<output>33</output>
<result>A</result>
|
A
| 33 |
22 buckets of water fill a tank when the capacity of each bucket is 13.5 litres. How many buckets will be required to fill the same tank if the capacity of each bucket is 9 litres?
|
{
"A": "33",
"B": "32",
"C": "60",
"D": "data inadequate",
"E": "none of these"
}
|
divide(multiply(13.5, 22), 9)
|
multiply(n0,n1)|divide(#0,n2)|
|
"capacity of the tank = 22 ã — 13.5 = 297 litres when the capacity of each bucket = 9 litres , then the required no . of buckets = 297 â „ 9 = 33 answer a"
|
physics
|
math_qa__vsropkQjkUIbYoY2
|
Find a positive number which when increased by 17 is equal to 60 times the reciprocal of the number? Choose the correct option:
A) 3 B) 5 C) 6 D) 7 E) 9
|
<gadget id="calculator">gcd(60, 17)</gadget>
<output>1</output>
<gadget id="calculator">2 + 1</gadget>
<output>3</output>
<result>A</result>
|
A
| 3 |
Find a positive number which when increased by 17 is equal to 60 times the reciprocal of the number?
|
{
"A": "3",
"B": "5",
"C": "6",
"D": "7",
"E": "9"
}
|
add(const_2, gcd(60, 17))
|
gcd(n0,n1)|add(#0,const_2)
|
let the number be x . then , x + 17 = 60 x x 2 + 17 x - 60 = 0 ( x + 20 ) ( x - 3 ) = 0 x = 3 option a
|
general
|
math_qa__ZQgY6JAXEjzdCzVX
|
The arithmetic mean and standard deviation of a certain normal distribution are 17.5 and 2.5, respectively. What value is exactly 2 standard deviations less than the mean? Answers.
A) 10.5
B) 11
C) 11.5
D) 12
E) 12.5
|
<gadget id="calculator">2 * 2.5</gadget>
<output>5</output>
<gadget id="calculator">17.5 - 5</gadget>
<output>12.5</output>
<result>E</result>
|
E
| 12.5 |
The arithmetic mean and standard deviation of a certain normal distribution are 17.5 and 2.5, respectively. What value is exactly 2 standard deviations less than the mean?
|
{
"A": "10.5",
"B": "11",
"C": "11.5",
"D": "12",
"E": "12.5"
}
|
subtract(17.5, multiply(2, 2.5))
|
multiply(n1,n2)|subtract(n0,#0)|
|
"mean = 17.5 two standard deviations is 2.5 + 2.5 = 5.0 there could be two calues for this . mean + two standard deviations = 22.5 mean - two standard deviations = 12.5 answer choice has 12.5 and so e is the answer ."
|
general
|
math_qa__kFy3jlTgf50PjpCx
|
In a group of 130 people, 90 have an age of more 30 years, and the others have an age of less than 20 years. If a person is selected at random from this group, what is the probability the person's age is less than 20? Choose the correct choice from the following options
A) 0.31
B) 0.55
C) 0.65
D) 0.75
E) 0.85
|
<gadget id="calculator">130 - 90</gadget>
<output>40</output>
<gadget id="calculator">40 / 130</gadget>
<output>4/13 = around 0.307692</output>
<result>A</result>
|
A
| 0.31 |
In a group of 130 people, 90 have an age of more 30 years, and the others have an age of less than 20 years. If a person is selected at random from this group, what is the probability the person's age is less than 20?
|
{
"A": "0.31",
"B": "0.55",
"C": "0.65",
"D": "0.75",
"E": "0.85"
}
|
divide(subtract(130, 90), 130)
|
subtract(n0,n1)|divide(#0,n0)|
|
"number of people whose age is less than 20 is given by 130 - 90 = 40 probability p that a person selected at random from the group is less than 20 is given by 40 / 130 = 0.31 correct answer a"
|
general
|
math_qa__l3dgyOiqmETAYt6t
|
A store reported total sales of $385 million for February of this year. If the total sales for the same month last year was $320 million, approximately what was the percent increase E in sales? Choose the correct choice from the following
A) 2 % B) 17 % C) 20 % D) 65 % E) 83 %
|
<gadget id="calculator">385 - 320</gadget>
<output>65</output>
<gadget id="calculator">65 / 320</gadget>
<output>13/64 = around 0.203125</output>
<gadget id="calculator">(13/64) * 100</gadget>
<output>325/16 = around 20.3125</output>
<result>C</result>
|
C
| 20 |
A store reported total sales of $385 million for February of this year. If the total sales for the same month last year was $320 million, approximately what was the percent increase E in sales?
|
{
"A": "2 %",
"B": "17 %",
"C": "20 %",
"D": "65 %",
"E": "83 %"
}
|
multiply(divide(subtract(385, 320), 320), const_100)
|
subtract(n0,n1)|divide(#0,n1)|multiply(#1,const_100)|
|
"last year ' s sales = $ 320 million ; this year ' s sales = $ 385 million ; increase e = $ 65 million . now , 20 % of $ 320 million is $ 64 million , which is very close to actual increase of $ 65 million . answer : c ."
|
general
|
math_qa__Nc8UadRzb1GPzAU7
|
If A = {17, 27, 31, 53, 61}, what is the sum of mean and median of the numbers in A? Select the correct option
A) 69 B) 75 C) 82 D) 91 E) 56
|
<gadget id="calculator">17 + 27</gadget>
<output>44</output>
<gadget id="calculator">44 + 31</gadget>
<output>75</output>
<gadget id="calculator">75 + 53</gadget>
<output>128</output>
<gadget id="calculator">128 + 61</gadget>
<output>189</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">189 / 5</gadget>
<output>189/5 = around 37.8</output>
<gadget id="calculator">(189/5) + 31</gadget>
<output>344/5 = around 68.8</output>
<result>A</result>
|
A
| 69 |
If A = {17, 27, 31, 53, 61}, what is the sum of mean and median of the numbers in A?
|
{
"A": "69",
"B": "75",
"C": "82",
"D": "91",
"E": "56"
}
|
add(divide(add(add(add(add(17, 27), 31), 53), 61), add(const_4, const_1)), 31)
|
add(n0,n1)|add(const_1,const_4)|add(n2,#0)|add(n3,#2)|add(n4,#3)|divide(#4,#1)|add(n2,#5)
|
mean = ( 17 + 27 + 31 + 53 + 62 ) / 5 = 38 median = 31 sum = 38 + 31 = 69 option a
|
general
|
math_qa__stYr1MwDFIBbskAE
|
The simple interest on a certain sum of money at the rate of 5% p.a. for 8 years is Rs. 840. At what rate of intrest the same amount of interest can be received on the same sum after 5 years. Options:
A) 5 % B) 6 % C) 7 % D) 8 % E) 9 %
|
<gadget id="calculator">840 / 5</gadget>
<output>168</output>
<gadget id="calculator">840 / 8</gadget>
<output>105</output>
<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">105 / (1/20)</gadget>
<output>2_100</output>
<gadget id="calculator">168 / 2_100</gadget>
<output>2/25 = around 0.08</output>
<gadget id="calculator">(2/25) * 100</gadget>
<output>8</output>
<result>D</result>
|
D
| 8 |
The simple interest on a certain sum of money at the rate of 5% p.a. for 8 years is Rs. 840. At what rate of intrest the same amount of interest can be received on the same sum after 5 years.
|
{
"A": "5 %",
"B": "6 %",
"C": "7 %",
"D": "8 %",
"E": "9 %"
}
|
multiply(divide(divide(840, 5), divide(divide(840, 8), divide(5, const_100))), const_100)
|
divide(n2,n0)|divide(n2,n1)|divide(n0,const_100)|divide(#1,#2)|divide(#0,#3)|multiply(#4,const_100)|
|
"explanation : here firstly we need to calculate the principal amount , then we can calculate the new rate . p = s . i . ∗ 100 / r ∗ t p = 840 ∗ 100 / 5 ∗ 8 p = 2100 required rate = 840 ∗ 100 / 5 ∗ 2100 r = 8 % option d"
|
gain
|
math_qa__JhyhsGj3Rb6hVCYP
|
Two cards are drawn together from a pack of 52 cards. The probability that one is a club and other is a diamond, is: Select the correct option:
A) 29 / 34 B) 47 / 100 C) 3 / 20 D) 13 / 102 E) none of these
|
<gadget id="calculator">52 / 4</gadget>
<output>13</output>
<gadget id="calculator">13 * 13</gadget>
<output>169</output>
<gadget id="calculator">52 * 52</gadget>
<output>2_704</output>
<gadget id="calculator">169 / 2_704</gadget>
<output>1/16 = around 0.0625</output>
<gadget id="calculator">(1/16) * 2</gadget>
<output>1/8 = around 0.125</output>
<result>D</result>
|
D
| 0.127451 |
Two cards are drawn together from a pack of 52 cards. The probability that one is a club and other is a diamond, is:
|
{
"A": "29 / 34",
"B": "47 / 100",
"C": "3 / 20",
"D": "13 / 102",
"E": "none of these"
}
|
multiply(divide(multiply(divide(52, const_4), divide(52, const_4)), multiply(52, 52)), const_2)
|
divide(n0,const_4)|multiply(n0,n0)|multiply(#0,#0)|divide(#2,#1)|multiply(#3,const_2)
|
explanation : one card drawn . probability of being it club or diamond = ( 13 x 2 ) / 52 . another card drawn . now , probability of being it of other suit ( the suit among the two , not selected in first draw ) = 13 / 51 . hence , probability of event = ( ( 13 x 2 ) / 52 ) x ( 13 / 51 ) = 13 / 102 . answer : d
|
probability
|
math_qa__COHnJrSZtadjbJHO
|
A rectangular tiled patio is composed of 160 square tiles. The rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles. After the change in layout, the patio will still have 160 tiles, and it will still be rectangular. How many rows are in the tile patio before the change in layout? Choose the correct choice from the following options: A) 5 B) 6 C) 10 D) 13 E) 28
|
<gadget id="calculator">-4</gadget>
<output>-4</output>
<gadget id="calculator">4 ** 2</gadget>
<output>16</output>
<gadget id="calculator">160 * 2</gadget>
<output>320</output>
<gadget id="calculator">4 * 320</gadget>
<output>1_280</output>
<gadget id="calculator">16 + 1_280</gadget>
<output>1_296</output>
<gadget id="calculator">1_296 ** (1/2)</gadget>
<output>36</output>
<gadget id="calculator">(-4) + 36</gadget>
<output>32</output>
<gadget id="calculator">32 / 2</gadget>
<output>16</output>
<gadget id="calculator">160 / 16</gadget>
<output>10</output>
<result>C</result>
|
C
| 10 |
A rectangular tiled patio is composed of 160 square tiles. The rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles. After the change in layout, the patio will still have 160 tiles, and it will still be rectangular. How many rows are in the tile patio before the change in layout?
|
{
"A": "5",
"B": "6",
"C": "10",
"D": "13",
"E": "28"
}
|
divide(160, divide(add(negate(4), sqrt(add(power(4, 2), multiply(4, multiply(160, 2))))), 2))
|
multiply(n0,n1)|negate(n2)|power(n2,n1)|multiply(n2,#0)|add(#3,#2)|sqrt(#4)|add(#1,#5)|divide(#6,n1)|divide(n0,#7)|
|
"suppose there are c columns and there are r rows original situation so , number of tiles = c * r = 160 also . reach column has r tiles and each row has c tiles new situation number of tiles in each column is r - 2 and number of tiles in each row is c + 4 so , number of rows = r - 2 and number of columns is c + 4 so , number of tiles = ( r - 2 ) * ( c + 4 ) = 160 comparing both of them we get c * r = ( r - 2 ) * ( c + 4 ) = > 4 r - 2 c = 8 c = 2 r - 4 putting it in c * r = 160 ( 2 r - 4 ) * r = 160 2 r ^ 2 - 4 r - 160 = 0 r can not be negative so r = 10 and c = 16 so , answer will be c"
|
geometry
|
math_qa__FTUdCLCVvzv7KylK
|
8 machines can do a work in 10days. How many machines are needed to complete the work in 40days? Pick.
A) 2 B) 6 C) 4 D) 7 E) 5
|
<gadget id="calculator">8 * 10</gadget>
<output>80</output>
<gadget id="calculator">80 / 40</gadget>
<output>2</output>
<result>A</result>
|
A
| 2 |
8 machines can do a work in 10days. How many machines are needed to complete the work in 40days?
|
{
"A": "2",
"B": "6",
"C": "4",
"D": "7",
"E": "5"
}
|
divide(multiply(8, 10), 40)
|
multiply(n0,n1)|divide(#0,n2)|
|
"required number of machines = 8 * 10 / 40 = 2 answer is a"
|
physics
|
math_qa__SS3ihu53EFnFSYje
|
A's speed is 15/13 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that B beats A by 40% of the length of the race? Choose the correct choice from the following answers:
A) 44 %
B) 48 %
C) 52 %
D) 42 %
E) 46 %
|
<gadget id="calculator">100 - 40</gadget>
<output>60</output>
<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">13 / 15</gadget>
<output>13/15 = around 0.866667</output>
<gadget id="calculator">(3/5) * (13/15)</gadget>
<output>13/25 = around 0.52</output>
<gadget id="calculator">1 - (13/25)</gadget>
<output>12/25 = around 0.48</output>
<gadget id="calculator">(12/25) * 100</gadget>
<output>48</output>
<result>B</result>
|
B
| 48 |
A's speed is 15/13 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that B beats A by 40% of the length of the race?
|
{
"A": "44 %",
"B": "48 %",
"C": "52 %",
"D": "42 %",
"E": "46 %"
}
|
multiply(subtract(const_1, multiply(divide(subtract(const_100, 40), const_100), divide(13, 15))), const_100)
|
divide(n1,n0)|subtract(const_100,n2)|divide(#1,const_100)|multiply(#2,#0)|subtract(const_1,#3)|multiply(#4,const_100)|
|
"first calculate the distance , b has covered with his speed in the time , in which a reached 60 % of the race . then add the remaining distance as head start for b to win the race . its best to apply ratios concept here . since a ' s speed is 15 / 13 of b , therefore , b ' s speed is 13 / 15 of a distance covered by b = speed x time = ( 13 / 15 ) x ( 0.6 ) = 0.52 % ( which means b would have covered 0.52 of the race length during the time in which a has covered 0.6 of the race length . therefore to win , b needs a headstart of ( 1 - 0.52 = ) 0.48 of the race length . so the answer is b"
|
general
|
math_qa__xlTJyq9N7OuqIrC6
|
What is the radius of the incircle of the triangle whose sides measure 5, 12 and 13 units? Pick
A) 2 units B) 12 units C) 6.5 units D) 6 units E) 7.5 units
|
<gadget id="calculator">5 * 12</gadget>
<output>60</output>
<gadget id="calculator">5 + 12</gadget>
<output>17</output>
<gadget id="calculator">17 + 13</gadget>
<output>30</output>
<gadget id="calculator">60 / 30</gadget>
<output>2</output>
<result>A</result>
|
A
| 2 |
What is the radius of the incircle of the triangle whose sides measure 5, 12 and 13 units?
|
{
"A": "2 units",
"B": "12 units",
"C": "6.5 units",
"D": "6 units",
"E": "7.5 units"
}
|
divide(multiply(5, 12), add(add(5, 12), 13))
|
add(n0,n1)|multiply(n0,n1)|add(n2,#0)|divide(#1,#2)
|
explanatory answer in a right angled triangle , the radius of the incircle = s - h , where ' s ' is the semi perimeter of the triangle and ' r ' is the radius of the inscribed circle . the semi perimeter of the triangle = a + b + c / 2 = 5 + 12 + 13 / 2 = 15 therefore , r = 15 - 13 = 2 units . choice a
|
geometry
|
math_qa__MX0uT0cvzepUGB1b
|
Along a yard 414 metres long, 24 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between two consecutive trees
Select:
A) 18 B) 19 C) 10 D) 11 E) 12
|
<gadget id="calculator">24 - 1</gadget>
<output>23</output>
<gadget id="calculator">414 / 23</gadget>
<output>18</output>
<result>A</result>
|
A
| 18 |
Along a yard 414 metres long, 24 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between two consecutive trees
|
{
"A": "18",
"B": "19",
"C": "10",
"D": "11",
"E": "12"
}
|
divide(414, subtract(24, const_1))
|
subtract(n1,const_1)|divide(n0,#0)
|
explanation : 24 trees have 23 gaps between them , required distance ( 414 / 23 ) = 18 option a
|
physics
|
math_qa__RUFOxvksfmixG3gF
|
At the opening of a trading day at a certain stock exchange, the price per share of stock K was $8. If the price per share of stock K was $9 at the closing of the day, what was the percent increase in the price per share of stock K for that day? Pick
A) 1.4 % B) 5.9 % C) 11.1 % D) 12.5 % E) 23.6 %
|
<gadget id="calculator">9 / 8</gadget>
<output>9/8 = around 1.125</output>
<gadget id="calculator">(9/8) - 1</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">(1/8) * 100</gadget>
<output>25/2 = around 12.5</output>
<result>D</result>
|
D
| 12.5 |
At the opening of a trading day at a certain stock exchange, the price per share of stock K was $8. If the price per share of stock K was $9 at the closing of the day, what was the percent increase in the price per share of stock K for that day?
|
{
"A": "1.4 %",
"B": "5.9 %",
"C": "11.1 %",
"D": "12.5 %",
"E": "23.6 %"
}
|
multiply(subtract(divide(9, 8), const_1), const_100)
|
divide(n1,n0)|subtract(#0,const_1)|multiply(#1,const_100)|
|
"opening = 8 closing = 9 rise in price = 1 so , percent increase = 18 ∗ 10018 ∗ 100 = > 12.50 % thus answer will be ( d )"
|
general
|
math_qa__7x2G7FARHZ1TyJg0
|
Fresh grapes contain 70% by weight while dried grapes contain 10% water by weight. What is the weight of dry grapes available from 100 kg of fresh grapes? Choose the correct choice from the following options
A) 18.33 kg B) 21.50 kg C) 25.00 kg D) 33.33 kg E) 40.39 kg
|
<gadget id="calculator">100 - 70</gadget>
<output>30</output>
<gadget id="calculator">30 * 100</gadget>
<output>3_000</output>
<gadget id="calculator">3_000 / 100</gadget>
<output>30</output>
<gadget id="calculator">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">30 / 90</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(1/3) * 100</gadget>
<output>100/3 = around 33.333333</output>
<result>D</result>
|
D
| 33.33 |
Fresh grapes contain 70% by weight while dried grapes contain 10% water by weight. What is the weight of dry grapes available from 100 kg of fresh grapes?
|
{
"A": "18.33 kg",
"B": "21.50 kg",
"C": "25.00 kg",
"D": "33.33 kg",
"E": "40.39 kg"
}
|
multiply(divide(divide(multiply(subtract(const_100, 70), 100), const_100), subtract(const_100, 10)), const_100)
|
subtract(const_100,n0)|subtract(const_100,n1)|multiply(n2,#0)|divide(#2,const_100)|divide(#3,#1)|multiply(#4,const_100)|
|
"from the question we know : 100 kg * 70 % = 70 kg of water in the fresh grapes 100 kg - 70 kg of water = 30 kg of non - water mass we are looking for the weight of the dry grapes ( x ) . since the question tells us that 10 % of the weight of the dry graps is water and we know that 30 kg is non - water mass we can set up the following equation : x = 1 / 10 ( x ) + 30 kg 9 / 10 ( x ) = 30 kg x = 33.33 kg answer - d"
|
gain
|
math_qa__G7VhUWS8a32NaIJ7
|
A hall 20m long and 15m broad is surrounded by a verandah of uniform width of 2.5m. The cost of flooring the verandah at the rate of Rs.3.50 per sq. meter is Choose the correct choice.
A) 500
B) 600
C) 650
D) 700
E) 750
|
<gadget id="calculator">2.5 * 2</gadget>
<output>5</output>
<gadget id="calculator">20 + 5</gadget>
<output>25</output>
<gadget id="calculator">15 + 5</gadget>
<output>20</output>
<gadget id="calculator">25 * 20</gadget>
<output>500</output>
<gadget id="calculator">20 * 15</gadget>
<output>300</output>
<gadget id="calculator">500 - 300</gadget>
<output>200</output>
<gadget id="calculator">200 * 3.5</gadget>
<output>700</output>
<result>D</result>
|
D
| 700 |
A hall 20m long and 15m broad is surrounded by a verandah of uniform width of 2.5m. The cost of flooring the verandah at the rate of Rs.3.50 per sq. meter is
|
{
"A": "500",
"B": "600",
"C": "650",
"D": "700",
"E": "750"
}
|
multiply(subtract(multiply(add(20, multiply(2.5, const_2)), add(15, multiply(2.5, const_2))), multiply(20, 15)), 3.5)
|
multiply(n2,const_2)|multiply(n0,n1)|add(n0,#0)|add(n1,#0)|multiply(#2,#3)|subtract(#4,#1)|multiply(n3,#5)
|
area of verandah = [ ( 25 ã ƒ â € ” 20 ) ? ( 20 ã ƒ â € ” 15 ) ] m â ² = 200 m â ² cost of flooring = rs . ( 200 ã ƒ â € ” 3.50 ) = rs . 700 answer : d
|
physics
|
math_qa__PHMtfgpu6sG7hZZC
|
A man rows his boat 90 km downstream and 55 km upstream, taking 3 hours each time. Find the speed of the stream?
Choose the correct choice from the following answers: A) 76 kmph B) 6 kmph C) 14 kmph D) 8 kmph E) 4 kmph
|
<gadget id="calculator">90 / 3</gadget>
<output>30</output>
<gadget id="calculator">55 / 3</gadget>
<output>55/3 = around 18.333333</output>
<gadget id="calculator">30 - (55/3)</gadget>
<output>35/3 = around 11.666667</output>
<gadget id="calculator">(35/3) / 2</gadget>
<output>35/6 = around 5.833333</output>
<result>B</result>
|
B
| 6 |
A man rows his boat 90 km downstream and 55 km upstream, taking 3 hours each time. Find the speed of the stream?
|
{
"A": "76 kmph",
"B": "6 kmph",
"C": "14 kmph",
"D": "8 kmph",
"E": "4 kmph"
}
|
divide(subtract(divide(90, 3), divide(55, 3)), const_2)
|
divide(n0,n2)|divide(n1,n2)|subtract(#0,#1)|divide(#2,const_2)|
|
"speed downstream = d / t = 90 / ( 3 ) = 30 kmph speed upstream = d / t = 55 / ( 3 ) = 18 kmph the speed of the stream = ( 30 - 18 ) / 2 = 6 kmph answer : b"
|
physics
|
math_qa__187NbVE6SyNsWhyO
|
Jim is able to sell a hand-carved statue for $540 which was a 35% profit over his cost. How much did the statue originally cost him? Choose the correct choice from the following choices: A) $ 400.00 B) $ 412.40 C) $ 455.40 D) $ 474.90 E) $ 488.20
|
<gadget id="calculator">35 / 100</gadget>
<output>7/20 = around 0.35</output>
<gadget id="calculator">(7/20) + 1</gadget>
<output>27/20 = around 1.35</output>
<gadget id="calculator">540 / (27/20)</gadget>
<output>400</output>
<result>A</result>
|
A
| 400 |
Jim is able to sell a hand-carved statue for $540 which was a 35% profit over his cost. How much did the statue originally cost him?
|
{
"A": "$ 400.00",
"B": "$ 412.40",
"C": "$ 455.40",
"D": "$ 474.90",
"E": "$ 488.20"
}
|
divide(540, add(divide(35, const_100), const_1))
|
divide(n1,const_100)|add(#0,const_1)|divide(n0,#1)
|
540 = 1.35 * x x = 540 / 1.35 = 400 $ 400 , which is ( a ) .
|
gain
|
math_qa__070CWhndLEQFQYpM
|
The standard deviation of a normal distribution of data is 2, and 3 standard deviations below the mean is greater than 45. What is a possible value for the mean of the distribution? Choose the correct choice from the following answers:
A) 52 B) 47 C) 48 D) 49 E) 50
|
<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">45 + 6</gadget>
<output>51</output>
<gadget id="calculator">51 + 1</gadget>
<output>52</output>
<result>A</result>
|
A
| 52 |
The standard deviation of a normal distribution of data is 2, and 3 standard deviations below the mean is greater than 45. What is a possible value for the mean of the distribution?
|
{
"A": "52",
"B": "47",
"C": "48",
"D": "49",
"E": "50"
}
|
add(add(45, multiply(3, 2)), const_1)
|
multiply(n0,n1)|add(n2,#0)|add(#1,const_1)|
|
"the standard deviation ( { sd } ) = 2 ; 3 standard deviations below the mean is greater than 45 : { mean } - 3 * { sd } > 45 ; { mean } - 6 > 45 ; { mean } > 51 . answer : a ."
|
general
|
math_qa__yJKvPvXug2WsYFFC
|
Two trains of length 100 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?
Choose the correct answer
A) 10 sec B) 32 sec C) 82 sec D) 20 sec E) 19 sec
|
<gadget id="calculator">100 + 280</gadget>
<output>380</output>
<gadget id="calculator">42 + 30</gadget>
<output>72</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">72 * (5/18)</gadget>
<output>20</output>
<gadget id="calculator">380 / 20</gadget>
<output>19</output>
<result>E</result>
|
E
| 19 |
Two trains of length 100 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?
|
{
"A": "10 sec",
"B": "32 sec",
"C": "82 sec",
"D": "20 sec",
"E": "19 sec"
}
|
divide(add(100, 280), multiply(add(42, 30), const_0_2778))
|
add(n0,n1)|add(n2,n3)|multiply(#1,const_0_2778)|divide(#0,#2)|
|
"relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 100 + 280 = 380 m . the time required = d / s = 380 / 20 = 19 sec . answer : e"
|
physics
|
math_qa__TDZqDzzUiO2iO8yc
|
The ratio of radius of a circle and the side of a square is 2 : 9. Find the ratio of their areas:
Select the correct option:
A) 2 : 1
B) 4 : 7
C) 8 : 77
D) 4 : 81
E) none
|
<gadget id="calculator">2 / 9</gadget>
<output>2/9 = around 0.222222</output>
<gadget id="calculator">(2/9) ** 2</gadget>
<output>4/81 = around 0.049383</output>
<result>D</result>
|
D
| 0.049383 |
The ratio of radius of a circle and the side of a square is 2 : 9. Find the ratio of their areas:
|
{
"A": "2 : 1",
"B": "4 : 7",
"C": "8 : 77",
"D": "4 : 81",
"E": "none"
}
|
power(divide(2, 9), 2)
|
divide(n0,n1)|power(#0,n0)|
|
"radius / side = 2 / 9 â ‡ ’ area of circle / area of square = 4 / 81 answer : d"
|
geometry
|
math_qa__59j42jkABS7KM554
|
If 12 men can reap 120 acres of land in 36 days, how many acres of land can 24 men reap in 62 days?
Select the correct option
A) 266.5 B) 413.3 C) 425.8 D) 189.3 E) 249.6
|
<gadget id="calculator">24 / 12</gadget>
<output>2</output>
<gadget id="calculator">62 / 36</gadget>
<output>31/18 = around 1.722222</output>
<gadget id="calculator">2 * (31/18)</gadget>
<output>31/9 = around 3.444444</output>
<gadget id="calculator">120 * (31/9)</gadget>
<output>1_240/3 = around 413.333333</output>
<result>B</result>
|
B
| 413.3 |
If 12 men can reap 120 acres of land in 36 days, how many acres of land can 24 men reap in 62 days?
|
{
"A": "266.5",
"B": "413.3",
"C": "425.8",
"D": "189.3",
"E": "249.6"
}
|
multiply(120, multiply(divide(24, 12), divide(62, 36)))
|
divide(n3,n0)|divide(n4,n2)|multiply(#0,#1)|multiply(n1,#2)|
|
"12 men 120 acres 36 days 24 men ? 62 days 120 * 24 / 12 * 62 / 36 120 * 2 * 31 / 18 240 * 1.72 = 413.3 answer : b"
|
physics
|
math_qa__dz0zvdU7dpGtuqs6
|
Evaluate: 10010 - 12*3*2 = ? Options:
A) 30002 B) 70002 C) 50002 D) 90002 E) 10002
|
<gadget id="calculator">12 * 3</gadget>
<output>36</output>
<gadget id="calculator">36 * 2</gadget>
<output>72</output>
<gadget id="calculator">10_010 - 72</gadget>
<output>9_938</output>
<result>E</result>
|
E
| 10,002 |
Evaluate: 10010 - 12*3*2 = ?
|
{
"A": "30002",
"B": "70002",
"C": "50002",
"D": "90002",
"E": "10002"
}
|
subtract(10010, multiply(multiply(12, 3), 2))
|
multiply(n1,n2)|multiply(n3,#0)|subtract(n0,#1)|
|
"according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 10010 - 12 * 3 * 2 = 10010 - 8 = 10002 correct answer e"
|
general
|
math_qa__0zDuzS9yfoRNk2cp
|
A car travels at a speed of 10 miles per hour. How far will it travel in 5 hours? Answers:
A) 50 miles B) 62 miles C) 325 miles D) 70 miles E) 20 miles
|
<gadget id="calculator">10 * 5</gadget>
<output>50</output>
<result>A</result>
|
A
| 50 |
A car travels at a speed of 10 miles per hour. How far will it travel in 5 hours?
|
{
"A": "50 miles",
"B": "62 miles",
"C": "325 miles",
"D": "70 miles",
"E": "20 miles"
}
|
multiply(10, 5)
|
multiply(n0,n1)|
|
"during each hour , the car travels 65 miles . for 5 hours it will travel 10 + 10 + 10 + 10 + 10 = 5 * 10 = 50 miles correct answer a"
|
physics
|
math_qa__qdWCmHUhFD0Az2hX
|
If 42 men do a work in 25 days, in how many days will 50 men do it? Choose the correct answer:
A) 23
B) 22
C) 19
D) 20
E) 21
|
<gadget id="calculator">42 * 25</gadget>
<output>1_050</output>
<gadget id="calculator">1_050 / 50</gadget>
<output>21</output>
<result>E</result>
|
E
| 21 |
If 42 men do a work in 25 days, in how many days will 50 men do it?
|
{
"A": "23",
"B": "22",
"C": "19",
"D": "20",
"E": "21"
}
|
divide(multiply(42, 25), 50)
|
multiply(n0,n1)|divide(#0,n2)|
|
"42 * 25 = 50 * x x = 21 days answer : e"
|
physics
|
math_qa__ZaR3RBYpgc2JWm8C
|
Find large number from below question The difference of two numbers is 1345. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder Choose the correct answer:
A) 1235
B) 1345
C) 1678
D) 1767
E) 1611
|
<gadget id="calculator">1_345 - 15</gadget>
<output>1_330</output>
<gadget id="calculator">6 - 1</gadget>
<output>5</output>
<gadget id="calculator">1_330 / 5</gadget>
<output>266</output>
<gadget id="calculator">266 * 6</gadget>
<output>1_596</output>
<result>E</result>
|
E
| 1,611 |
Find large number from below question The difference of two numbers is 1345. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
|
{
"A": "1235",
"B": "1345",
"C": "1678",
"D": "1767",
"E": "1611"
}
|
multiply(divide(subtract(1345, 15), subtract(6, const_1)), 6)
|
subtract(n0,n2)|subtract(n1,const_1)|divide(#0,#1)|multiply(n1,#2)
|
let the smaller number be x . then larger number = ( x + 1345 ) . x + 1345 = 6 x + 15 5 x = 1330 x = 266 large number = 266 + 1345 = 1611 e
|
general
|
math_qa__73J4ho4aFamu3hsT
|
A train 250 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is? Answers: A) 32 B) 28 C) 29 D) 44 E) 21
|
<gadget id="calculator">250 + 300</gadget>
<output>550</output>
<gadget id="calculator">550 / 1_000</gadget>
<output>11/20 = around 0.55</output>
<gadget id="calculator">45 / 3_600</gadget>
<output>1/80 = around 0.0125</output>
<gadget id="calculator">(11/20) / (1/80)</gadget>
<output>44</output>
<result>D</result>
|
D
| 44 |
A train 250 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is?
|
{
"A": "32",
"B": "28",
"C": "29",
"D": "44",
"E": "21"
}
|
divide(divide(add(250, 300), const_1000), divide(45, const_3600))
|
add(n0,n1)|divide(n2,const_3600)|divide(#0,const_1000)|divide(#2,#1)|
|
"s = ( 250 + 300 ) / 45 = 550 / 45 * 18 / 5 = 44 answer : d"
|
physics
|
math_qa__eMJfY80jUgFBCN1W
|
If there are 10 peanuts in a box and Mary puts 8 more peanuts inside, how many peanuts are in the box? Choose the correct choice from the following answers:
A) 8 B) 9 C) 10 D) 11 E) 18
|
<gadget id="calculator">10 + 8</gadget>
<output>18</output>
<result>E</result>
|
E
| 18 |
If there are 10 peanuts in a box and Mary puts 8 more peanuts inside, how many peanuts are in the box?
|
{
"A": "8",
"B": "9",
"C": "10",
"D": "11",
"E": "18"
}
|
add(10, 8)
|
add(n0,n1)|
|
"10 + 8 = 18 correct answer is e ) 18"
|
general
|
math_qa__7fd9JUv8gDmHCfN8
|
how many positive integers less than 1960 are such that the product of their digits is 10. Choose the correct choice from the following:
A) 220 B) 230 C) 280 D) 220 E) 240
|
<gadget id="calculator">4 + 10</gadget>
<output>14</output>
<gadget id="calculator">14 - 1</gadget>
<output>13</output>
<gadget id="calculator">factorial(13)</gadget>
<output>6_227_020_800</output>
<gadget id="calculator">factorial(10)</gadget>
<output>3_628_800</output>
<gadget id="calculator">4 - 1</gadget>
<output>3</output>
<gadget id="calculator">factorial(3)</gadget>
<output>6</output>
<gadget id="calculator">3_628_800 * 6</gadget>
<output>21_772_800</output>
<gadget id="calculator">6_227_020_800 / 21_772_800</gadget>
<output>286</output>
<result>C</result>
|
C
| 280 |
how many positive integers less than 1960 are such that the product of their digits is 10.
|
{
"A": "220",
"B": "230",
"C": "280",
"D": "220",
"E": "240"
}
|
divide(factorial(subtract(add(const_4, 10), const_1)), multiply(factorial(10), factorial(subtract(const_4, const_1))))
|
add(n1,const_4)|factorial(n1)|subtract(const_4,const_1)|factorial(#2)|subtract(#0,const_1)|factorial(#4)|multiply(#1,#3)|divide(#5,#6)|
|
"1960 is divisible by 10 ( or 2 * 5 ) = 196 196 is divisible by 4 = > 49 49 = 7 * 7 hence 1960 is divisible by 2 , 4,5 , 7 , 7 if there were only one 7 , i . e if the problem were 280 c"
|
general
|
math_qa__eqQyY5NQ5MhyQElW
|
The average runs of a cricket player of 10 innings was 32. How many runs must he makes ih his next innings so as to increase his average of runs by 4? Choose the correct choice from the following choices
A) 2
B) 4
C) 70
D) 76
E) none
|
<gadget id="calculator">10 + 1</gadget>
<output>11</output>
<gadget id="calculator">32 + 4</gadget>
<output>36</output>
<gadget id="calculator">11 * 36</gadget>
<output>396</output>
<gadget id="calculator">32 * 10</gadget>
<output>320</output>
<gadget id="calculator">396 - 320</gadget>
<output>76</output>
<result>D</result>
|
D
| 76 |
The average runs of a cricket player of 10 innings was 32. How many runs must he makes ih his next innings so as to increase his average of runs by 4?
|
{
"A": "2",
"B": "4",
"C": "70",
"D": "76",
"E": "none"
}
|
subtract(multiply(add(10, const_1), add(32, 4)), multiply(32, 10))
|
add(n0,const_1)|add(n1,n2)|multiply(n0,n1)|multiply(#0,#1)|subtract(#3,#2)|
|
"sol . average after 11 innings = 36 . therefore required numbert of runs = ( 36 × 11 ) – ( 32 × 10 ) = 396 - 320 = 76 . answer d"
|
general
|
math_qa__ZTShjpe24qcn3N2D
|
An outlet pipe can empty 2/3 of a cistern in 16 minutes. In 4 minutes, what part of the cistern will be emptied? Choose one
A) 1 / 2 B) 1 / 3 C) 1 / 4 D) 1 / 6 E) 1 / 8
|
<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">4 * (2/3)</gadget>
<output>8/3 = around 2.666667</output>
<gadget id="calculator">(8/3) / 16</gadget>
<output>1/6 = around 0.166667</output>
<result>D</result>
|
D
| 0.166667 |
An outlet pipe can empty 2/3 of a cistern in 16 minutes. In 4 minutes, what part of the cistern will be emptied?
|
{
"A": "1 / 2",
"B": "1 / 3",
"C": "1 / 4",
"D": "1 / 6",
"E": "1 / 8"
}
|
divide(multiply(4, divide(2, 3)), 16)
|
divide(n0,n1)|multiply(n3,#0)|divide(#1,n2)|
|
"4 / 16 * 2 / 3 = 1 / 6 the answer is d ."
|
physics
|
math_qa__6Tf3xvNb7zTE5tsI
|
The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is Rs. 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is? Choose the most appropriate option:
A) rs . 3000 B) rs . 4000 C) rs . 5000 D) rs . 6000 E) rs . 7000
|
<gadget id="calculator">5_050 + 5_200</gadget>
<output>10_250</output>
<gadget id="calculator">10_250 - 6_250</gadget>
<output>4_000</output>
<result>B</result>
|
B
| 4,000 |
The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is Rs. 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is?
|
{
"A": "rs . 3000",
"B": "rs . 4000",
"C": "rs . 5000",
"D": "rs . 6000",
"E": "rs . 7000"
}
|
subtract(add(5050, 5200), 6250)
|
add(n0,n2)|subtract(#0,n1)|
|
"let p , q and r represent their respective monthly incomes . then , we have : p + q = ( 5050 x 2 ) = 10100 . . . . ( i ) q + r = ( 6250 x 2 ) = 12500 . . . . ( ii ) p + r = ( 5200 x 2 ) = 10400 . . . . ( iii ) adding ( i ) , ( ii ) and ( iii ) , we get : 2 ( p + q + r ) = 33000 or p + q + r = 16500 . . . . ( iv ) subtracting ( ii ) from ( iv ) , we get p = 4000 . p ' s monthly income = rs . 4000 . b )"
|
general
|
math_qa__0YSWIY06XaJZBumU
|
A rectangular wall is covered entirely with two kinds of decorative tiles: regular and jumbo. 1/3 of the tiles are jumbo tiles, which have a length three times that of regular tiles and have the same ratio of length to width as the regular tiles. If regular tiles cover 60 square feet of the wall, and no tiles overlap, what is the area of the entire wall? Choose the correct choice from the following answers: A) 160 B) 240 C) 330 D) 440 E) 560
|
<gadget id="calculator">60 * 3</gadget>
<output>180</output>
<gadget id="calculator">180 / 2</gadget>
<output>90</output>
<gadget id="calculator">90 * 3</gadget>
<output>270</output>
<gadget id="calculator">60 + 270</gadget>
<output>330</output>
<result>C</result>
|
C
| 330 |
A rectangular wall is covered entirely with two kinds of decorative tiles: regular and jumbo. 1/3 of the tiles are jumbo tiles, which have a length three times that of regular tiles and have the same ratio of length to width as the regular tiles. If regular tiles cover 60 square feet of the wall, and no tiles overlap, what is the area of the entire wall?
|
{
"A": "160",
"B": "240",
"C": "330",
"D": "440",
"E": "560"
}
|
add(60, multiply(divide(multiply(60, const_3), const_2), 3))
|
multiply(n2,const_3)|divide(#0,const_2)|multiply(n1,#1)|add(n2,#2)
|
the number of jumbo tiles = x . the number of regular tiles = 2 x . assume the ratio of the dimensions of a regular tile is a : a - - > area = a ^ 2 . the dimensions of a jumbo tile is 3 a : 3 a - - > area = 9 a ^ 2 . the area of regular tiles = 2 x * a ^ 2 = 60 . the area of jumbo tiles = x * 9 a ^ 2 = 4.5 ( 2 x * a ^ 2 ) = 4.5 * 60 = 270 . total area = 60 + 270 = 330 . answer : c .
|
geometry
|
math_qa__SXowWM0yAv0NVMxI
|
What is the sum of the multiples of 4 between 19 and 130 inclusive?
Choose the correct answer
A) 2012 B) 2044 C) 2060 D) 2072 E) 2080
|
<gadget id="calculator">130 - 3</gadget>
<output>127</output>
<gadget id="calculator">19 + 2</gadget>
<output>21</output>
<gadget id="calculator">127 + 21</gadget>
<output>148</output>
<gadget id="calculator">148 / 2</gadget>
<output>74</output>
<gadget id="calculator">127 - 21</gadget>
<output>106</output>
<gadget id="calculator">106 / 4</gadget>
<output>53/2 = around 26.5</output>
<gadget id="calculator">(53/2) + 1</gadget>
<output>55/2 = around 27.5</output>
<gadget id="calculator">74 * (55/2)</gadget>
<output>2_035</output>
<result>D</result>
|
D
| 2,072 |
What is the sum of the multiples of 4 between 19 and 130 inclusive?
|
{
"A": "2012",
"B": "2044",
"C": "2060",
"D": "2072",
"E": "2080"
}
|
multiply(divide(add(subtract(130, const_3), add(19, const_2)), const_2), add(divide(subtract(subtract(130, const_3), add(19, const_2)), 4), const_1))
|
add(n1,const_2)|subtract(n2,const_3)|add(#0,#1)|subtract(#1,#0)|divide(#3,n0)|divide(#2,const_2)|add(#4,const_1)|multiply(#6,#5)|
|
"the fastest way in an ap is to find the average and multiply with total integers . . between 19 and 130 , the smallest multiple of 4 is 20 and largest = 128 . . average = ( 20 + 128 ) / 2 = 148 / 2 = 74 . total numbers = ( 128 - 20 ) / 4 + 1 = 27 + 1 = 28 . . sum = 28 * 74 = 2072 ans d"
|
general
|
math_qa__kTbSHdLCeNLFisIz
|
A certain article of clothing was discounted during a special sale to 3/4 of its original retail price. When the clothing didn't sell, it was discounted even further to 2/5 of its original retail price during a second sale. By what percent did the price of this article of clothing decrease from the first sale to the second sale?
Choose the most appropriate option
A) 50 %
B) 33.33 %
C) 25 %
D) 46.66 %
E) 12.5 %
|
<gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">2 / 5</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(3/4) * (2/5)</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(3/4) - (3/10)</gadget>
<output>9/20 = around 0.45</output>
<gadget id="calculator">(9/20) * 100</gadget>
<output>45</output>
<result>D</result>
|
D
| 46.66 |
A certain article of clothing was discounted during a special sale to 3/4 of its original retail price. When the clothing didn't sell, it was discounted even further to 2/5 of its original retail price during a second sale. By what percent did the price of this article of clothing decrease from the first sale to the second sale?
|
{
"A": "50 %",
"B": "33.33 %",
"C": "25 %",
"D": "46.66 %",
"E": "12.5 %"
}
|
multiply(subtract(divide(3, 4), multiply(divide(3, 4), divide(2, 5))), const_100)
|
divide(n0,n1)|divide(n2,n3)|multiply(#0,#1)|subtract(#0,#2)|multiply(#3,const_100)
|
say the original retail price of the item was $ 200 . the price after the first sale = 3 / 4 * $ 200 = $ 150 . the price after the second sale = 2 / 5 * $ 200 = $ 80 . the percent change from the first sale to the second = ( 150 - 80 ) / 150 = 1 / 3 = 46.66 % . answer : d .
|
gain
|
math_qa__cs3JMJu8UFKNSSvl
|
Bruce and Anne can clean their house in 4 hours working together at their respective constant rates. If Anne’s speed were doubled, they could clean their house in 3 hours working at their respective rates. How many hours does it currently take Anne to clean the house on her own? Pick.
A) 6
B) 7
C) 8
D) 12
E) 14
|
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/3) - (1/4)</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">1 / (1/12)</gadget>
<output>12</output>
<result>D</result>
|
D
| 12 |
Bruce and Anne can clean their house in 4 hours working together at their respective constant rates. If Anne’s speed were doubled, they could clean their house in 3 hours working at their respective rates. How many hours does it currently take Anne to clean the house on her own?
|
{
"A": "6",
"B": "7",
"C": "8",
"D": "12",
"E": "14"
}
|
inverse(subtract(divide(const_1, 3), divide(const_1, 4)))
|
divide(const_1,n1)|divide(const_1,n0)|subtract(#0,#1)|inverse(#2)|
|
"lets suppose anne and bruce take a and b hrs working separately so in 1 hour they can together finish 1 / a + 1 / b portion of the work which equals 1 / 4 ( as the work is completed in 4 hours ) after anne doubles her rate of work the portion completed by the both is 1 / a + 2 / b which is equal to 1 / 3 ( as the work is completed in 3 hours ) solving these 2 equations we can find b as 12 answer : d"
|
physics
|
math_qa__n8E3Pp67NqHl3RGQ
|
If p and q are prime numbers, how many divisors does the product p^3 * q^6 have? Choices:
A) 9 B) 12 C) 18 D) 28 E) 363
|
<gadget id="calculator">3 + 1</gadget>
<output>4</output>
<gadget id="calculator">6 + 1</gadget>
<output>7</output>
<gadget id="calculator">4 * 7</gadget>
<output>28</output>
<result>D</result>
|
D
| 28 |
If p and q are prime numbers, how many divisors does the product p^3 * q^6 have?
|
{
"A": "9",
"B": "12",
"C": "18",
"D": "28",
"E": "363"
}
|
multiply(add(3, const_1), add(6, const_1))
|
add(n0,const_1)|add(n1,const_1)|multiply(#0,#1)|
|
", p ^ 2 , p ^ 3 and q , q ^ 1 , q ^ 2 . . . . q ^ 6 together essentially there are 18 different combinations you can make ( 3 x 6 ) also you have to include the different combinations the p and q exponents can be a divisor . there are 3 different p exponents and 6 different q exponents : p , p ^ 2 , p ^ 3 , q , q ^ 2 , q ^ 3 . . . q ^ 6 also add 1 since ` ` 1 ' ' can also be a divisor . 18 + 3 + 6 + 1 = 28 , answer : d"
|
general
|
math_qa__riy1BiAZ3SLjjFcs
|
In a renowned city, the average birth rate is 6 people every two seconds and the death rate is 2 people every two seconds. Estimate the size of the population net increase that occurs in one day. Choose the correct choice from the following.
A) 32,300
B) 172,800
C) 468,830
D) 338,200
E) 259,200
|
<gadget id="calculator">6 - 2</gadget>
<output>4</output>
<gadget id="calculator">4 * 3_600</gadget>
<output>14_400</output>
<gadget id="calculator">14_400 * 12</gadget>
<output>172_800</output>
<result>B</result>
|
B
| 172,800 |
In a renowned city, the average birth rate is 6 people every two seconds and the death rate is 2 people every two seconds. Estimate the size of the population net increase that occurs in one day.
|
{
"A": "32,300",
"B": "172,800",
"C": "468,830",
"D": "338,200",
"E": "259,200"
}
|
multiply(multiply(subtract(6, 2), const_3600), const_12)
|
subtract(n0,n1)|multiply(#0,const_3600)|multiply(#1,const_12)|
|
"every 2 seconds , 4 persons are added ( 6 - 2 ) . every second 2 persons are added . in a day 24 hrs = 24 * 60 minutes = 24 * 60 * 60 = 86400 seconds . 86400 * 2 = 172800 option b is the answer ."
|
general
|
math_qa__navXPplyR53Sz3jM
|
For every X, the action [X] is defined: [X] is the greatest integer less than or equal to X. What is the value of [6.5] x [2/3] + [2] x 7.2 + [8.3] - 6.6? Choose the most appropriate option:
A) 12.6 .
B) 15.8 .
C) 14.4 .
D) 16.2 .
E) 16.4 .
|
<gadget id="calculator">2 * 7.2</gadget>
<output>14.4</output>
<gadget id="calculator">4 / 10</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">8.3 - (2/5)</gadget>
<output>7.9</output>
<gadget id="calculator">14.4 + 7.9</gadget>
<output>22.3</output>
<gadget id="calculator">22.3 - 6.6</gadget>
<output>15.7</output>
<result>B</result>
|
B
| 15.8 |
For every X, the action [X] is defined: [X] is the greatest integer less than or equal to X. What is the value of [6.5] x [2/3] + [2] x 7.2 + [8.3] - 6.6?
|
{
"A": "12.6 .",
"B": "15.8 .",
"C": "14.4 .",
"D": "16.2 .",
"E": "16.4 ."
}
|
subtract(add(multiply(2, 7.2), subtract(8.3, divide(const_4, const_10))), 6.6)
|
divide(const_4,const_10)|multiply(n1,n4)|subtract(n5,#0)|add(#1,#2)|subtract(#3,n6)|
|
"[ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.3 ] - 6.6 = 6 * 0 + 2 * 7.2 + 8 - 6.6 = 0 + 14.4 + 1.4 15.8 answer b"
|
general
|
math_qa__DhzXOoLNy1kezI66
|
In a group of 25, 13 can speak Latin, 15 can speak French, and 6 don't speak either. How many of these speak both Latin and French? Options
A) 9 B) 10 C) 11 D) 12 E) 8
|
<gadget id="calculator">13 + 15</gadget>
<output>28</output>
<gadget id="calculator">28 + 6</gadget>
<output>34</output>
<gadget id="calculator">34 - 25</gadget>
<output>9</output>
<result>A</result>
|
A
| 9 |
In a group of 25, 13 can speak Latin, 15 can speak French, and 6 don't speak either. How many of these speak both Latin and French?
|
{
"A": "9",
"B": "10",
"C": "11",
"D": "12",
"E": "8"
}
|
subtract(add(add(13, 15), 6), 25)
|
add(n1,n2)|add(n3,#0)|subtract(#1,n0)
|
let no . of persons who speeks booth latin and french = x so , no . of persons who speeks only latin = 13 - x no . of persons who speeks only french = 15 - x no . of persons who speeks dont speek any lag = 6 therefore ( 13 - x ) + ( 15 - x ) + x + 6 = 25 34 - x = 25 x = 9 answer : a
|
other
|
math_qa__k0A0vXTRnrJcShXk
|
In what ratio should a 20% methyl alcohol solution be mixed with a 50% methyl alcohol solution so that the resultant solution has 40% methyl alcohol in it? Choose the correct choice: A) 1 : 3 B) 1 : 2 C) 2 : 3 D) 2 : 1 E) 3 : 1
|
<gadget id="calculator">50 - 40</gadget>
<output>10</output>
<gadget id="calculator">40 - 20</gadget>
<output>20</output>
<gadget id="calculator">10 / 20</gadget>
<output>1/2 = around 0.5</output>
<result>B</result>
|
B
| 0.5 |
In what ratio should a 20% methyl alcohol solution be mixed with a 50% methyl alcohol solution so that the resultant solution has 40% methyl alcohol in it?
|
{
"A": "1 : 3",
"B": "1 : 2",
"C": "2 : 3",
"D": "2 : 1",
"E": "3 : 1"
}
|
divide(subtract(50, 40), subtract(40, 20))
|
subtract(n1,n2)|subtract(n2,n0)|divide(#0,#1)
|
two things to remember : - 1 ) the ratio of quantity mixed to get an average is related to the ratio of each qty ' s distance from average . 2 ) more the qty of x from that of y , more closer will be average to x . . qty of 20 % / qty of 50 % = ( 50 − 40 ) / ( 40 − 20 ) = 1 / 2 = 1 : 2 answer : b
|
other
|
math_qa__XuNk5gaQ04ec4GG8
|
Each of the 42 points is placed either inside or on the surface of a perfect sphere. If 65% or fewer of the points touch the surface, what is the maximum number of segments which, if connected from those points to form chords, could be the diameter of the sphere? Choose the correct choice from the following
A) 7
B) 11
C) 13
D) 23
E) 38
|
<gadget id="calculator">65 / 100</gadget>
<output>13/20 = around 0.65</output>
<gadget id="calculator">42 * (13/20)</gadget>
<output>273/10 = around 27.3</output>
<gadget id="calculator">(273/10) / 2</gadget>
<output>273/20 = around 13.65</output>
<result>C</result>
|
C
| 13 |
Each of the 42 points is placed either inside or on the surface of a perfect sphere. If 65% or fewer of the points touch the surface, what is the maximum number of segments which, if connected from those points to form chords, could be the diameter of the sphere?
|
{
"A": "7",
"B": "11",
"C": "13",
"D": "23",
"E": "38"
}
|
divide(multiply(42, divide(65, const_100)), const_2)
|
divide(n1,const_100)|multiply(n0,#0)|divide(#1,const_2)|
|
"maximum number of points on the surface is 65 % * 42 = 27.3 . . . or 27 since it has to be an integer now note that if two points form a diameter , they can not be part of any other diameter . so in the best case we can pair up the points we have 27 points , so at best we can form 13 pairs ( 26 ) . so , answer is ( c )"
|
geometry
|
math_qa__cUF1Qq6PktUZ2kwT
|
Rs. 800 becomes Rs. 956 in 3 years at a certain rate of simple interest. If the rate of interest is increased by 4%, what amount will Rs. 800 become in 3 years.
Pick one
A) rupees 1052
B) rs 1152
C) rs 1252
D) rs 1352
E) none of these
|
<gadget id="calculator">956 - 800</gadget>
<output>156</output>
<gadget id="calculator">156 * 100</gadget>
<output>15_600</output>
<gadget id="calculator">800 * 3</gadget>
<output>2_400</output>
<gadget id="calculator">15_600 / 2_400</gadget>
<output>13/2 = around 6.5</output>
<gadget id="calculator">(13/2) + 4</gadget>
<output>21/2 = around 10.5</output>
<gadget id="calculator">800 * (21/2)</gadget>
<output>8_400</output>
<gadget id="calculator">8_400 * 3</gadget>
<output>25_200</output>
<gadget id="calculator">25_200 / 100</gadget>
<output>252</output>
<gadget id="calculator">800 + 252</gadget>
<output>1_052</output>
<result>A</result>
|
A
| 1,052 |
Rs. 800 becomes Rs. 956 in 3 years at a certain rate of simple interest. If the rate of interest is increased by 4%, what amount will Rs. 800 become in 3 years.
|
{
"A": "rupees 1052",
"B": "rs 1152",
"C": "rs 1252",
"D": "rs 1352",
"E": "none of these"
}
|
add(800, divide(multiply(multiply(800, add(divide(multiply(subtract(956, 800), const_100), multiply(800, 3)), 4)), 3), const_100))
|
multiply(n0,n2)|subtract(n1,n0)|multiply(#1,const_100)|divide(#2,#0)|add(n3,#3)|multiply(n0,#4)|multiply(n2,#5)|divide(#6,const_100)|add(n0,#7)
|
explanation : s . i . = 956 - 800 = rs 156 r = 156 ∗ 100 / 800 ∗ 3 r = 6 1 / 2 % new rate = 6 1 / 2 + 4 = 21 / 2 % new s . i . = 800 × 21 / 2 × 3100 = 252 now amount will be 800 + 252 = 1052 option a
|
gain
|
math_qa__NVfMgrJEJuSTzEYI
|
In the rectangular coordinate system, if the line x = 8y + 5 passes through points (m,n) and (m + 2,n + p), what is the value of p? Pick:
A) 1 / 2 B) 1 / 3 C) 1 / 4 D) 1 / 5 E) 1 / 6
|
<gadget id="calculator">2 / 8</gadget>
<output>1/4 = around 0.25</output>
<result>C</result>
|
C
| 0.25 |
In the rectangular coordinate system, if the line x = 8y + 5 passes through points (m,n) and (m + 2,n + p), what is the value of p?
|
{
"A": "1 / 2",
"B": "1 / 3",
"C": "1 / 4",
"D": "1 / 5",
"E": "1 / 6"
}
|
divide(2, 8)
|
divide(n2,n0)|
|
"x = 8 y + 5 , and thus y = x / 8 - 5 / 8 the slope is 1 / 8 . the slope of a line through points ( m , n ) and ( m + 2 , n + p ) is ( n + p - n ) / ( m + 2 - m ) = p / 2 p / 2 = 1 / 8 and thus p = 1 / 4 the answer is c ."
|
general
|
math_qa__gfDnomqG9VsEkyqA
|
If x,y ,and z are positive real numbers such that x+y-z = 62, y-z+x =82 , and z-x+y = 100, then find the x+y+z value?
Select the correct option.
A) 80 B) 91 C) 62 D) 74 E) 82
|
<gadget id="calculator">82 - 62</gadget>
<output>20</output>
<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<result>E</result>
|
E
| 82 |
If x,y ,and z are positive real numbers such that x+y-z = 62, y-z+x =82 , and z-x+y = 100, then find the x+y+z value?
|
{
"A": "80",
"B": "91",
"C": "62",
"D": "74",
"E": "82"
}
|
subtract(100, subtract(82, 62))
|
subtract(n1,n0)|subtract(n2,#0)|
|
"x + y - z = 62 , - - - - - - 1 ) y - z + x = 82 , - - - - - - 2 ) z - x + y = 100 - - - - - - 3 ) from ( 1 ) & ( 2 ) 2 z = 20 z = 10 from ( 2 ) & ( 3 ) 2 y = 182 y = 91 then x = 62 - 81 = - 19 x + y + z = 82 correct option is e"
|
general
|
math_qa__VXZKGuxWqZfsQ9iL
|
How many seconds will a 400 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
Choices
A) 24
B) 30
C) 40
D) 45
E) 50
|
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">63 - 3</gadget>
<output>60</output>
<gadget id="calculator">(5/18) * 60</gadget>
<output>50/3 = around 16.666667</output>
<gadget id="calculator">400 / (50/3)</gadget>
<output>24</output>
<result>A</result>
|
A
| 24 |
How many seconds will a 400 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
|
{
"A": "24",
"B": "30",
"C": "40",
"D": "45",
"E": "50"
}
|
divide(400, multiply(const_0_2778, subtract(63, 3)))
|
subtract(n2,n1)|multiply(#0,const_0_2778)|divide(n0,#1)|
|
"relative speed of the train = 63 - 3 = 60 kmph = 60 * 5 / 18 = 50 / 3 m / sec t = 400 * 3 / 50 = 24 sec answer : a"
|
physics
|
math_qa__flHcqw6goqvlud2X
|
The population of a town is 10000. It decreases annually at the rate of 10% p.a. What will be its population after 2 years?
Select the correct option
A) 4300 B) 4500 C) 8100 D) 5230 E) 5366
|
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">10_000 * (1/10)</gadget>
<output>1_000</output>
<gadget id="calculator">10_000 - 1_000</gadget>
<output>9_000</output>
<gadget id="calculator">9_000 * (1/10)</gadget>
<output>900</output>
<gadget id="calculator">9_000 - 900</gadget>
<output>8_100</output>
<result>C</result>
|
C
| 8,100 |
The population of a town is 10000. It decreases annually at the rate of 10% p.a. What will be its population after 2 years?
|
{
"A": "4300",
"B": "4500",
"C": "8100",
"D": "5230",
"E": "5366"
}
|
subtract(subtract(10000, multiply(10000, divide(10, const_100))), multiply(subtract(10000, multiply(10000, divide(10, const_100))), divide(10, const_100)))
|
divide(n1,const_100)|multiply(n0,#0)|subtract(n0,#1)|multiply(#0,#2)|subtract(#2,#3)|
|
"10000 × 90 / 100 × 90 / 100 = 8100 answer : c"
|
gain
|
math_qa__kwNMBOajtjXqj2MH
|
A boat running downstream covers a distance of 10km in 3hr while for covering the same distance upstream, it takes 6hr.
What is the speed of the boat?
Choose the correct choice from the following options
A) 2.5 kmph B) 3.5 kmph C) 4.5 kmph D) 1.5 kmph E) 9.5 kmph
|
<gadget id="calculator">10 / 3</gadget>
<output>10/3 = around 3.333333</output>
<gadget id="calculator">10 / 6</gadget>
<output>5/3 = around 1.666667</output>
<gadget id="calculator">(10/3) + (5/3)</gadget>
<output>5</output>
<gadget id="calculator">5 / 2</gadget>
<output>5/2 = around 2.5</output>
<result>A</result>
|
A
| 2.5 |
A boat running downstream covers a distance of 10km in 3hr while for covering the same distance upstream, it takes 6hr.
What is the speed of the boat?
|
{
"A": "2.5 kmph",
"B": "3.5 kmph",
"C": "4.5 kmph",
"D": "1.5 kmph",
"E": "9.5 kmph"
}
|
divide(add(divide(10, 3), divide(10, 6)), const_2)
|
divide(n0,n1)|divide(n0,n2)|add(#0,#1)|divide(#2,const_2)
|
speed upstream = 10 / 3 speed of boat down stream = 10 / 6 speed of boat = 1 / 2 ( 10 / 3 + 10 / 6 ) = 2.5 kmph answer : a
|
physics
|
math_qa__hacI1Mk6K2ssIWbL
|
The length of a room is 8 m and width is 4.75 m. What is the cost of paying the floor by slabs at the rate of Rs. 900 per sq. metre. Choose the correct answer:
A) 25650
B) 25750
C) 26550
D) 26750
E) 34200
|
<gadget id="calculator">8 * 4.75</gadget>
<output>38</output>
<gadget id="calculator">900 * 38</gadget>
<output>34_200</output>
<result>E</result>
|
E
| 34,200 |
The length of a room is 8 m and width is 4.75 m. What is the cost of paying the floor by slabs at the rate of Rs. 900 per sq. metre.
|
{
"A": "25650",
"B": "25750",
"C": "26550",
"D": "26750",
"E": "34200"
}
|
multiply(900, multiply(8, 4.75))
|
multiply(n0,n1)|multiply(n2,#0)|
|
"area = 8 × 4.75 sq . metre . cost for 1 sq . metre . = rs . 900 hence total cost = 8 × 4.75 × 900 = 8 × 4275 = rs . 34200 answer is e ."
|
physics
|
math_qa__QS1T3Q0IMp8xL9HN
|
A person distributed 15% of his income to his 3 children each. He deposited 30% of his income to his wife's account. He donated 5% of remaining amount to an orphan house.Finally he has $40000. Find his total income? Choices: A) 452000 B) 200000 C) 800000 D) 500000 E) 652000
|
<gadget id="calculator">15 * 3</gadget>
<output>45</output>
<gadget id="calculator">45 + 30</gadget>
<output>75</output>
<gadget id="calculator">75 + 5</gadget>
<output>80</output>
<gadget id="calculator">100 - 80</gadget>
<output>20</output>
<gadget id="calculator">40_000 / 20</gadget>
<output>2_000</output>
<gadget id="calculator">2_000 * 100</gadget>
<output>200_000</output>
<result>B</result>
|
B
| 200,000 |
A person distributed 15% of his income to his 3 children each. He deposited 30% of his income to his wife's account. He donated 5% of remaining amount to an orphan house.Finally he has $40000. Find his total income?
|
{
"A": "452000",
"B": "200000",
"C": "800000",
"D": "500000",
"E": "652000"
}
|
multiply(divide(40000, subtract(const_100, add(add(multiply(15, 3), 30), 5))), const_100)
|
multiply(n0,n1)|add(n2,#0)|add(n3,#1)|subtract(const_100,#2)|divide(n4,#3)|multiply(#4,const_100)|
|
"3 children got = 3 * 15 % = 45 % wife got = 30 % orphan house = 5 % total = 45 + 30 + 5 = 80 % remaining = 100 - 80 = 20 % 20 % = 40000 100 % = 40000 * 100 / 20 = $ 200000 answer is b"
|
gain
|
math_qa__Xv4OpTC1oXjxZOEN
|
The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 81. What is the difference between the two digits of that number? Choose one: A) 4 B) 5 C) 6 D) 8 E) 9
|
<gadget id="calculator">10 - 1</gadget>
<output>9</output>
<gadget id="calculator">81 / 9</gadget>
<output>9</output>
<result>E</result>
|
E
| 9 |
The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 81. What is the difference between the two digits of that number?
|
{
"A": "4",
"B": "5",
"C": "6",
"D": "8",
"E": "9"
}
|
divide(81, subtract(const_10, const_1))
|
subtract(const_10,const_1)|divide(n0,#0)|
|
"sol . let the ten ’ s digit be x and unit ’ s digit be y , then , ( 10 x + y ) - ( 10 y + x ) = 81 ⇔ 9 ( x - y ) = 81 ⇔ x - y = 9 answer e"
|
general
|
math_qa__vXtOfb1Z0JFxUrSP
|
A and B runs around a circular track. A beats B by one round or 10 minutes. In this race, they had completed 4 rounds. If the race was only of one round, find the A's time over the course: Pick one: A) 8.5 min B) 7.5 min C) 1.5 min D) 9.5 min E) 4.5 min
|
<gadget id="calculator">4 - 1</gadget>
<output>3</output>
<gadget id="calculator">3 * 10</gadget>
<output>30</output>
<gadget id="calculator">30 / 4</gadget>
<output>15/2 = around 7.5</output>
<result>B</result>
|
B
| 7.5 |
A and B runs around a circular track. A beats B by one round or 10 minutes. In this race, they had completed 4 rounds. If the race was only of one round, find the A's time over the course:
|
{
"A": "8.5 min",
"B": "7.5 min",
"C": "1.5 min",
"D": "9.5 min",
"E": "4.5 min"
}
|
divide(multiply(subtract(4, const_1), 10), 4)
|
subtract(n1,const_1)|multiply(n0,#0)|divide(#1,n1)
|
explanation : b runs around the track in 10 min . i . e , speed of b = 10 min per round a beats b by 1 round time taken by a to complete 4 rounds = time taken by b to complete 3 rounds = 30 min a ' s speed = 30 / 4 min per round = 7.5 min per round hence , if the race is only of one round a ' s time over the course = 7 min 30 sec answer : b
|
physics
|
math_qa__EL59unClkDc0imOF
|
A certain industrial loom weaves 0.127 meters of cloth every second. Approximately how many seconds will it take for the loom to weave 15 meters of cloth?
Choose the correct choice:
A) 114 B) 115 C) 116 D) 117 E) 118
|
<gadget id="calculator">15 / 0.127</gadget>
<output>118.110236</output>
<result>E</result>
|
E
| 118 |
A certain industrial loom weaves 0.127 meters of cloth every second. Approximately how many seconds will it take for the loom to weave 15 meters of cloth?
|
{
"A": "114",
"B": "115",
"C": "116",
"D": "117",
"E": "118"
}
|
divide(15, 0.127)
|
divide(n1,n0)|
|
"let the required number of seconds be x more cloth , more time , ( direct proportion ) hence we can write as ( cloth ) 0.127 : 15 : : 1 : x = > 0.127 * x = 15 = > x = 15 / 0.127 = > x = 118 answer : e"
|
physics
|
math_qa__jdnW9MnqBXfWerAQ
|
The average marks of a class of 35 students is 45 and that of another class of 55 students is 65. Find the average marks of all the students?
Choose the correct choice from the following options.
A) 52.6 B) 52.4 C) 52.1 D) 57 E) 52.9
|
<gadget id="calculator">35 * 45</gadget>
<output>1_575</output>
<gadget id="calculator">55 * 65</gadget>
<output>3_575</output>
<gadget id="calculator">1_575 + 3_575</gadget>
<output>5_150</output>
<gadget id="calculator">35 + 55</gadget>
<output>90</output>
<gadget id="calculator">5_150 / 90</gadget>
<output>515/9 = around 57.222222</output>
<result>D</result>
|
D
| 57 |
The average marks of a class of 35 students is 45 and that of another class of 55 students is 65. Find the average marks of all the students?
|
{
"A": "52.6",
"B": "52.4",
"C": "52.1",
"D": "57",
"E": "52.9"
}
|
divide(add(multiply(35, 45), multiply(55, 65)), add(35, 55))
|
add(n0,n2)|multiply(n0,n1)|multiply(n2,n3)|add(#1,#2)|divide(#3,#0)|
|
"sum of the marks for the class of 35 students = 35 * 45 = 1575 sum of the marks for the class of 55 students = 55 * 65 = 3575 sum of the marks for the class of 90 students = 1575 + 3575 = 5150 average marks of all the students = 5150 / 90 = 57 . answer : d"
|
general
|
math_qa__pUllKJeAPiuWCgzf
|
A and B together have $100. If 3/10 of A's amount is equal to 1/5 of B's amount, how much amount does B have? Choose the correct choice from the following
A) $ 60 B) $ 55 C) $ 42 D) $ 31 E) $ 100
|
<gadget id="calculator">1 / 5</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">3 / 10</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(1/5) / (3/10)</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(2/3) + 1</gadget>
<output>5/3 = around 1.666667</output>
<gadget id="calculator">100 / (5/3)</gadget>
<output>60</output>
<result>A</result>
|
A
| 60 |
A and B together have $100. If 3/10 of A's amount is equal to 1/5 of B's amount, how much amount does B have?
|
{
"A": "$ 60",
"B": "$ 55",
"C": "$ 42",
"D": "$ 31",
"E": "$ 100"
}
|
divide(100, add(divide(divide(1, 5), divide(3, 10)), const_1))
|
divide(n3,n4)|divide(n1,n2)|divide(#0,#1)|add(#2,const_1)|divide(n0,#3)|
|
"3 / 10 a = 1 / 5 b a = 1 / 5 * 10 / 3 b a = 2 / 3 b a / b = 2 / 3 a : b = 2 : 3 b ' s share = 100 * 3 / 5 = $ 60 answer is a"
|
general
|
math_qa__zAxyC46BbMVM85I8
|
If the given two numbers are respectively 6% and 30% of a third number, then what percentage is the first of the second ? Select the correct option: A) 20 % B) 25 % C) 18 % D) 30 % E) none of these
|
<gadget id="calculator">6 / 100</gadget>
<output>3/50 = around 0.06</output>
<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(3/50) / (3/10)</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 100</gadget>
<output>20</output>
<result>A</result>
|
A
| 20 |
If the given two numbers are respectively 6% and 30% of a third number, then what percentage is the first of the second ?
|
{
"A": "20 %",
"B": "25 %",
"C": "18 %",
"D": "30 %",
"E": "none of these"
}
|
multiply(divide(divide(6, const_100), divide(30, const_100)), const_100)
|
divide(n0,const_100)|divide(n1,const_100)|divide(#0,#1)|multiply(#2,const_100)
|
here , l = 6 and m = 30 therefore , first number = l / m x 100 % of second number = 6 / 30 x 100 % of second number = 20 % of second number answer : a
|
gain
|
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