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__UX8c8f1mSGLhEsuZ
|
David obtained 76, 65, 82, 67 and 85 marks (out of 100) in English, mathematics, physics, chemistry and biology. What are his average marks? Choose the correct choice from the following options.
A) 65 B) 69 C) 75 D) none of these E) can not be determined
|
<gadget id="calculator">76 + 65</gadget>
<output>141</output>
<gadget id="calculator">141 + 82</gadget>
<output>223</output>
<gadget id="calculator">223 + 67</gadget>
<output>290</output>
<gadget id="calculator">290 + 85</gadget>
<output>375</output>
<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">375 / 5</gadget>
<output>75</output>
<result>C</result>
|
C
| 75 |
David obtained 76, 65, 82, 67 and 85 marks (out of 100) in English, mathematics, physics, chemistry and biology. What are his average marks?
|
{
"A": "65",
"B": "69",
"C": "75",
"D": "none of these",
"E": "can not be determined"
}
|
divide(add(add(add(add(76, 65), 82), 67), 85), add(const_2, const_3))
|
add(n0,n1)|add(const_2,const_3)|add(n2,#0)|add(n3,#2)|add(n4,#3)|divide(#4,#1)|
|
"solution : average = ( 76 + 65 + 82 + 67 + 85 ) / 5 = 375 / 5 = 75 . hence , average = 75 . answer : option c"
|
general
|
math_qa__NHp9sl8N8vtiUdYK
|
if the ratio of s.i earned on certain amount on same rate is 4:5.what is the ratio of time? Choose one
A) 1 : 2 B) 6 : 9 C) 4 : 5 D) 2 : 3 E) not possible to calculate
|
<gadget id="calculator">4 / 5</gadget>
<output>4/5 = around 0.8</output>
<result>C</result>
|
C
| 0.8 |
if the ratio of s.i earned on certain amount on same rate is 4:5.what is the ratio of time?
|
{
"A": "1 : 2",
"B": "6 : 9",
"C": "4 : 5",
"D": "2 : 3",
"E": "not possible to calculate"
}
|
divide(4, 5)
|
divide(n0,n1)
|
s . i 1 / s . i 2 = [ ( p * r * t 1 ) / 100 ] / [ ( p * r * t 2 ) / 100 ] 4 / 5 = t 1 / t 2 ratio = 4 : 5 answer c
|
other
|
math_qa__KDwlJzxgNOxnNMAm
|
Dick and Jane each saved $2,000 in 1989. In 1990 Dick saved 10 percent more than in 1989, and together he and Jane saved a total of $4,000. Approximately what percent less did Jane save in 1990 than in 1989? Pick one.
A) 10 % B) 20 % C) 25 % D) 30 % E) 35 %
|
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/10) + 1</gadget>
<output>11/10 = around 1.1</output>
<gadget id="calculator">2 - (11/10)</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">1 - (9/10)</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/10) * 100</gadget>
<output>10</output>
<result>A</result>
|
A
| 10 |
Dick and Jane each saved $2,000 in 1989. In 1990 Dick saved 10 percent more than in 1989, and together he and Jane saved a total of $4,000. Approximately what percent less did Jane save in 1990 than in 1989?
|
{
"A": "10 %",
"B": "20 %",
"C": "25 %",
"D": "30 %",
"E": "35 %"
}
|
multiply(subtract(const_1, subtract(const_2, add(divide(10, const_100), const_1))), const_100)
|
divide(n3,const_100)|add(#0,const_1)|subtract(const_2,#1)|subtract(const_1,#2)|multiply(#3,const_100)|
|
"1990 dick saved = $ 2200 jane saved = $ 1800 ( jane saved $ 200 less than she did the prior year ) jane saved approximately $ 200 / 2000 $ ( 10 % ) less in 1990 answer : a"
|
general
|
math_qa__Q2HDnMLw6aqvCOYl
|
Tough and Tricky questions: Exponents.
If 7^(3x-1)*3^(4y-3) = 49^x*27^y, then x + y = Choose the correct choice from the following answers:
A) 3
B) 4
C) 2
D) 1
E) 5
|
<gadget id="calculator">1 + 3</gadget>
<output>4</output>
<result>B</result>
|
B
| 4 |
Tough and Tricky questions: Exponents.
If 7^(3x-1)*3^(4y-3) = 49^x*27^y, then x + y =
|
{
"A": "3",
"B": "4",
"C": "2",
"D": "1",
"E": "5"
}
|
add(1, 3)
|
add(n1,n2)
|
here is my solution . 7 ^ ( 3 x - 1 ) * 3 ^ ( 4 y - 3 ) = 49 ^ x * 27 ^ y here rhs 49 ^ x * 27 ^ y = 7 ^ ( 2 x ) * 3 ^ ( 3 y ) equating powers on both sides - - > 3 x - 1 = 2 x , thus x = 1 and 4 y - 3 = 3 y giving y = 3 so , x + y = 4 option : b
|
general
|
math_qa__dcNUKi3JGtWBX32s
|
A candidate got 35% of the votes polled and he lost to his rival by 2250 votes. How many votes were cast? Select:
A) 7500
B) 3388
C) 2665
D) 2888
E) 2661
|
<gadget id="calculator">35 / 100</gadget>
<output>7/20 = around 0.35</output>
<gadget id="calculator">1 - (7/20)</gadget>
<output>13/20 = around 0.65</output>
<gadget id="calculator">(13/20) - (7/20)</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">2_250 / (3/10)</gadget>
<output>7_500</output>
<result>A</result>
|
A
| 7,500 |
A candidate got 35% of the votes polled and he lost to his rival by 2250 votes. How many votes were cast?
|
{
"A": "7500",
"B": "3388",
"C": "2665",
"D": "2888",
"E": "2661"
}
|
divide(2250, subtract(subtract(const_1, divide(35, const_100)), divide(35, const_100)))
|
divide(n0,const_100)|subtract(const_1,#0)|subtract(#1,#0)|divide(n1,#2)
|
35 % - - - - - - - - - - - l 65 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 30 % - - - - - - - - - - 2250 100 % - - - - - - - - - ? = > 7500 answer : a
|
gain
|
math_qa__zSfndFeXT9jQ19CH
|
Find the ratio in which rice at Rs. 7.20 a kg be mixed with rice at Rs. 5.70 a kg to produce a mixture worth Rs. 6.30 a kg. Pick one
A) 1 : 2 B) 2 : 3 C) 3 : 4 D) 3 : 5 E) 4 : 5
|
<gadget id="calculator">6.3 - 5.7</gadget>
<output>0.6</output>
<gadget id="calculator">7.2 - 6.3</gadget>
<output>0.9</output>
<gadget id="calculator">0.6 / 0.9</gadget>
<output>0.666667</output>
<result>B</result>
|
B
| 0.666667 |
Find the ratio in which rice at Rs. 7.20 a kg be mixed with rice at Rs. 5.70 a kg to produce a mixture worth Rs. 6.30 a kg.
|
{
"A": "1 : 2",
"B": "2 : 3",
"C": "3 : 4",
"D": "3 : 5",
"E": "4 : 5"
}
|
divide(subtract(6.30, 5.70), subtract(7.20, 6.30))
|
subtract(n2,n1)|subtract(n0,n2)|divide(#0,#1)|
|
"req = 60 : 90 = 2 : 3 answer b"
|
other
|
math_qa__SYuSJfhXLe4yUl38
|
A volume of 11248 l water is in a container of sphere. How many hemisphere of volume 4l each will be required to transfer all the water into the small hemispheres?
Options: A) 2812 B) 8231 C) 2734 D) 4222 E) 4254
|
<gadget id="calculator">11_248 / 4</gadget>
<output>2_812</output>
<result>A</result>
|
A
| 2,812 |
A volume of 11248 l water is in a container of sphere. How many hemisphere of volume 4l each will be required to transfer all the water into the small hemispheres?
|
{
"A": "2812",
"B": "8231",
"C": "2734",
"D": "4222",
"E": "4254"
}
|
divide(11248, 4)
|
divide(n0,n1)|
|
"a volume of 4 l can be kept in 1 hemisphere therefore , a volume of 11248 l can be kept in ( 11248 / 4 ) hemispheres ans . 2812 answer : a"
|
geometry
|
math_qa__EjdMvsjIcyOoUcua
|
A man can row upstream at 20 kmph and downstream at 28 kmph, and then find the speed of the man in still water? Choose the correct option
A) 24
B) 37
C) 30
D) 27
E) 18
|
<gadget id="calculator">20 + 28</gadget>
<output>48</output>
<gadget id="calculator">48 / 2</gadget>
<output>24</output>
<result>A</result>
|
A
| 24 |
A man can row upstream at 20 kmph and downstream at 28 kmph, and then find the speed of the man in still water?
|
{
"A": "24",
"B": "37",
"C": "30",
"D": "27",
"E": "18"
}
|
divide(add(20, 28), const_2)
|
add(n0,n1)|divide(#0,const_2)|
|
"us = 20 ds = 28 m = ( 28 + 20 ) / 2 = 24 answer : a"
|
physics
|
math_qa__gd8UV6BrkyGHEiwU
|
If x and y are integers such that x^2= 2y and xy = 256, then x – y = ?
Pick one
A) - 30 B) - 24 C) - 5 D) 5 E) 20
|
<gadget id="calculator">256 * 2</gadget>
<output>512</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">512 ** (1/3)</gadget>
<output>8</output>
<gadget id="calculator">256 / 8</gadget>
<output>32</output>
<gadget id="calculator">8 - 32</gadget>
<output>-24</output>
<result>B</result>
|
B
| -24 |
If x and y are integers such that x^2= 2y and xy = 256, then x – y = ?
|
{
"A": "- 30",
"B": "- 24",
"C": "- 5",
"D": "5",
"E": "20"
}
|
subtract(power(multiply(256, 2), const_0_33), divide(256, power(multiply(256, 2), const_0_33)))
|
multiply(n1,n2)|power(#0,const_0_33)|divide(n2,#1)|subtract(#1,#2)|
|
"here x and y are integers . x ^ 2 = 2 y , xy = 256 . substitute ( x ^ 2 ) / 2 = y in xy = > x ^ 3 = 256 * 2 = > x ^ 3 = 512 . here x ^ 3 is positive , x is also positive . x = 8 then y = 32 . x - y = - 24 so option b is correct"
|
general
|
math_qa__YW70Hr6oZM9mXWS6
|
If a tire rotates at 400 revolutions per minute when the car is traveling 144km/h, what is the circumference of the tire? Choose the correct choice from the following answers
A) 2 meters
B) 6 meters
C) 5 meters
D) 3 meters
E) 7 meters
|
<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">6 * 10</gadget>
<output>60</output>
<gadget id="calculator">60 * 400</gadget>
<output>24_000</output>
<gadget id="calculator">144 / 24_000</gadget>
<output>3/500 = around 0.006</output>
<gadget id="calculator">(3/500) * 1_000</gadget>
<output>6</output>
<result>B</result>
|
B
| 6 |
If a tire rotates at 400 revolutions per minute when the car is traveling 144km/h, what is the circumference of the tire?
|
{
"A": "2 meters",
"B": "6 meters",
"C": "5 meters",
"D": "3 meters",
"E": "7 meters"
}
|
multiply(divide(144, multiply(multiply(multiply(const_2, const_3), const_10), 400)), const_1000)
|
multiply(const_2,const_3)|multiply(#0,const_10)|multiply(n0,#1)|divide(n1,#2)|multiply(#3,const_1000)|
|
"400 rev / minute = 400 * 60 rev / 60 minutes = 24,000 rev / hour 24,000 * c = 144,000 m : c is the circumference c = 6 meters correct answer b"
|
physics
|
math_qa__XafbDZJG8st5tuMT
|
The average of runs of a cricket player of 10 innings was 18. How many runs must he make in his next innings so as to increase his average of runs by 4? Choose the correct choice from the following answers:
A) 87
B) 16
C) 62
D) 76
E) 17
|
<gadget id="calculator">10 + 1</gadget>
<output>11</output>
<gadget id="calculator">4 + 18</gadget>
<output>22</output>
<gadget id="calculator">11 * 22</gadget>
<output>242</output>
<gadget id="calculator">10 * 18</gadget>
<output>180</output>
<gadget id="calculator">242 - 180</gadget>
<output>62</output>
<result>C</result>
|
C
| 62 |
The average of runs of a cricket player of 10 innings was 18. How many runs must he make in his next innings so as to increase his average of runs by 4?
|
{
"A": "87",
"B": "16",
"C": "62",
"D": "76",
"E": "17"
}
|
subtract(multiply(add(10, const_1), add(4, 18)), multiply(10, 18))
|
add(n0,const_1)|add(n1,n2)|multiply(n0,n1)|multiply(#0,#1)|subtract(#3,#2)|
|
"average after 11 innings = 22 required number of runs = ( 33 * 11 ) - ( 18 * 10 ) = 242 - 180 = 62 . answer : c"
|
general
|
math_qa__grQTIn8shxwLfU9M
|
If a = 105 and a^3= 21 * 25 * 15 * b, what is the value of b? Choose the correct choice from the following: A) 35 B) 42 C) 45 D) 147 E) 54
|
<gadget id="calculator">105 ** 3</gadget>
<output>1_157_625</output>
<gadget id="calculator">21 * 25</gadget>
<output>525</output>
<gadget id="calculator">525 * 15</gadget>
<output>7_875</output>
<gadget id="calculator">1_157_625 / 7_875</gadget>
<output>147</output>
<result>D</result>
|
D
| 147 |
If a = 105 and a^3= 21 * 25 * 15 * b, what is the value of b?
|
{
"A": "35",
"B": "42",
"C": "45",
"D": "147",
"E": "54"
}
|
divide(power(105, 3), multiply(multiply(21, 25), 15))
|
multiply(n2,n3)|power(n0,n1)|multiply(n4,#0)|divide(#1,#2)|
|
"first step will be to break down all the numbers into their prime factors . 105 = 3 * 5 * 7 21 = 7 * 3 25 = 5 * 5 15 = 3 * 5 so , ( 105 ) ^ 3 = 3 * 7 * 5 * 5 * 3 * 5 * b therefore ( 3 * 5 * 7 ) ^ 3 = 3 ^ 2 * 5 ^ 3 * 7 * b therefore , b = 3 ^ 3 * 5 ^ 3 * 7 ^ 3 / 3 ^ 2 * 5 ^ 3 * 7 b = 3 * 7 ^ 2 = 3 * 49 = 147 correct answer d ."
|
general
|
math_qa__C7BKE7vgd3YV0lg3
|
If the difference of two numbers is 3 and the difference of their square is 39, then the larger number is:
Pick
A) 9 B) 2 C) 12 D) 14 E) 8
|
<gadget id="calculator">39 / 3</gadget>
<output>13</output>
<gadget id="calculator">13 - 3</gadget>
<output>10</output>
<gadget id="calculator">10 / 2</gadget>
<output>5</output>
<gadget id="calculator">5 + 3</gadget>
<output>8</output>
<result>E</result>
|
E
| 8 |
If the difference of two numbers is 3 and the difference of their square is 39, then the larger number is:
|
{
"A": "9",
"B": "2",
"C": "12",
"D": "14",
"E": "8"
}
|
add(divide(subtract(divide(39, 3), 3), const_2), 3)
|
divide(n1,n0)|subtract(#0,n0)|divide(#1,const_2)|add(n0,#2)
|
let the numbers be x and y then x 2 - y 2 = 39 and x - y = 3 we get x + y = 13 solving x - y = 3 , x + y = 13 x = 8 , y = 5 larger number 8 answer e
|
geometry
|
math_qa__czbkbCNO5bizngy9
|
The ratio of two numbers is 3:4 and their sum is 21. The greater of the two numbers is? Choose the correct choice from the following answers
A) 12 B) 14 C) 16 D) 17 E) 19
|
<gadget id="calculator">21 * 3</gadget>
<output>63</output>
<gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">63 / 7</gadget>
<output>9</output>
<gadget id="calculator">21 - 9</gadget>
<output>12</output>
<result>A</result>
|
A
| 12 |
The ratio of two numbers is 3:4 and their sum is 21. The greater of the two numbers is?
|
{
"A": "12",
"B": "14",
"C": "16",
"D": "17",
"E": "19"
}
|
subtract(21, divide(multiply(21, 3), add(3, 4)))
|
add(n0,n1)|multiply(n0,n2)|divide(#1,#0)|subtract(n2,#2)
|
3 : 4 total parts = 7 = 7 parts - - > 21 ( 7 ã — 3 = 21 ) = 1 part - - - - > 3 ( 1 ã — 3 = 4 ) = the greater of the two number is = 4 = 4 parts - - - - > 12 ( 4 ã — 3 = 12 ) a
|
other
|
math_qa__5xeG34v3e3x01jTO
|
Working alone at its constant rate, machine A produces x boxes in 10 minutes and working alone at its constant rate, machine B produces 2x boxes in 5 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce 6x boxes? Choose one: A) 3 minutes B) 4 minutes C) 5 minutes D) 6 minutes E) 12 minutes
|
<gadget id="calculator">6 * 10</gadget>
<output>60</output>
<gadget id="calculator">10 / 10</gadget>
<output>1</output>
<gadget id="calculator">2 * 10</gadget>
<output>20</output>
<gadget id="calculator">20 / 5</gadget>
<output>4</output>
<gadget id="calculator">1 + 4</gadget>
<output>5</output>
<gadget id="calculator">60 / 5</gadget>
<output>12</output>
<result>E</result>
|
E
| 12 |
Working alone at its constant rate, machine A produces x boxes in 10 minutes and working alone at its constant rate, machine B produces 2x boxes in 5 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce 6x boxes?
|
{
"A": "3 minutes",
"B": "4 minutes",
"C": "5 minutes",
"D": "6 minutes",
"E": "12 minutes"
}
|
divide(multiply(6, 10), add(speed(10, 10), speed(multiply(2, 10), 5)))
|
multiply(n0,n3)|multiply(n0,n1)|speed(n0,n0)|speed(#1,n2)|add(#2,#3)|divide(#0,#4)|
|
"rate = work / time given rate of machine a = x / 10 min machine b produces 2 x boxes in 5 min hence , machine b produces 4 x boxes in 10 min . rate of machine b = 4 x / 10 we need tofind the combined time that machines a and b , working simultaneouslytakeat their respective constant rates let ' s first find the combined rate of machine a and b rate of machine a = x / 10 min + rate of machine b = 4 x / 10 = 5 x / 10 now combine time = combine work needs to be done / combine rate = 6 x / 5 x * 10 = 12 min ans : e"
|
physics
|
math_qa__WLaD9tWG6FvdMIvG
|
a light flashes every 15 seconds, how many times will it flash in ? of an hour? Pick
A) 550
B) 600
C) 240
D) 700
E) 750
|
<gadget id="calculator">3_600 / 15</gadget>
<output>240</output>
<result>C</result>
|
C
| 240 |
a light flashes every 15 seconds, how many times will it flash in ? of an hour?
|
{
"A": "550",
"B": "600",
"C": "240",
"D": "700",
"E": "750"
}
|
divide(const_3600, 15)
|
divide(const_3600,n0)|
|
"1 flash = 15 sec for 1 min = 4 flashes so for 1 hour = 4 * 60 = 240 flashes . answer : c"
|
physics
|
math_qa__8ufoVBapi8EOpbAk
|
A train running at the speed of 60 km/hr crosses a pole in 7 seconds. Find the length of the train. Pick one:
A) 116.67 B) 882 C) 772 D) 252 E) 121
|
<gadget id="calculator">60 * 1_000</gadget>
<output>60_000</output>
<gadget id="calculator">60_000 / 3_600</gadget>
<output>50/3 = around 16.666667</output>
<gadget id="calculator">(50/3) * 7</gadget>
<output>350/3 = around 116.666667</output>
<result>A</result>
|
A
| 116.67 |
A train running at the speed of 60 km/hr crosses a pole in 7 seconds. Find the length of the train.
|
{
"A": "116.67",
"B": "882",
"C": "772",
"D": "252",
"E": "121"
}
|
multiply(divide(multiply(60, const_1000), const_3600), 7)
|
multiply(n0,const_1000)|divide(#0,const_3600)|multiply(n1,#1)|
|
"speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 7 = 116.67 meter . answer : a"
|
physics
|
math_qa__EVdBLiqAtmsoeeK5
|
In what time will a train 40 m long cross an electric pole, it its speed be 144 km/hr? Choose the most appropriate option.
A) 2.5 sec B) 1.0 sec C) 7.5 sec D) 2.3 sec E) 1.5 sec
|
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">144 * (5/18)</gadget>
<output>40</output>
<gadget id="calculator">40 / 40</gadget>
<output>1</output>
<result>B</result>
|
B
| 1 |
In what time will a train 40 m long cross an electric pole, it its speed be 144 km/hr?
|
{
"A": "2.5 sec",
"B": "1.0 sec",
"C": "7.5 sec",
"D": "2.3 sec",
"E": "1.5 sec"
}
|
divide(40, multiply(144, const_0_2778))
|
multiply(n1,const_0_2778)|divide(n0,#0)|
|
"speed = 144 * 5 / 18 = 40 m / sec time taken = 40 / 40 = 1.0 sec . answer : b"
|
physics
|
math_qa__ZJz2kdsKWxNAeKJm
|
A certain country had a total annual expenditure of $1.2x10^12. If the population of the country was 240 million last year, what was the per capita expenditure? Pick:
A) $ 500 B) $ 1000 C) $ 2000 D) $ 3000 E) $ 5000
|
<gadget id="calculator">10 ** 12</gadget>
<output>1_000_000_000_000</output>
<gadget id="calculator">1.2 * 1_000_000_000_000</gadget>
<output>1_200_000_000_000</output>
<gadget id="calculator">4 + 2</gadget>
<output>6</output>
<gadget id="calculator">10 ** 6</gadget>
<output>1_000_000</output>
<gadget id="calculator">240 * 1_000_000</gadget>
<output>240_000_000</output>
<gadget id="calculator">1_200_000_000_000 / 240_000_000</gadget>
<output>5_000</output>
<result>E</result>
|
E
| 5,000 |
A certain country had a total annual expenditure of $1.2x10^12. If the population of the country was 240 million last year, what was the per capita expenditure?
|
{
"A": "$ 500",
"B": "$ 1000",
"C": "$ 2000",
"D": "$ 3000",
"E": "$ 5000"
}
|
divide(multiply(1.2, power(10, 12)), multiply(240, power(10, add(const_4, const_2))))
|
add(const_2,const_4)|power(n1,n2)|multiply(n0,#1)|power(n1,#0)|multiply(n3,#3)|divide(#2,#4)|
|
"explanation : in scientific notation 240 million is 2.4 x 10 ^ 8 . so the per capita expenditure was : ( $ 1.2 x 10 ^ 12 ) / ( 2.4 x 10 ^ 8 ) = ( $ 1.2 ) / ( 2.4 ) x 10 ^ 12 - 8 = $ 0.5 x 10 ^ 4 = $ 5000 answer : option e"
|
general
|
math_qa__ahvUWTyX0Ck4kLMP
|
In a dairy farm, 50 cows eat 50 bags of husk in 50 days. In how many days one cow will eat one bag of husk ? Choose the correct choice from the following options:
A) 34 days
B) 40 days
C) 46 days
D) 50 days
E) none of these
|
<gadget id="calculator">50 / 50</gadget>
<output>1</output>
<gadget id="calculator">1 * 50</gadget>
<output>50</output>
<result>D</result>
|
D
| 50 |
In a dairy farm, 50 cows eat 50 bags of husk in 50 days. In how many days one cow will eat one bag of husk ?
|
{
"A": "34 days",
"B": "40 days",
"C": "46 days",
"D": "50 days",
"E": "none of these"
}
|
multiply(divide(50, 50), 50)
|
divide(n0,n0)|multiply(n0,#0)|
|
"explanation : less cows , more days ( indirect proportion ) less bags , less days ( direct proportion ) [ cows 1 50 bags 50 1 ] : : 50 : x = > x ∗ 50 ∗ 1 = 50 ∗ 1 ∗ 50 = > x = 50 option d"
|
physics
|
math_qa__hLUazUQgCtsv98GZ
|
What is the range of all the roots of |x^2 - 1| = x ? Choose the correct choice from the following.
A) 4 B) 3 C) 2 D) 1 E) 0
|
<gadget id="calculator">1 ** (1/2)</gadget>
<output>1</output>
<result>D</result>
|
D
| 1 |
What is the range of all the roots of |x^2 - 1| = x ?
|
{
"A": "4",
"B": "3",
"C": "2",
"D": "1",
"E": "0"
}
|
sqrt(1)
|
sqrt(n1)
|
we get 2 quadratic equations here . . 1 ) x ^ 2 - x - 1 = 0 . . . . . . . roots 2 , - 1 2 ) x ^ 2 + x - 1 = 0 . . . . . . . . roots - 2 , 1 inserting each root in given equation , it can be seen that - 1 and - 2 do not satisfy the equations . so value of x for given equation . . . . x = 2 or x = 1 i guess range is 2 - 1 = 1 d
|
general
|
math_qa__ip4yyQLG2SWiuhIc
|
Roja and Pooja start moving in the opposite directions from a pole. They are moving at the speeds of 2 km/hr and 3 km/hr respectively. After 4 hours what will be the distance between them?
Choose the correct choice.
A) 11 B) 20 C) 77 D) 26 E) 12
|
<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">5 * 4</gadget>
<output>20</output>
<result>B</result>
|
B
| 20 |
Roja and Pooja start moving in the opposite directions from a pole. They are moving at the speeds of 2 km/hr and 3 km/hr respectively. After 4 hours what will be the distance between them?
|
{
"A": "11",
"B": "20",
"C": "77",
"D": "26",
"E": "12"
}
|
multiply(add(2, 3), 4)
|
add(n0,n1)|multiply(n2,#0)|
|
"distance = relative speed * time = ( 2 + 3 ) * 4 = 20 km [ they are travelling in the opposite direction , relative speed = sum of the speeds ] . answer : b"
|
physics
|
math_qa__oPb9MKPUOVxn0k4p
|
The proportion of water to alcohol in Solution A is 4:1 and the proportion of water to alcohol in Solution B is 3:1. If an equal amount of each solution is mixed together, what is the concentration of alcohol in the new solution? Choose one
A) 16.5 % B) 18.5 % C) 20.5 % D) 22.5 % E) 24.5 %
|
<gadget id="calculator">1 + 1</gadget>
<output>2</output>
<gadget id="calculator">4 + 3</gadget>
<output>7</output>
<gadget id="calculator">7 + 2</gadget>
<output>9</output>
<gadget id="calculator">2 / 9</gadget>
<output>2/9 = around 0.222222</output>
<gadget id="calculator">(2/9) * 100</gadget>
<output>200/9 = around 22.222222</output>
<result>D</result>
|
D
| 22.5 |
The proportion of water to alcohol in Solution A is 4:1 and the proportion of water to alcohol in Solution B is 3:1. If an equal amount of each solution is mixed together, what is the concentration of alcohol in the new solution?
|
{
"A": "16.5 %",
"B": "18.5 %",
"C": "20.5 %",
"D": "22.5 %",
"E": "24.5 %"
}
|
multiply(divide(add(1, 1), add(add(4, 3), add(1, 1))), const_100)
|
add(n1,n3)|add(n0,n2)|add(#1,#0)|divide(#0,#2)|multiply(#3,const_100)|
|
"let v be the total volume of the new solution . then a volume of v / 2 was added from each solution a and b . the amount of alcohol added to the new solution was : ( 1 / 5 ) ( v / 2 ) + ( 1 / 4 ) ( v / 2 ) = v / 10 + v / 8 = 9 v / 40 . the concentration of alcohol is 9 / 40 = 22.5 % the answer is d ."
|
general
|
math_qa__G9nqLF5Oj2FiDr10
|
Find the area of the quadrilateral of one of its diagonals is 20 cm and its off sets 9 cm and 6 cm? Pick:
A) 188 cm 2 B) 150 cm 2 C) 168 cm 2 D) 198 cm 2 E) 987 cm 2
|
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">6 + 9</gadget>
<output>15</output>
<gadget id="calculator">(1/2) * 15</gadget>
<output>15/2 = around 7.5</output>
<gadget id="calculator">(15/2) * 20</gadget>
<output>150</output>
<result>B</result>
|
B
| 150 |
Find the area of the quadrilateral of one of its diagonals is 20 cm and its off sets 9 cm and 6 cm?
|
{
"A": "188 cm 2",
"B": "150 cm 2",
"C": "168 cm 2",
"D": "198 cm 2",
"E": "987 cm 2"
}
|
multiply(multiply(divide(const_1, const_2), add(6, 9)), 20)
|
add(n1,n2)|divide(const_1,const_2)|multiply(#0,#1)|multiply(n0,#2)|
|
"1 / 2 * 20 ( 9 + 6 ) = 150 cm 2 answer : b"
|
geometry
|
math_qa__Wr5YKbMQc8gY5wdR
|
How many integers between 0 and 1000 DO NOT contain the integer 1
Choose one.
A) 727
B) 728
C) 758
D) 748
E) 792
|
<gadget id="calculator">2 * 100</gadget>
<output>200</output>
<gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">7 * 10</gadget>
<output>70</output>
<gadget id="calculator">200 + 70</gadget>
<output>270</output>
<gadget id="calculator">270 + 2</gadget>
<output>272</output>
<gadget id="calculator">1_000 - 272</gadget>
<output>728</output>
<result>B</result>
|
B
| 728 |
How many integers between 0 and 1000 DO NOT contain the integer 1
|
{
"A": "727",
"B": "728",
"C": "758",
"D": "748",
"E": "792"
}
|
subtract(1000, add(add(multiply(const_2, const_100), multiply(add(const_3, const_4), const_10)), const_2))
|
add(const_3,const_4)|multiply(const_100,const_2)|multiply(#0,const_10)|add(#1,#2)|add(#3,const_2)|subtract(n1,#4)
|
from 1 to 99 = 19 integers having 1 from 101 to 199 = all are having 1 similarly 201 - 299 , 301 - 399 , 401 - 499 , . . . . . so on , will have 19 integers having 1 answer = 1000 - ( 19 * 9 + 99 + 2 ) / / 2 is added for 100 and 1000 = 728 answer : b
|
general
|
math_qa__Avyf0GaHfAwnHST7
|
Working simultaneously and independently at an identical constant rate, 4 machines of a certain type can produce a total of x units of product P in 6 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 3x units of product P in 6 days? Pick.
A) 24 B) 18 C) 16 D) 12 E) 8
|
<gadget id="calculator">4 * 3</gadget>
<output>12</output>
<gadget id="calculator">6 / 6</gadget>
<output>1</output>
<gadget id="calculator">12 * 1</gadget>
<output>12</output>
<result>D</result>
|
D
| 12 |
Working simultaneously and independently at an identical constant rate, 4 machines of a certain type can produce a total of x units of product P in 6 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 3x units of product P in 6 days?
|
{
"A": "24",
"B": "18",
"C": "16",
"D": "12",
"E": "8"
}
|
multiply(multiply(4, 3), divide(6, 6))
|
divide(n1,n3)|multiply(n0,n2)|multiply(#0,#1)|
|
"4 machines do x units in 6 days we have x / 6 = > rate of the 4 machines we know that we need to have 4 x units in 6 days therefore , we need to get to 4 x / 6 rate of the machines . rate of one machine is x / 6 * 1 / 4 = x / 24 . now , we need to know how many machines need to work simultaneously , to get 3 x done in 6 days . 3 x / 6 work needs to be done by machines that work at x / 24 rate . let ' s assign a constant y for the number of machines : ( x / 24 ) * y = 3 x / 6 y = 3 x / 6 * 24 / x cancel 6 with 24 , and x with x and get - > 12 . answer choice d"
|
general
|
math_qa__66uDOiRwS2JDp8SZ
|
A batsman in his 12th innings makes a score of 65 and thereby increases his average by 2 runs. What is his average after the 12th innings if he had never been ‘not out’?
Pick one.
A) 42 B) 43 C) 44 D) 45 E) 46
|
<gadget id="calculator">12 * 2</gadget>
<output>24</output>
<gadget id="calculator">65 - 24</gadget>
<output>41</output>
<gadget id="calculator">41 + 2</gadget>
<output>43</output>
<result>B</result>
|
B
| 43 |
A batsman in his 12th innings makes a score of 65 and thereby increases his average by 2 runs. What is his average after the 12th innings if he had never been ‘not out’?
|
{
"A": "42",
"B": "43",
"C": "44",
"D": "45",
"E": "46"
}
|
add(subtract(65, multiply(12, 2)), 2)
|
multiply(n0,n2)|subtract(n1,#0)|add(n2,#1)|
|
"let ‘ x ’ be the average score after 12 th innings ⇒ 12 x = 11 × ( x – 2 ) + 65 ∴ x = 43 answer b"
|
general
|
math_qa__hGN50YnkSskBWJuZ
|
If the number is decreased by 5 and divided by 7 the result is 7. What would be the result if 14 is subtracted and divided by 10?
Pick:
A) 4 B) 7 C) 8 D) 5 E) 3
|
<gadget id="calculator">7 * 7</gadget>
<output>49</output>
<gadget id="calculator">49 + 5</gadget>
<output>54</output>
<gadget id="calculator">54 - 14</gadget>
<output>40</output>
<gadget id="calculator">40 / 10</gadget>
<output>4</output>
<result>A</result>
|
A
| 4 |
If the number is decreased by 5 and divided by 7 the result is 7. What would be the result if 14 is subtracted and divided by 10?
|
{
"A": "4",
"B": "7",
"C": "8",
"D": "5",
"E": "3"
}
|
divide(subtract(add(multiply(7, 7), 5), 14), 10)
|
multiply(n1,n1)|add(n0,#0)|subtract(#1,n3)|divide(#2,n4)|
|
"explanation : let the number be x . then , ( x - 5 ) / 7 = 7 = > x - 5 = 49 x = 54 . : ( x - 14 ) / 10 = ( 54 - 14 ) / 10 = 4 answer : option a"
|
general
|
math_qa__kIlJ3W8NrTZ4s0nR
|
When the number 1y92355 is exactly divisible by 11, then the smallest whole number in place of y is?
Select.
A) 1 B) 3 C) 7 D) 9 E) 0
|
<gadget id="calculator">1 - 1</gadget>
<output>0</output>
<result>E</result>
|
E
| 0 |
When the number 1y92355 is exactly divisible by 11, then the smallest whole number in place of y is?
|
{
"A": "1",
"B": "3",
"C": "7",
"D": "9",
"E": "0"
}
|
subtract(1, const_1)
|
subtract(n0,const_1)
|
the given number = 1 y 92355 sum of the odd places = 5 + 3 + 9 + 1 = 18 sum of the even places = 5 + 2 + y ( sum of the odd places ) - ( sum of even places ) = number ( exactly divisible by 11 ) 18 - ( 7 + y ) = divisible by 11 11 � y = divisible by 11 . y must be 0 , to make given number divisible by 11 . e
|
general
|
math_qa__2XA3CF3XvkEbvmRP
|
How many liters of oil at Rs.40 per liter should be mixed with 240 liters of a second variety of oil at Rs.60 per liter so as to get a mixture whose cost is Rs.52 per liter? Options
A) 120 B) 150 C) 160 D) 180 E) 200
|
<gadget id="calculator">240 * 60</gadget>
<output>14_400</output>
<gadget id="calculator">52 * 240</gadget>
<output>12_480</output>
<gadget id="calculator">14_400 - 12_480</gadget>
<output>1_920</output>
<gadget id="calculator">52 - 40</gadget>
<output>12</output>
<gadget id="calculator">1_920 / 12</gadget>
<output>160</output>
<result>C</result>
|
C
| 160 |
How many liters of oil at Rs.40 per liter should be mixed with 240 liters of a second variety of oil at Rs.60 per liter so as to get a mixture whose cost is Rs.52 per liter?
|
{
"A": "120",
"B": "150",
"C": "160",
"D": "180",
"E": "200"
}
|
divide(subtract(multiply(240, 60), multiply(52, 240)), subtract(52, 40))
|
multiply(n1,n2)|multiply(n1,n3)|subtract(n3,n0)|subtract(#0,#1)|divide(#3,#2)
|
8 : 12 = 2 : 3 if 240 lrs of the 2 nd variety taken then the 1 st variety should be taken as 160 lr answer c
|
physics
|
math_qa__EcMamMKI0bZexoNq
|
If w/x = 1/3 and w/y = 2/3, then (x + y)/y =
Pick one
A) 2 B) 4 C) 5 D) 3 E) 7
|
<gadget id="calculator">2 / 1</gadget>
<output>2</output>
<gadget id="calculator">3 / 3</gadget>
<output>1</output>
<gadget id="calculator">2 + 1</gadget>
<output>3</output>
<result>D</result>
|
D
| 3 |
If w/x = 1/3 and w/y = 2/3, then (x + y)/y =
|
{
"A": "2",
"B": "4",
"C": "5",
"D": "3",
"E": "7"
}
|
add(divide(divide(2, 1), divide(3, 3)), const_1)
|
divide(n2,n0)|divide(n3,n1)|divide(#0,#1)|add(#2,const_1)|
|
"ratio 1 : 3 w = x ratio 2 : 3 w = 2 y x = 2 y ( x + y ) / y = ( 2 y + y ) / y = y ( 2 + 1 ) / y = 3 answer is d"
|
general
|
math_qa__ZWfqMEZ4mTfpnFwB
|
The charge for a single room at Hotel P is 25 percent less than the charge for a single room at Hotel R and 10 percent less than the charge for a single room at Hotel G. The charge for a single room at Hotel R is what percent greater than the charge for a single room at Hotel G ? Choose the most appropriate option:
A) 15 % B) 20 % C) 40 % D) 50 % E) 150 %
|
<gadget id="calculator">100 - 25</gadget>
<output>75</output>
<gadget id="calculator">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">75 / 90</gadget>
<output>5/6 = around 0.833333</output>
<gadget id="calculator">(5/6) * 100</gadget>
<output>250/3 = around 83.333333</output>
<gadget id="calculator">100 - (250/3)</gadget>
<output>50/3 = around 16.666667</output>
<gadget id="calculator">(50/3) / (250/3)</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 100</gadget>
<output>20</output>
<result>B</result>
|
B
| 20 |
The charge for a single room at Hotel P is 25 percent less than the charge for a single room at Hotel R and 10 percent less than the charge for a single room at Hotel G. The charge for a single room at Hotel R is what percent greater than the charge for a single room at Hotel G ?
|
{
"A": "15 %",
"B": "20 %",
"C": "40 %",
"D": "50 %",
"E": "150 %"
}
|
multiply(divide(subtract(const_100, multiply(divide(subtract(const_100, 25), subtract(const_100, 10)), const_100)), multiply(divide(subtract(const_100, 25), subtract(const_100, 10)), const_100)), const_100)
|
subtract(const_100,n0)|subtract(const_100,n1)|divide(#0,#1)|multiply(#2,const_100)|subtract(const_100,#3)|divide(#4,#3)|multiply(#5,const_100)|
|
"let rate in r = 100 x then p = 75 x g = 100 y p = 90 y thus 75 x = 90 y or x = 1.20 y ans r = 120 y so increase = 20 % answer : b ."
|
gain
|
math_qa__l2TLPLjmxspPgE2e
|
Farm Tax is levied on the 60% of the cultivated Land. The tax department collected total $ 4000 through the farm Tax from the village of Mr. willam. Mr. willam paid only $ 500 as farm tax. The percentage of total land of Mr. willam over the total taxable land of the village is : Choices
A) 15 %
B) 25 %
C) 12.5 %
D) 20.83 %
E) none
|
<gadget id="calculator">500 / 4_000</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">(1/8) * 100</gadget>
<output>25/2 = around 12.5</output>
<gadget id="calculator">(25/2) * 100</gadget>
<output>1_250</output>
<gadget id="calculator">1_250 / 60</gadget>
<output>125/6 = around 20.833333</output>
<result>D</result>
|
D
| 20.83 |
Farm Tax is levied on the 60% of the cultivated Land. The tax department collected total $ 4000 through the farm Tax from the village of Mr. willam. Mr. willam paid only $ 500 as farm tax. The percentage of total land of Mr. willam over the total taxable land of the village is :
|
{
"A": "15 %",
"B": "25 %",
"C": "12.5 %",
"D": "20.83 %",
"E": "none"
}
|
divide(multiply(multiply(divide(500, 4000), const_100), const_100), 60)
|
divide(n2,n1)|multiply(#0,const_100)|multiply(#1,const_100)|divide(#2,n0)|
|
"only trick n this question is to ignore 60 % information as farm tax is levied uniformly in the village and that includes mr william ' s land . what percentage of tax mr william paid ? this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to ( 500 / 4000 ) x 100 = 12.5 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 12.5 % x ( 100 / 60 ) = 20.833 % and the answer is not there in the options . the correct answer is ( d ) ."
|
general
|
math_qa__F0YwXlZPz0EGdb5h
|
The S.I. on a certain sum of money for 2 years at 6% per annum is half the C.I. on Rs. 4000 for 2 years at 10% per annum. The sum placed on S.I. is? Choose one
A) 2197 B) 1267 C) 3500 D) 2267 E) 1262
|
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 + (1/10)</gadget>
<output>11/10 = around 1.1</output>
<gadget id="calculator">(11/10) ** 2</gadget>
<output>121/100 = around 1.21</output>
<gadget id="calculator">4_000 * (121/100)</gadget>
<output>4_840</output>
<gadget id="calculator">4_840 - 4_000</gadget>
<output>840</output>
<gadget id="calculator">840 / 2</gadget>
<output>420</output>
<gadget id="calculator">6 / 100</gadget>
<output>3/50 = around 0.06</output>
<gadget id="calculator">2 * (3/50)</gadget>
<output>3/25 = around 0.12</output>
<gadget id="calculator">420 / (3/25)</gadget>
<output>3_500</output>
<result>C</result>
|
C
| 3,500 |
The S.I. on a certain sum of money for 2 years at 6% per annum is half the C.I. on Rs. 4000 for 2 years at 10% per annum. The sum placed on S.I. is?
|
{
"A": "2197",
"B": "1267",
"C": "3500",
"D": "2267",
"E": "1262"
}
|
divide(divide(subtract(multiply(4000, power(add(const_1, divide(10, const_100)), 2)), 4000), 2), multiply(2, divide(6, const_100)))
|
divide(n4,const_100)|divide(n1,const_100)|add(#0,const_1)|multiply(n0,#1)|power(#2,n3)|multiply(n2,#4)|subtract(#5,n2)|divide(#6,n3)|divide(#7,#3)|
|
"explanation : c . i . = [ 4000 * ( 1 + 10 / 100 ) 2 - 4000 ] = ( 4000 * 11 / 10 * 11 / 10 - 4000 ) = rs . 840 . sum = ( 420 * 100 ) / ( 2 * 6 ) = rs . 3500 answer : c"
|
gain
|
math_qa__LqQeBaj7lW7fI4G4
|
The avg weight of A,B & C is 60 kg. If D joins the group, the avg weight of the group becomes 65 kg.If another man E who weights is 3 kg more than D Replaces A, Then the avgof B,C,D&E becomes 64 kg. What is the weight of A? Select the correct option.
A) 56 B) 65 C) 75 D) 89 E) 87
|
<gadget id="calculator">65 * 4</gadget>
<output>260</output>
<gadget id="calculator">64 * 4</gadget>
<output>256</output>
<gadget id="calculator">60 * 3</gadget>
<output>180</output>
<gadget id="calculator">260 - 180</gadget>
<output>80</output>
<gadget id="calculator">3 + 80</gadget>
<output>83</output>
<gadget id="calculator">256 - 83</gadget>
<output>173</output>
<gadget id="calculator">260 - 173</gadget>
<output>87</output>
<result>E</result>
|
E
| 87 |
The avg weight of A,B & C is 60 kg. If D joins the group, the avg weight of the group becomes 65 kg.If another man E who weights is 3 kg more than D Replaces A, Then the avgof B,C,D&E becomes 64 kg. What is the weight of A?
|
{
"A": "56",
"B": "65",
"C": "75",
"D": "89",
"E": "87"
}
|
subtract(multiply(65, const_4), subtract(multiply(64, const_4), add(3, subtract(multiply(65, const_4), multiply(60, 3)))))
|
multiply(n1,const_4)|multiply(n3,const_4)|multiply(n0,n2)|subtract(#0,#2)|add(n2,#3)|subtract(#1,#4)|subtract(#0,#5)|
|
"a + b + c = 3 * 60 = 180 a + b + c + d = 4 * 65 = 260 - - - - ( i ) so , d = 80 & e = 80 + 3 = 83 b + c + d + e = 64 * 4 = 256 - - - ( ii ) from eq . ( i ) & ( ii ) a - e = 260 – 256 = 4 a = e + 4 = 83 + 4 = 87 answer : e"
|
general
|
math_qa__J5IamTqZdjPI6BTJ
|
A reduction of 40% in the price of bananas would enable a man to obtain 66 more for Rs.40, what is reduced price per dozen? Choose the correct choice from the following answers
A) 1.91 B) 2.91 C) 4.91 D) 3.91 E) 5.91
|
<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">40 * (2/5)</gadget>
<output>16</output>
<gadget id="calculator">16 / 66</gadget>
<output>8/33 = around 0.242424</output>
<gadget id="calculator">12 * (8/33)</gadget>
<output>32/11 = around 2.909091</output>
<result>B</result>
|
B
| 2.91 |
A reduction of 40% in the price of bananas would enable a man to obtain 66 more for Rs.40, what is reduced price per dozen?
|
{
"A": "1.91",
"B": "2.91",
"C": "4.91",
"D": "3.91",
"E": "5.91"
}
|
multiply(const_12, divide(multiply(40, divide(40, const_100)), 66))
|
divide(n0,const_100)|multiply(n0,#0)|divide(#1,n1)|multiply(#2,const_12)|
|
"40 * ( 40 / 100 ) = 16 - - - 66 ? - - - 12 = > rs . 2.91 answer : b"
|
gain
|
math_qa__zWl2uy2GPit6GqBy
|
A car travels uphill at 30 km/hr and downhill at 80 km/hr. It goes 100 km uphill and 50 km downhill. Find the average speed of the car?
Select: A) 38 kmph B) 33 kmph C) 34 kmph D) 35 kmph E) 36 kmph
|
<gadget id="calculator">100 + 50</gadget>
<output>150</output>
<gadget id="calculator">100 / 30</gadget>
<output>10/3 = around 3.333333</output>
<gadget id="calculator">50 / 80</gadget>
<output>5/8 = around 0.625</output>
<gadget id="calculator">(10/3) + (5/8)</gadget>
<output>95/24 = around 3.958333</output>
<gadget id="calculator">150 / (95/24)</gadget>
<output>720/19 = around 37.894737</output>
<result>A</result>
|
A
| 38 |
A car travels uphill at 30 km/hr and downhill at 80 km/hr. It goes 100 km uphill and 50 km downhill. Find the average speed of the car?
|
{
"A": "38 kmph",
"B": "33 kmph",
"C": "34 kmph",
"D": "35 kmph",
"E": "36 kmph"
}
|
divide(add(100, 50), add(divide(100, 30), divide(50, 80)))
|
add(n2,n3)|divide(n2,n0)|divide(n3,n1)|add(#1,#2)|divide(#0,#3)|
|
"avg speed = total distance / total time . total distance traveled = 100 + 50 = 150 km ; time taken for uphill journey = 100 / 30 = 10 / 3 ; time taken for down hill journey = 50 / 80 = 5 / 8 ; avg speed = 150 / ( 10 / 3 + 5 / 8 ) = 38 kmph answer : a"
|
general
|
math_qa__tMOjHLsBRKuxHomu
|
If 15 machine can finish a job in 36 days, then how many more machines would be needed to finish the job in one -fourth less time?
Select the correct option: A) a . 5 B) b . 8 C) c . 10 D) d . 12 E) e . 16
|
<gadget id="calculator">15 * 36</gadget>
<output>540</output>
<gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(3/4) * 36</gadget>
<output>27</output>
<gadget id="calculator">540 / 27</gadget>
<output>20</output>
<gadget id="calculator">20 - 15</gadget>
<output>5</output>
<result>A</result>
|
A
| 5 |
If 15 machine can finish a job in 36 days, then how many more machines would be needed to finish the job in one -fourth less time?
|
{
"A": "a . 5",
"B": "b . 8",
"C": "c . 10",
"D": "d . 12",
"E": "e . 16"
}
|
subtract(divide(multiply(15, 36), multiply(divide(const_3, const_4), 36)), 15)
|
divide(const_3,const_4)|multiply(n0,n1)|multiply(n1,#0)|divide(#1,#2)|subtract(#3,n0)|
|
"you might think of this in a management context - we can use the principle of ' person - hours ' to solve any problem where we have identical workers . so , using simpler numbers , suppose you know that 6 identical employees , working simultaneously , would finish a job in 5 hours . then that job requires 6 * 5 = 30 total hours of person - work . if instead you wanted the job done in 3 hours , you ' d assign 30 / 3 = 10 employees to do the job , because you want to get a total of 30 hours of work from the employees . we can solve this problem identically . if 15 machines ( identical ones , i assume ) work simultaneously for 36 days , they will do a total of 15 * 36 machine - days of work . so the job requires 15 * 36 days of machine work in total . we instead want the job done in 1 / 4 less time , so in 27 days . so we ' ll need 15 * 36 / 27 = 20 machines , or 5 additional machines . a"
|
general
|
math_qa__E1eiAZeIpjqAW3gO
|
If a randomly selected non-negative single digit integer is added to {2, 3, 6, 8}. What is the probability that the median of the set will increase but the range still remains the same?
Choose the correct choice from the following answers: A) 0.2 B) 0.3 C) 0.4 D) 0.5 E) 0.6
|
<gadget id="calculator">4 / 10</gadget>
<output>2/5 = around 0.4</output>
<result>C</result>
|
C
| 0.4 |
If a randomly selected non-negative single digit integer is added to {2, 3, 6, 8}. What is the probability that the median of the set will increase but the range still remains the same?
|
{
"A": "0.2",
"B": "0.3",
"C": "0.4",
"D": "0.5",
"E": "0.6"
}
|
divide(const_4, const_10)
|
divide(const_4,const_10)|
|
"we are selecting from non - negative single digit integers , so from { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } . these 10 digits represent the total number of outcomes . hence , the total number of outcomes is 10 . we need to find the probability that the median of the set will increase but the range still remains the same . the median of the set is ( 3 + 6 ) / 2 = 4.5 , thus the number selected must be 5 or greater . for the range to remain the same , the number must be between 2 and 8 inclusive . to satisfy both conditions , the number selected must be 5 , 6 , 7 , or 8 . the probability is 4 / 10 = 0.4 the answer is c ."
|
general
|
math_qa__hH3nr8iDtIFdATs2
|
In what time will a train 140 m long cross an electric pole, it its speed be 108 km/hr? Choose the correct choice: A) 2.5 B) 4.7 C) 2.9 D) 2.3 E) 2.1
|
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">108 * (5/18)</gadget>
<output>30</output>
<gadget id="calculator">140 / 30</gadget>
<output>14/3 = around 4.666667</output>
<result>B</result>
|
B
| 4.7 |
In what time will a train 140 m long cross an electric pole, it its speed be 108 km/hr?
|
{
"A": "2.5",
"B": "4.7",
"C": "2.9",
"D": "2.3",
"E": "2.1"
}
|
divide(140, multiply(108, const_0_2778))
|
multiply(n1,const_0_2778)|divide(n0,#0)|
|
"speed = 108 * 5 / 18 = 30 m / sec time taken = 140 / 30 = 4.7 sec . answer : b"
|
physics
|
math_qa__u15QXACIXsF1tjnU
|
A small water pump would take 2 hours to fill an empty tank. A larger pump would take 1/3 hour to fill the same tank. How many hours would it take both pumps, working at their respective constant rates, to fill the empty tank if they began pumping at the same time? Pick one
A) 3 / 7 B) 2 / 7 C) 1 / 4 D) 2 / 3 E) 5 / 7
|
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) + 3</gadget>
<output>7/2 = around 3.5</output>
<gadget id="calculator">1 / (7/2)</gadget>
<output>2/7 = around 0.285714</output>
<result>B</result>
|
B
| 0.285714 |
A small water pump would take 2 hours to fill an empty tank. A larger pump would take 1/3 hour to fill the same tank. How many hours would it take both pumps, working at their respective constant rates, to fill the empty tank if they began pumping at the same time?
|
{
"A": "3 / 7",
"B": "2 / 7",
"C": "1 / 4",
"D": "2 / 3",
"E": "5 / 7"
}
|
inverse(add(inverse(2), 3))
|
inverse(n0)|add(n2,#0)|inverse(#1)|
|
"rate of the small pump is 1 / 2 tank / hour rate of the larger pump is 1 / ( 1 / 3 ) or 3 tank / hour ; combined rate of the two pumps is 1 / 2 + 3 = 7 / 2 tank / hour , together they will fill the empty tank in 1 / ( 7 / 2 ) = 2 / 7 hours ( time = job / rate ) . answer : b"
|
physics
|
math_qa__ERqQ9zK1YThbTm7i
|
In a certain company 20% of the men and 40% of the women attended the annual company picnic.If 45% of all the employees are men .What % of all the employee went to the picnic?
Pick
A) 31 % B) 34 % C) 35 % D) 36 % E) 37 %
|
<gadget id="calculator">45 / 100</gadget>
<output>9/20 = around 0.45</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(9/20) * (1/5)</gadget>
<output>9/100 = around 0.09</output>
<gadget id="calculator">100 - 45</gadget>
<output>55</output>
<gadget id="calculator">55 / 100</gadget>
<output>11/20 = around 0.55</output>
<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(11/20) * (2/5)</gadget>
<output>11/50 = around 0.22</output>
<gadget id="calculator">(9/100) + (11/50)</gadget>
<output>31/100 = around 0.31</output>
<gadget id="calculator">(31/100) * 100</gadget>
<output>31</output>
<result>A</result>
|
A
| 31 |
In a certain company 20% of the men and 40% of the women attended the annual company picnic.If 45% of all the employees are men .What % of all the employee went to the picnic?
|
{
"A": "31 %",
"B": "34 %",
"C": "35 %",
"D": "36 %",
"E": "37 %"
}
|
multiply(add(multiply(divide(45, const_100), divide(20, const_100)), multiply(divide(subtract(const_100, 45), const_100), divide(40, const_100))), const_100)
|
divide(n2,const_100)|divide(n0,const_100)|divide(n1,const_100)|subtract(const_100,n2)|divide(#3,const_100)|multiply(#0,#1)|multiply(#4,#2)|add(#5,#6)|multiply(#7,const_100)|
|
"total men in company 45 % means total women in company 55 % ( assume total people in company 100 % ) no of men employees attended picnic = 45 x ( 20 / 100 ) = 9 no of women employees attend picnic = 55 x ( 40 / 100 ) = 22 total percentage of employees attend the picnic = 9 + 22 = 31 % answer : a"
|
gain
|
math_qa__yn3G4xhc0ddYUtrR
|
The ratio by weight, measured in pounds, of books to clothes to electronics in a suitcase initially stands at 5:4:2. Someone removes 7 pounds of clothing from the suitcase, thereby doubling the ratio of books to clothes. How many pounds do the electronics in the suitcase weigh? Pick:
A) 6 B) 7 C) 8 D) 9 E) 10
|
<gadget id="calculator">5 + 4</gadget>
<output>9</output>
<gadget id="calculator">9 + 2</gadget>
<output>11</output>
<gadget id="calculator">11 * 7</gadget>
<output>77</output>
<gadget id="calculator">-77</gadget>
<output>-77</output>
<gadget id="calculator">11 * 2</gadget>
<output>22</output>
<gadget id="calculator">11 * 4</gadget>
<output>44</output>
<gadget id="calculator">22 - 44</gadget>
<output>-22</output>
<gadget id="calculator">(-77) / (-22)</gadget>
<output>7/2 = around 3.5</output>
<gadget id="calculator">2 * (7/2)</gadget>
<output>7</output>
<result>B</result>
|
B
| 7 |
The ratio by weight, measured in pounds, of books to clothes to electronics in a suitcase initially stands at 5:4:2. Someone removes 7 pounds of clothing from the suitcase, thereby doubling the ratio of books to clothes. How many pounds do the electronics in the suitcase weigh?
|
{
"A": "6",
"B": "7",
"C": "8",
"D": "9",
"E": "10"
}
|
multiply(2, divide(negate(multiply(add(add(5, 4), 2), 7)), subtract(multiply(add(add(5, 4), 2), const_2), multiply(add(add(5, 4), 2), 4))))
|
add(n0,n1)|add(n2,#0)|multiply(n3,#1)|multiply(#1,const_2)|multiply(n1,#1)|negate(#2)|subtract(#3,#4)|divide(#5,#6)|multiply(n2,#7)|
|
"the weights of the items in the suitcase are 5 k , 4 k , and 2 k . if removing 7 pounds of clothes doubles the ratio of books to clothes , then 7 pounds represents half the weight of the clothes . 2 k = 7 pounds and then k = 3.5 pounds . the electronics weigh 2 ( 3.5 ) = 7 pounds . the answer is b ."
|
other
|
math_qa__jRTUjIIgeQwpVCwe
|
If a#b = ab – b + b^2, then 2#3 = Choose the correct option.
A) 2
B) 8
C) 12
D) 21
E) 35
|
<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">6 - 3</gadget>
<output>3</output>
<gadget id="calculator">3 ** 2</gadget>
<output>9</output>
<gadget id="calculator">3 + 9</gadget>
<output>12</output>
<result>C</result>
|
C
| 12 |
If a#b = ab – b + b^2, then 2#3 =
|
{
"A": "2",
"B": "8",
"C": "12",
"D": "21",
"E": "35"
}
|
add(subtract(multiply(2, 3), 3), power(3, 2))
|
multiply(n1,n2)|power(n2,n0)|subtract(#0,n2)|add(#1,#2)|
|
"solution - simply substitute 2 and 3 in equation in the place of a and b respectively . 2 # 3 = 2 * 3 - 3 + 3 ^ 2 = 6 - 3 + 9 = 12 . ans c"
|
general
|
math_qa__d8OsptDXtc3ddEiQ
|
Andy solves problems 70 to 125 inclusive in a Math exercise. How many problems does he solve?
Answers: A) 56 B) 52 C) 51 D) 50 E) 49
|
<gadget id="calculator">125 - 70</gadget>
<output>55</output>
<gadget id="calculator">55 + 1</gadget>
<output>56</output>
<result>A</result>
|
A
| 56 |
Andy solves problems 70 to 125 inclusive in a Math exercise. How many problems does he solve?
|
{
"A": "56",
"B": "52",
"C": "51",
"D": "50",
"E": "49"
}
|
add(subtract(125, 70), const_1)
|
subtract(n1,n0)|add(#0,const_1)
|
125 - 70 + 1 = 56 ' a ' is the answer
|
general
|
math_qa__im6OQW517X73DI8M
|
Share Rs.4200 among John, Jose & Binoy in the ration 2 : 4 : 6.Find the amount received by John? Choose the correct choice from the following answers: A) 900 B) 980 C) 1200 D) 1240 E) 1400
|
<gadget id="calculator">4_200 / 2</gadget>
<output>2_100</output>
<gadget id="calculator">4_200 / 6</gadget>
<output>700</output>
<gadget id="calculator">2_100 - 700</gadget>
<output>1_400</output>
<result>E</result>
|
E
| 1,400 |
Share Rs.4200 among John, Jose & Binoy in the ration 2 : 4 : 6.Find the amount received by John?
|
{
"A": "900",
"B": "980",
"C": "1200",
"D": "1240",
"E": "1400"
}
|
subtract(divide(4200, 2), divide(4200, 6))
|
divide(n0,n1)|divide(n0,n3)|subtract(#0,#1)|
|
"amount received by sanjay . 4 / 12 x 4200 = 1400 = ( related ratio / sum of ratio ) x total amount so , the amount received by sanjay is 1400 . e"
|
other
|
math_qa__ftC70TWk6gtPamho
|
If k is a non-negative integer and 21^k is a divisor of 435,961 then 7^k - k^7 = Choose the correct choice from the following choices.
A) 0 B) 1 C) 42 D) 118 E) 242
|
<gadget id="calculator">1 - 1</gadget>
<output>0</output>
<gadget id="calculator">7 ** 0</gadget>
<output>1</output>
<gadget id="calculator">0 ** 7</gadget>
<output>0</output>
<gadget id="calculator">1 - 0</gadget>
<output>1</output>
<result>B</result>
|
B
| 1 |
If k is a non-negative integer and 21^k is a divisor of 435,961 then 7^k - k^7 =
|
{
"A": "0",
"B": "1",
"C": "42",
"D": "118",
"E": "242"
}
|
subtract(power(7, subtract(const_1, const_1)), power(subtract(const_1, const_1), 7))
|
subtract(const_1,const_1)|power(n2,#0)|power(#0,n2)|subtract(#1,#2)|
|
"4 + 3 + 5 + 9 + 6 + 1 = 28 , so this number is not divisible by 3 and thus not divisible by 21 . therefore , k = 0 7 ^ k - k ^ 7 = 1 - 0 = 1 the answer is b ."
|
general
|
math_qa__8Y7dPxxhu2BXMsUH
|
A train 90 meters long completely crosses a 200 meters long bridge in 36 seconds. What is the speed of the train is?
Pick:
A) 29 B) 40 C) 25 D) 66 E) 09
|
<gadget id="calculator">90 + 200</gadget>
<output>290</output>
<gadget id="calculator">290 / 1_000</gadget>
<output>29/100 = around 0.29</output>
<gadget id="calculator">36 / 3_600</gadget>
<output>1/100 = around 0.01</output>
<gadget id="calculator">(29/100) / (1/100)</gadget>
<output>29</output>
<result>A</result>
|
A
| 29 |
A train 90 meters long completely crosses a 200 meters long bridge in 36 seconds. What is the speed of the train is?
|
{
"A": "29",
"B": "40",
"C": "25",
"D": "66",
"E": "09"
}
|
divide(divide(add(90, 200), const_1000), divide(36, const_3600))
|
add(n0,n1)|divide(n2,const_3600)|divide(#0,const_1000)|divide(#2,#1)|
|
"s = ( 90 + 200 ) / 36 = 290 / 36 * 18 / 5 = 29 answer : a"
|
physics
|
math_qa__FhN4xXk8GItIVesQ
|
A circular plate with a diameter of 10 inches is kept on another plate of 12 inches diameter. What fraction of the big plate's surface is not covered by the small plate?
Choose the correct choice from the following choices: A) 11 / 36 B) 23 / 10 C) 5 / 14 D) 22 / 11 E) 3 / 4
|
<gadget id="calculator">12 / 2</gadget>
<output>6</output>
<gadget id="calculator">pi * (6 ** 2)</gadget>
<output>36*pi = around 113.097336</output>
<gadget id="calculator">10 / 2</gadget>
<output>5</output>
<gadget id="calculator">pi * (5 ** 2)</gadget>
<output>25*pi = around 78.539816</output>
<gadget id="calculator">(36*pi) - (25*pi)</gadget>
<output>11*pi = around 34.557519</output>
<gadget id="calculator">(11*pi) / (36*pi)</gadget>
<output>11/36 = around 0.305556</output>
<result>A</result>
|
A
| 0.305556 |
A circular plate with a diameter of 10 inches is kept on another plate of 12 inches diameter. What fraction of the big plate's surface is not covered by the small plate?
|
{
"A": "11 / 36",
"B": "23 / 10",
"C": "5 / 14",
"D": "22 / 11",
"E": "3 / 4"
}
|
divide(subtract(circle_area(divide(12, const_2)), circle_area(divide(10, const_2))), circle_area(divide(12, const_2)))
|
divide(n1,const_2)|divide(n0,const_2)|circle_area(#0)|circle_area(#1)|subtract(#2,#3)|divide(#4,#2)
|
the questions asks us to find the surface which is not covered by the plate i . e . , area of the surface not covered . where as circumference is the length along the edge of the circle , 2 * pi * r implies the length of the curve pi * r ^ 2 implies area enclosed by that curve . . hence area of the circle is considered for this problem area of the big plate = pi * r ^ 2 , where r = 6 = > pi * 36 area of the small plate = pi * 25 surface not covered by the plate = pi * 36 - pi * 25 = pi * 11 fraction of big plate ' s surface is not covered by small plate = pi * 11 / total area of the big plate = > pi * 11 / pi * 36 answer a
|
geometry
|
math_qa__ea2HLx4ETOxmFiWb
|
A contractor undertakes to do a job within 100 days and hires 10 people to do it. After 20 days, he realizes that one fourth of the work is done so he fires 2 people. In how many more days B will the work get over? Choose the correct option:
A) 60
B) 70
C) b = 75
D) b = 80
E) 100
|
<gadget id="calculator">10 * 20</gadget>
<output>200</output>
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">200 / (1/4)</gadget>
<output>800</output>
<gadget id="calculator">1 - (1/4)</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">800 * (3/4)</gadget>
<output>600</output>
<gadget id="calculator">10 - 2</gadget>
<output>8</output>
<gadget id="calculator">600 / 8</gadget>
<output>75</output>
<result>C</result>
|
C
| 75 |
A contractor undertakes to do a job within 100 days and hires 10 people to do it. After 20 days, he realizes that one fourth of the work is done so he fires 2 people. In how many more days B will the work get over?
|
{
"A": "60",
"B": "70",
"C": "b = 75",
"D": "b = 80",
"E": "100"
}
|
divide(multiply(divide(multiply(10, 20), const_0_25), subtract(const_1, const_0_25)), subtract(10, 2))
|
multiply(n1,n2)|subtract(const_1,const_0_25)|subtract(n1,n3)|divide(#0,const_0_25)|multiply(#3,#1)|divide(#4,#2)|
|
"we can also use the concept of man - days here 100 days - - > 10 men so the job includes 100 * 10 = 1000 man - days after 20 days 1 / 4 of job is completed so 1 / 4 x 1000 man - days = 250 man - days job is done now the balance job = 1000 - 250 = 750 man - days worth of job since 2 men are fired so b / l men = 8 therefore total no . of days of job = 750 man - day / 8 days = 375 / 4 = 94 days ( approx . ) now since this is total and ques . is asking for additional no . of days , so 94 - 20 = 74 days the nearest approx . to answer is 75 ans : c ( 75 days )"
|
physics
|
math_qa__TjetASim98xZZtHq
|
If the cost price is 25% of selling price. Then what is the profit percent Answers: A) 238 B) 278 C) 300 D) 166 E) 129
|
<gadget id="calculator">100 - 25</gadget>
<output>75</output>
<gadget id="calculator">75 / 25</gadget>
<output>3</output>
<gadget id="calculator">3 * 100</gadget>
<output>300</output>
<result>C</result>
|
C
| 300 |
If the cost price is 25% of selling price. Then what is the profit percent
|
{
"A": "238",
"B": "278",
"C": "300",
"D": "166",
"E": "129"
}
|
multiply(divide(subtract(const_100, 25), 25), const_100)
|
subtract(const_100,n0)|divide(#0,n0)|multiply(#1,const_100)|
|
"explanation : let the s . p = 100 then c . p . = 25 profit = 75 profit % = ( 75 / 25 ) * 100 = 300 % answer : c"
|
gain
|
math_qa__COFqI7tq1aChAYHU
|
A man rows downstream 32 km and 14 km upstream. If he takes 6 hours to cover each distance, then the velocity (in kmph) of the current is: Choose the most appropriate option: A) 1.5 kmph B) 1.75 kmph C) 2 kmph D) 3 kmph E) none
|
<gadget id="calculator">32 / 6</gadget>
<output>16/3 = around 5.333333</output>
<gadget id="calculator">14 / 6</gadget>
<output>7/3 = around 2.333333</output>
<gadget id="calculator">(16/3) - (7/3)</gadget>
<output>3</output>
<gadget id="calculator">3 / 2</gadget>
<output>3/2 = around 1.5</output>
<result>A</result>
|
A
| 1.5 |
A man rows downstream 32 km and 14 km upstream. If he takes 6 hours to cover each distance, then the velocity (in kmph) of the current is:
|
{
"A": "1.5 kmph",
"B": "1.75 kmph",
"C": "2 kmph",
"D": "3 kmph",
"E": "none"
}
|
divide(subtract(divide(32, 6), divide(14, 6)), const_2)
|
divide(n0,n2)|divide(n1,n2)|subtract(#0,#1)|divide(#2,const_2)
|
sol . rate downstream = [ 32 / 6 ] kmph ; rate upstream = [ 14 / 6 ] kmph . ∴ velocity of current = 1 / 2 [ 32 / 6 - 14 / 6 ] kmph = 3 / 2 kmph = 1.5 kmph . answer a
|
physics
|
math_qa__MNnVyFqOXaOnRFet
|
The average weight of 10 person's increases by 4 kg when a new person comes in place of one of them weighing 70kg. What is the weight of the new person? Choose the correct choice from the following choices
A) 85 B) 86.5 C) 90 D) 88.5 E) 110
|
<gadget id="calculator">10 * 4</gadget>
<output>40</output>
<gadget id="calculator">40 + 70</gadget>
<output>110</output>
<result>E</result>
|
E
| 110 |
The average weight of 10 person's increases by 4 kg when a new person comes in place of one of them weighing 70kg. What is the weight of the new person?
|
{
"A": "85",
"B": "86.5",
"C": "90",
"D": "88.5",
"E": "110"
}
|
add(multiply(10, 4), 70)
|
multiply(n0,n1)|add(n2,#0)|
|
"total increase in weight = 10 x 4 = 40 if x is the weight of the new person , total increase in weight = x − 70 = > 40 = x - 70 = > x = 40 + 70 = 110 answer : e"
|
general
|
math_qa__AAabzfeVhqWZLc6B
|
The price of rice falls by 20%. How much rice can be bought now with the money that was sufficient to buy 20 kg of rice previously? Choose one:
A) 5 kg B) 15 kg C) 25 kg D) 30 kg E) none
|
<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">80 / 20</gadget>
<output>4</output>
<gadget id="calculator">100 / 4</gadget>
<output>25</output>
<result>C</result>
|
C
| 25 |
The price of rice falls by 20%. How much rice can be bought now with the money that was sufficient to buy 20 kg of rice previously?
|
{
"A": "5 kg",
"B": "15 kg",
"C": "25 kg",
"D": "30 kg",
"E": "none"
}
|
divide(const_100, divide(subtract(const_100, 20), 20))
|
subtract(const_100,n0)|divide(#0,n1)|divide(const_100,#1)|
|
"solution : let rs . 100 be spend on rice initially for 20 kg . as the price falls by 20 % , new price for 20 kg rice , = ( 100 - 20 % of 100 ) = 80 new price of rice = 80 / 20 = rs . 4 per kg . rice can bought now at = 100 / 4 = 25 kg . answer : option c"
|
gain
|
math_qa__DOIT82j1p7wG9QoL
|
A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is Pick one.
A) 2 mph B) 2.5 mph C) 3 mph D) 4 mph E) none
|
<gadget id="calculator">10 ** 2</gadget>
<output>100</output>
<gadget id="calculator">100 * 4</gadget>
<output>400</output>
<gadget id="calculator">90 / 60</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">36 / (3/2)</gadget>
<output>24</output>
<gadget id="calculator">24 * 2</gadget>
<output>48</output>
<gadget id="calculator">48 ** 2</gadget>
<output>2_304</output>
<gadget id="calculator">400 + 2_304</gadget>
<output>2_704</output>
<gadget id="calculator">2_704 ** (1/2)</gadget>
<output>52</output>
<gadget id="calculator">52 - 48</gadget>
<output>4</output>
<gadget id="calculator">4 / 2</gadget>
<output>2</output>
<result>A</result>
|
A
| 2 |
A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is
|
{
"A": "2 mph",
"B": "2.5 mph",
"C": "3 mph",
"D": "4 mph",
"E": "none"
}
|
divide(subtract(sqrt(add(multiply(power(10, const_2), const_4), power(multiply(divide(36, divide(90, const_60)), const_2), const_2))), multiply(divide(36, divide(90, const_60)), const_2)), const_2)
|
divide(n0,const_60)|power(n2,const_2)|divide(n1,#0)|multiply(#1,const_4)|multiply(#2,const_2)|power(#4,const_2)|add(#3,#5)|sqrt(#6)|subtract(#7,#4)|divide(#8,const_2)|
|
"solution speed downstreams = ( 10 + x ) mph . speed upstreams = ( 10 - x ) mph . = 18 kmph . 36 / ( 10 - x ) - 36 / ( 10 + x ) = 90 / 60 = 72 x × 60 = 90 ( 100 - x ² ) x ² + 48 x + 100 = 0 . x = 2 mph . answer a"
|
physics
|
math_qa__pIrvyanpbwV36n89
|
IF 2+3=10 ; 2+5=27 ; 2+7=53 Then 2+11=? Answers: A) 124 B) 129 C) 128 D) 125 E) 120
|
<gadget id="calculator">2 ** 2</gadget>
<output>4</output>
<gadget id="calculator">11 ** 2</gadget>
<output>121</output>
<gadget id="calculator">4 + 121</gadget>
<output>125</output>
<result>B</result>
|
B
| 129 |
IF 2+3=10 ; 2+5=27 ; 2+7=53 Then 2+11=?
|
{
"A": "124",
"B": "129",
"C": "128",
"D": "125",
"E": "120"
}
|
add(power(2, 2), power(11, 2))
|
power(n9,n3)|power(n10,n0)|add(#0,#1)|
|
"2 ^ 0 + 3 ^ 2 = 1 + 9 = 10 2 ^ 1 + 5 ^ 2 = 2 + 25 = 27 2 ^ 2 + 7 ^ 2 = 4 + 49 = 53 and 2 ^ 3 + 11 ^ 2 = 8 + 121 = 129 answer : b"
|
general
|
math_qa__OoHcMX40c40OhkVU
|
If the sides of a cube are in the ratio 7:3. What is the ratio of their diagonals? Choose one: A) 9 : 4 B) 8 : 4 C) 7 : 4 D) 7 : 3 E) 6 : 4
|
<gadget id="calculator">7 / 3</gadget>
<output>7/3 = around 2.333333</output>
<result>D</result>
|
D
| 2.333333 |
If the sides of a cube are in the ratio 7:3. What is the ratio of their diagonals?
|
{
"A": "9 : 4",
"B": "8 : 4",
"C": "7 : 4",
"D": "7 : 3",
"E": "6 : 4"
}
|
divide(7, 3)
|
divide(n0,n1)|
|
"explanation : diagonal of a cube = a √ 3 where a is side a 1 : a 2 = 7 : 3 d 1 : d 2 = 7 : 3 where √ 3 cancelled both side answer : d"
|
geometry
|
math_qa__Feg5YEPZ8TcA2b2E
|
the average of 4 consecutive odd numbers is 24 . find the largest number
Choose the correct choice from the following answers:
A) 25
B) 27
C) 29
D) 31
E) 32
|
<gadget id="calculator">4 * 24</gadget>
<output>96</output>
<gadget id="calculator">96 / 4</gadget>
<output>24</output>
<gadget id="calculator">24 + 3</gadget>
<output>27</output>
<result>B</result>
|
B
| 27 |
the average of 4 consecutive odd numbers is 24 . find the largest number
|
{
"A": "25",
"B": "27",
"C": "29",
"D": "31",
"E": "32"
}
|
add(divide(multiply(4, 24), 4), const_3)
|
multiply(n0,n1)|divide(#0,n0)|add(#1,const_3)
|
explanation : let the numbers are x , x + 2 , x + 4 , x + 6 , then = > x + ( x + 2 ) + ( x + 4 ) + ( x + 6 ) / 4 = 24 = > 4 x + 12 ) / 4 = 24 = > x + 3 = 24 = > x = 21 so largest number is 21 + 6 = 27 option b
|
general
|
math_qa__4pJCnkSqTTKknVHk
|
what is the smallest integer that is multiple of 8,7 and 20 Select
A) 141 B) 180 C) 130 D) 122 E) 280
|
<gadget id="calculator">2 * 4</gadget>
<output>8</output>
<gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">lcm(8, 7)</gadget>
<output>56</output>
<gadget id="calculator">lcm(56, 20)</gadget>
<output>280</output>
<result>E</result>
|
E
| 280 |
what is the smallest integer that is multiple of 8,7 and 20
|
{
"A": "141",
"B": "180",
"C": "130",
"D": "122",
"E": "280"
}
|
lcm(lcm(multiply(const_2, const_4), add(const_3, const_4)), 20)
|
add(const_3,const_4)|multiply(const_2,const_4)|lcm(#0,#1)|lcm(n1,#2)
|
correct answer : e it is the lcm of 8,7 and 20 which is 280
|
general
|
math_qa__flBO00fd5GLA7ILb
|
By travelling at 40 kmph, a person reaches his destination on time. He covered two-third the total distance in one-third of the total time. What speed should he maintain for the remaining distance to reach his destination on time? Choose the correct choice from the following:
A) 20 kmph B) 17 kmph C) 15 kmph D) 14 kmph E) 13 kmph
|
<gadget id="calculator">40 * 3</gadget>
<output>120</output>
<gadget id="calculator">120 * 2</gadget>
<output>240</output>
<gadget id="calculator">240 / 3</gadget>
<output>80</output>
<gadget id="calculator">120 - 80</gadget>
<output>40</output>
<gadget id="calculator">3 - 1</gadget>
<output>2</output>
<gadget id="calculator">40 / 2</gadget>
<output>20</output>
<result>A</result>
|
A
| 20 |
By travelling at 40 kmph, a person reaches his destination on time. He covered two-third the total distance in one-third of the total time. What speed should he maintain for the remaining distance to reach his destination on time?
|
{
"A": "20 kmph",
"B": "17 kmph",
"C": "15 kmph",
"D": "14 kmph",
"E": "13 kmph"
}
|
divide(subtract(multiply(40, const_3), divide(multiply(multiply(40, const_3), const_2), const_3)), subtract(const_3, const_1))
|
multiply(n0,const_3)|subtract(const_3,const_1)|multiply(#0,const_2)|divide(#2,const_3)|subtract(#0,#3)|divide(#4,#1)|
|
"let the time taken to reach the destination be 3 x hours . total distance = 40 * 3 x = 120 x km he covered 2 / 3 * 120 x = 80 x km in 1 / 3 * 3 x = x hours so , the remaining 40 x km , he has to cover in 2 x hours . required speed = 40 x / 2 x = 20 kmph . answer : a"
|
physics
|
math_qa__6DWmzdR9BhdnJZep
|
The present population of a town is 260. Population increase rate is 10% p.a. Find the population of town after 1 years? Choose the correct choice from the following choices: A) 100 B) 120 C) 200 D) 226 E) 286
|
<gadget id="calculator">260 * 10</gadget>
<output>2_600</output>
<gadget id="calculator">2_600 / 100</gadget>
<output>26</output>
<gadget id="calculator">260 + 26</gadget>
<output>286</output>
<result>E</result>
|
E
| 286 |
The present population of a town is 260. Population increase rate is 10% p.a. Find the population of town after 1 years?
|
{
"A": "100",
"B": "120",
"C": "200",
"D": "226",
"E": "286"
}
|
add(260, divide(multiply(260, 10), const_100))
|
multiply(n0,n1)|divide(#0,const_100)|add(n0,#1)|
|
"p = 260 r = 10 % required population of town = p * ( 1 + r / 100 ) ^ t = 260 * ( 1 + 10 / 100 ) = 260 * ( 11 / 10 ) = 286 answer is e"
|
gain
|
math_qa__XHjvzXBctWse010j
|
In 1996, the property tax of a community is increased by 6% over the 1995 tax.
An additional surcharge of $200 is also added for a special project.
If the Petersons' 1996 tax totals $2108, find their property tax for the year 1995 Choose the correct choice from the following options: A) 1600 B) 1800 C) 1900 D) 2000 E) 2500
|
<gadget id="calculator">2_108 - 200</gadget>
<output>1_908</output>
<gadget id="calculator">6 / 100</gadget>
<output>3/50 = around 0.06</output>
<gadget id="calculator">1 + (3/50)</gadget>
<output>53/50 = around 1.06</output>
<gadget id="calculator">1_908 / (53/50)</gadget>
<output>1_800</output>
<result>B</result>
|
B
| 1,800 |
In 1996, the property tax of a community is increased by 6% over the 1995 tax.
An additional surcharge of $200 is also added for a special project.
If the Petersons' 1996 tax totals $2108, find their property tax for the year 1995
|
{
"A": "1600",
"B": "1800",
"C": "1900",
"D": "2000",
"E": "2500"
}
|
divide(subtract(2108, 200), add(const_1, divide(6, const_100)))
|
divide(n1,const_100)|subtract(n5,n3)|add(#0,const_1)|divide(#1,#2)
|
tax for the year 1996 = 2108 surcharge add : 200 ie 2000 - 200 = 1800 1800 * 6 % = 108 + 2000 = 2108 so the answer is b
|
general
|
math_qa__GswS8VQDI5at0UbY
|
In an election, candidate Douglas won 64 percent of the total vote in Counties X and Y. He won 76 percent of the vote in County X. If the ratio of people who voted in County X to County Y is 2: 1, what percent of the vote did candidate Douglas win in County Y? Choose the correct choice from the following choices.
A) 10 % B) 25 % C) 30 % D) 35 % E) 40 %
|
<gadget id="calculator">64 / 100</gadget>
<output>16/25 = around 0.64</output>
<gadget id="calculator">76 / 100</gadget>
<output>19/25 = around 0.76</output>
<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(19/25) * (2/3)</gadget>
<output>38/75 = around 0.506667</output>
<gadget id="calculator">(16/25) - (38/75)</gadget>
<output>2/15 = around 0.133333</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(2/15) / (1/3)</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) * 100</gadget>
<output>40</output>
<result>E</result>
|
E
| 40 |
In an election, candidate Douglas won 64 percent of the total vote in Counties X and Y. He won 76 percent of the vote in County X. If the ratio of people who voted in County X to County Y is 2: 1, what percent of the vote did candidate Douglas win in County Y?
|
{
"A": "10 %",
"B": "25 %",
"C": "30 %",
"D": "35 %",
"E": "40 %"
}
|
multiply(divide(subtract(divide(64, const_100), multiply(divide(76, const_100), divide(2, const_3))), divide(1, const_3)), const_100)
|
divide(n0,const_100)|divide(n1,const_100)|divide(n2,const_3)|divide(n3,const_3)|multiply(#1,#2)|subtract(#0,#4)|divide(#5,#3)|multiply(#6,const_100)|
|
"given voters in ratio 2 : 1 let x has 200 votersy has 100 voters for x 76 % voted means 76 * 200 = 152 votes combined for xy has 300 voters and voted 64 % so total votes = 192 balance votes = 192 - 152 = 40 as y has 100 voters so 40 votes means 40 % of votes required ans e"
|
general
|
math_qa__0CGP8rd4WqOXZB4d
|
16* 16 * 16 * 16 * 16 = 4^ ? Choices
A) 8 B) 6 C) 10 D) 4 E) 3
|
<gadget id="calculator">max(4, 10)</gadget>
<output>10</output>
<result>C</result>
|
C
| 10 |
16* 16 * 16 * 16 * 16 = 4^ ?
|
{
"A": "8",
"B": "6",
"C": "10",
"D": "4",
"E": "3"
}
|
max(4, const_10)
|
max(n5,const_10)
|
4 ^ 2 * 4 ^ 2 * 4 ^ 2 * 4 ^ 2 * 4 ^ 2 = 4 ^ ( 2 + 2 + 2 + 2 + 2 ) = 4 ^ 10 answer : 10 option : c
|
general
|
math_qa__DS0hGUOCSUkhkUep
|
Fox jeans regularly sell for $15 a pair and Pony jeans regularly sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $8.82 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the two discount rates is 22 percent, what is the discount rate on Pony jeans? Pick one: A) 9 % B) 10 % C) 11 % D) 12 % E) 15 %
|
<gadget id="calculator">22 / 100</gadget>
<output>11/50 = around 0.22</output>
<gadget id="calculator">18 * 2</gadget>
<output>36</output>
<gadget id="calculator">(11/50) * 36</gadget>
<output>198/25 = around 7.92</output>
<gadget id="calculator">8.82 - (198/25)</gadget>
<output>0.9</output>
<gadget id="calculator">15 * 3</gadget>
<output>45</output>
<gadget id="calculator">45 - 36</gadget>
<output>9</output>
<gadget id="calculator">0.9 / 9</gadget>
<output>0.1</output>
<gadget id="calculator">(11/50) - 0.1</gadget>
<output>0.12</output>
<gadget id="calculator">0.12 * 100</gadget>
<output>12</output>
<result>D</result>
|
D
| 12 |
Fox jeans regularly sell for $15 a pair and Pony jeans regularly sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $8.82 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the two discount rates is 22 percent, what is the discount rate on Pony jeans?
|
{
"A": "9 %",
"B": "10 %",
"C": "11 %",
"D": "12 %",
"E": "15 %"
}
|
multiply(subtract(divide(22, const_100), divide(subtract(8.82, multiply(divide(22, const_100), multiply(18, 2))), subtract(multiply(15, 3), multiply(18, 2)))), const_100)
|
divide(n6,const_100)|multiply(n1,n5)|multiply(n0,n4)|multiply(#0,#1)|subtract(#2,#1)|subtract(n2,#3)|divide(#5,#4)|subtract(#0,#6)|multiply(#7,const_100)|
|
"let x be the discount on pony jeans . then 0.22 - x is the discount on fox jeans . 3 ( 0.22 - x ) ( 15 ) + 2 x ( 18 ) = 8.82 9.9 - 45 x + 36 x = 8.82 9 x = 1.08 x = 0.12 the answer is d ."
|
gain
|
math_qa__BCqhhc4jusurzrU2
|
When average age of 25 members are 0, how many members greater than 0?
Choose the correct choice from the following options: A) 17 B) 24 C) 21 D) 23 E) 25
|
<gadget id="calculator">25 - 1</gadget>
<output>24</output>
<result>B</result>
|
B
| 24 |
When average age of 25 members are 0, how many members greater than 0?
|
{
"A": "17",
"B": "24",
"C": "21",
"D": "23",
"E": "25"
}
|
subtract(25, const_1)
|
subtract(n0,const_1)|
|
"average of 25 numbers = 0 . sum of 25 numbers ( 0 x 25 ) = 0 . it is quite possible that 24 of these numbers may be positive and if their sum is a then 25 th number is ( - a ) answer is 24 ( b )"
|
general
|
math_qa__BCK5Nl43KusGJ06u
|
The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is: Pick:
A) 200 meters
B) 225 meters
C) 245 meters
D) 250 meters
E) 300 meters
|
<gadget id="calculator">1_000 / 1</gadget>
<output>1_000</output>
<gadget id="calculator">45 * 1_000</gadget>
<output>45_000</output>
<gadget id="calculator">3_600 / 1</gadget>
<output>3_600</output>
<gadget id="calculator">45_000 / 3_600</gadget>
<output>25/2 = around 12.5</output>
<gadget id="calculator">(25/2) * 30</gadget>
<output>375</output>
<gadget id="calculator">375 - 130</gadget>
<output>245</output>
<result>C</result>
|
C
| 245 |
The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
|
{
"A": "200 meters",
"B": "225 meters",
"C": "245 meters",
"D": "250 meters",
"E": "300 meters"
}
|
subtract(multiply(divide(multiply(45, speed(const_1000, const_1)), speed(const_3600, const_1)), 30), 130)
|
speed(const_1000,const_1)|speed(const_3600,const_1)|multiply(n1,#0)|divide(#2,#1)|multiply(n2,#3)|subtract(#4,n0)|
|
"given , length of the train = 130 meters speed of the train = 45 km / hr = 45 * 518 m / sec = 252 m / sec time = 30 secs let the length of the bridge be x meters . the distance travelled by the train while crossing the bridge will be sum of the length of train and length of the bridge = ( x + 130 ) meters so , 252 = x + 13030 = 30 * 25 = 2 x + 260 = 750 - 260 = 2 x = 490 = 2 x = x = 245 meters . answer c"
|
physics
|
math_qa__5OwWpyiF3kLqnn3b
|
Sakshi can do a piece of work in 10 days.Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work : Choose the correct option
A) 8 B) 16 C) 18 D) 25 E) 10
|
<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 + (1/4)</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">10 / (5/4)</gadget>
<output>8</output>
<result>A</result>
|
A
| 8 |
Sakshi can do a piece of work in 10 days.Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work :
|
{
"A": "8",
"B": "16",
"C": "18",
"D": "25",
"E": "10"
}
|
divide(10, add(const_1, divide(25, const_100)))
|
divide(n1,const_100)|add(#0,const_1)|divide(n0,#1)|
|
"solution ratio of times taken by sakshi and tanya = 125 : 100 = 5 : 4 . suppose tanya taken x days to do the work . 5 : 4 : : 10 : x ⇒ x = ( 10 x 4 / 5 ) ⇒ x = 8 days . hence , tanya takes 8 days is complete the work . answer a"
|
physics
|
math_qa__UItyWUyUK0SCxhHF
|
There were two candidates in an election. Winner candidate received 65% of votes and won the election by 300 votes. Find the number of votes casted to the winning candidate?
Choose the correct choice.
A) 228 B) 744 C) 255 D) 650 E) 231
|
<gadget id="calculator">100 - 65</gadget>
<output>35</output>
<gadget id="calculator">65 - 35</gadget>
<output>30</output>
<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">300 / (3/10)</gadget>
<output>1_000</output>
<gadget id="calculator">1_000 * 65</gadget>
<output>65_000</output>
<gadget id="calculator">65_000 / 100</gadget>
<output>650</output>
<result>D</result>
|
D
| 650 |
There were two candidates in an election. Winner candidate received 65% of votes and won the election by 300 votes. Find the number of votes casted to the winning candidate?
|
{
"A": "228",
"B": "744",
"C": "255",
"D": "650",
"E": "231"
}
|
divide(multiply(divide(300, divide(subtract(65, subtract(const_100, 65)), const_100)), 65), const_100)
|
subtract(const_100,n0)|subtract(n0,#0)|divide(#1,const_100)|divide(n1,#2)|multiply(n0,#3)|divide(#4,const_100)|
|
"w = 65 % l = 35 % 65 % - 35 % = 30 % 30 % - - - - - - - - 300 65 % - - - - - - - - ? = > 650 answer : d"
|
gain
|
math_qa__GRrmYwZC9rA9vOen
|
A grocer purchased a quantity of bananas at 3 pounds for $0.50 and sold the entire quantity at 4 pounds for $1.00. How many pounds did the grocer purchase if the profit from selling the bananas was $6.00? Choose the correct choice from the following:
A) 72 B) 60 C) 90 D) 120 E) 240
|
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">0.5 / 3</gadget>
<output>0.166667</output>
<gadget id="calculator">(1/4) - 0.166667</gadget>
<output>0.083333</output>
<gadget id="calculator">6 / 0.083333</gadget>
<output>72.000288</output>
<result>A</result>
|
A
| 72 |
A grocer purchased a quantity of bananas at 3 pounds for $0.50 and sold the entire quantity at 4 pounds for $1.00. How many pounds did the grocer purchase if the profit from selling the bananas was $6.00?
|
{
"A": "72",
"B": "60",
"C": "90",
"D": "120",
"E": "240"
}
|
divide(6.00, subtract(divide(1.00, 4), divide(0.50, 3)))
|
divide(n3,n2)|divide(n1,n0)|subtract(#0,#1)|divide(n4,#2)|
|
"cost price of 1 pound of bananas = 0.5 / 3 = 1 / 6 selling price of 1 pound of bananas = 1 / 4 profit per pound = ( 1 / 4 - 1 / 6 ) = ( 1 / 12 ) total profit is given as 6 ( 1 / 12 ) * x = 6 x = 72 answer : a"
|
gain
|
math_qa__1it3fj8PtWiGTK4w
|
2500 - (1002 / 20.04) = ? Pick one: A) 2984 B) 2983 C) 2982 D) 2450 E) none of these
|
<gadget id="calculator">1_002 / 20.04</gadget>
<output>50</output>
<gadget id="calculator">2_500 - 50</gadget>
<output>2_450</output>
<result>D</result>
|
D
| 2,450 |
2500 - (1002 / 20.04) = ?
|
{
"A": "2984",
"B": "2983",
"C": "2982",
"D": "2450",
"E": "none of these"
}
|
subtract(2500, divide(1002, 20.04))
|
divide(n1,n2)|subtract(n0,#0)|
|
"2500 - 50 = 2450 answer : d"
|
general
|
math_qa__ITzBTcKyxmkTW6Ay
|
What is the probability of getting equilateral triangles from the vertices of regular hexagon? Choose the correct choice from the following choices:
A) 1 / 10
B) 2 / 10
C) 3 / 10
D) 4 / 10
E) 5 / 10
|
<gadget id="calculator">3 + 3</gadget>
<output>6</output>
<gadget id="calculator">binomial(6, 3)</gadget>
<output>20</output>
<gadget id="calculator">2 / 20</gadget>
<output>1/10 = around 0.1</output>
<result>A</result>
|
A
| 0.1 |
What is the probability of getting equilateral triangles from the vertices of regular hexagon?
|
{
"A": "1 / 10",
"B": "2 / 10",
"C": "3 / 10",
"D": "4 / 10",
"E": "5 / 10"
}
|
divide(const_2, choose(add(const_3, const_3), const_3))
|
add(const_3,const_3)|choose(#0,const_3)|divide(const_2,#1)
|
total no . of triangles that can b made with the vetices hexagon = 6 c 3 = 20 no . of possible outcomes i . e . no . of equality triangles = 2 . . ' . probability = 2 / 20 = 1 / 10 answer : a
|
geometry
|
math_qa__at3PRcCtphPGIcNJ
|
Solomon taken a loan Rs.15000/- from Co-operative Society with an interest @ 11.5% per month. At the same time he deposited Rs. 10000/- as Fixed Deposit with an interest @ 9.5% per month. After one week sam asked the manager to calculate the interest to be paid. What is the interest amount for 7 days? Choose the correct choice:
A) 165 B) 220 C) 310 D) 185 E) 181
|
<gadget id="calculator">15_000 * 11.5</gadget>
<output>172_500</output>
<gadget id="calculator">172_500 / 100</gadget>
<output>1_725</output>
<gadget id="calculator">3 * 10</gadget>
<output>30</output>
<gadget id="calculator">1_725 / 30</gadget>
<output>115/2 = around 57.5</output>
<gadget id="calculator">7 * (115/2)</gadget>
<output>805/2 = around 402.5</output>
<gadget id="calculator">10_000 * 9.5</gadget>
<output>95_000</output>
<gadget id="calculator">95_000 / 100</gadget>
<output>950</output>
<gadget id="calculator">950 / 30</gadget>
<output>95/3 = around 31.666667</output>
<gadget id="calculator">(95/3) * 7</gadget>
<output>665/3 = around 221.666667</output>
<gadget id="calculator">(805/2) - (665/3)</gadget>
<output>1_085/6 = around 180.833333</output>
<result>E</result>
|
E
| 181 |
Solomon taken a loan Rs.15000/- from Co-operative Society with an interest @ 11.5% per month. At the same time he deposited Rs. 10000/- as Fixed Deposit with an interest @ 9.5% per month. After one week sam asked the manager to calculate the interest to be paid. What is the interest amount for 7 days?
|
{
"A": "165",
"B": "220",
"C": "310",
"D": "185",
"E": "181"
}
|
subtract(multiply(7, divide(divide(multiply(15000, 11.5), const_100), multiply(const_3, const_10))), multiply(divide(divide(multiply(10000, 9.5), const_100), multiply(const_3, const_10)), 7))
|
multiply(n0,n1)|multiply(const_10,const_3)|multiply(n2,n3)|divide(#0,const_100)|divide(#2,const_100)|divide(#3,#1)|divide(#4,#1)|multiply(n4,#5)|multiply(n4,#6)|subtract(#7,#8)
|
loan amount : rs . 15000 / - @ 11.5 % interest per month = 15000 / - * 11.5 % = rs . 1725 interest for one day = 1725 / 30 = 57.50 interest for 7 days is = 57.50 * 7 = 403 fd amount is = rs . 10000 / - @ 9.5 % interest per month = 10000 * 9.5 % = 950 / - interest for 7 days = 950 / 30 * 7 = 222 interest amount to be paid by solomon = 403 - 222 = 181 / - for 7 days answer is e
|
general
|
math_qa__DaAW7VHdY6zhiOSx
|
The sum of the first 50 positive even integers is 2,550. What is the sum of the odd integers from 101 to 200, inclusive? Select the correct option:
A) 5,050
B) 7,500
C) 10,500
D) 15,000
E) 19,600
|
<gadget id="calculator">200 + 101</gadget>
<output>301</output>
<gadget id="calculator">301 / 2</gadget>
<output>301/2 = around 150.5</output>
<gadget id="calculator">200 - 101</gadget>
<output>99</output>
<gadget id="calculator">99 / 2</gadget>
<output>99/2 = around 49.5</output>
<gadget id="calculator">(99/2) + 1</gadget>
<output>101/2 = around 50.5</output>
<gadget id="calculator">(301/2) * (101/2)</gadget>
<output>30_401/4 = around 7_600.25</output>
<result>B</result>
|
B
| 7,500 |
The sum of the first 50 positive even integers is 2,550. What is the sum of the odd integers from 101 to 200, inclusive?
|
{
"A": "5,050",
"B": "7,500",
"C": "10,500",
"D": "15,000",
"E": "19,600"
}
|
multiply(divide(add(200, 101), const_2), add(divide(subtract(200, 101), const_2), const_1))
|
add(n2,n3)|subtract(n3,n2)|divide(#1,const_2)|divide(#0,const_2)|add(#2,const_1)|multiply(#4,#3)|
|
"101 + 103 + . . . . . . . 199 if we remove 100 from each of these it will be sum of 1 st 100 odd numbers . so 101 + 103 + . . . . . . . 199 = 50 * 100 + ( 1 + 3 + 5 + 7 + . . . . . . ) sum of 1 st 100 natural numbers = ( 100 * 101 ) / 2 = 5050 sum of 1 st 50 positive even integers = 2550 sum of 1 st 100 odd numbers = 5050 - 2550 = 2500 so 101 + 103 + . . . . . . . 199 = 50 * 100 + ( 1 + 3 + 5 + 7 + . . . . . . ) = 5000 + 2500 = 7500 b is the answer ."
|
general
|
math_qa__3UfIMDv3GOyxJlQS
|
Johnny makes $2.35 per hour at his work. If he works 5 hours, how much money will he earn? Choose the correct choice from the following:
A) $ 30
B) $ 54
C) $ 28.50
D) $ 12
E) $ 11.75
|
<gadget id="calculator">2.35 * 5</gadget>
<output>11.75</output>
<result>E</result>
|
E
| 11.75 |
Johnny makes $2.35 per hour at his work. If he works 5 hours, how much money will he earn?
|
{
"A": "$ 30",
"B": "$ 54",
"C": "$ 28.50",
"D": "$ 12",
"E": "$ 11.75"
}
|
multiply(2.35, 5)
|
multiply(n0,n1)|
|
2.35 * 5 = 11.75 . answer is e .
|
physics
|
math_qa__JN7rVQlEfTe2bXFt
|
A and B together can plough a field in 10 hours but by himself A requires 15 hours. How long would B take to plough the same field?
Select the correct option:
A) 10 hours B) 20 hours C) 30 hours D) 40 hours E) 50 hours
|
<gadget id="calculator">1 / 10</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 / 15</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">(1/10) - (1/15)</gadget>
<output>1/30 = around 0.033333</output>
<gadget id="calculator">1 / (1/30)</gadget>
<output>30</output>
<result>C</result>
|
C
| 30 |
A and B together can plough a field in 10 hours but by himself A requires 15 hours. How long would B take to plough the same field?
|
{
"A": "10 hours",
"B": "20 hours",
"C": "30 hours",
"D": "40 hours",
"E": "50 hours"
}
|
inverse(subtract(inverse(10), inverse(15)))
|
inverse(n0)|inverse(n1)|subtract(#0,#1)|inverse(#2)
|
if a and b together can do a piece of work in x days and a alone can do the same work in y days , then b alone can do the same work in x y / y – x days . therefore , the no . of hours required by b = 10 × 15 / 15 – 10 = 150 / 5 = 30 hours . answer : c
|
physics
|
math_qa__cfKbQoTsQNkAtRfR
|
The roof of an apartment building is rectangular and its length is 4 times longer than its width. If the area of the roof is 576 feet squared, what is the difference between the length and the width of the roof? Choose one:
A) 38 . B) 40 . C) 36 . D) 44 . E) 46 .
|
<gadget id="calculator">576 / 4</gadget>
<output>144</output>
<gadget id="calculator">144 ** (1/2)</gadget>
<output>12</output>
<gadget id="calculator">12 * 4</gadget>
<output>48</output>
<gadget id="calculator">48 - 12</gadget>
<output>36</output>
<result>C</result>
|
C
| 36 |
The roof of an apartment building is rectangular and its length is 4 times longer than its width. If the area of the roof is 576 feet squared, what is the difference between the length and the width of the roof?
|
{
"A": "38 .",
"B": "40 .",
"C": "36 .",
"D": "44 .",
"E": "46 ."
}
|
subtract(multiply(sqrt(divide(576, 4)), 4), sqrt(divide(576, 4)))
|
divide(n1,n0)|sqrt(#0)|multiply(#1,n0)|subtract(#2,#1)|
|
"let the width = x x * 4 x = 576 x ^ 2 = 144 x = 12 length = 4 * 12 = 48 difference = 48 - 12 = 36 c is the answer"
|
geometry
|
math_qa__zVA9epVAxTrw1afs
|
If two girls starting from same point, walking in the opposite directions with 7km/hr and 3km/hr as average speeds respectively. Then the distance between them after 12 hours is? Select the correct option.
A) 120
B) 121
C) 122
D) 123
E) 124
|
<gadget id="calculator">7 + 3</gadget>
<output>10</output>
<gadget id="calculator">10 * 12</gadget>
<output>120</output>
<result>A</result>
|
A
| 120 |
If two girls starting from same point, walking in the opposite directions with 7km/hr and 3km/hr as average speeds respectively. Then the distance between them after 12 hours is?
|
{
"A": "120",
"B": "121",
"C": "122",
"D": "123",
"E": "124"
}
|
multiply(add(7, 3), 12)
|
add(n0,n1)|multiply(n2,#0)
|
explanation : total distance = distance traveled by person a + distance traveled by person b = ( 7 ã — 12 ) + ( 3 ã — 12 ) = 84 + 36 = 120 km answer : a
|
physics
|
math_qa__dUIYyXaOGQpDWCoV
|
Two persons A and B can complete a piece of work in 30 days and 45 days respectively. If they work together, what part of the work will be completed in 7 days?
Options.
A) 2 / 5 B) 7 / 18 C) 1 / 4 D) 1 / 9 E) 2 / 6
|
<gadget id="calculator">1 / 30</gadget>
<output>1/30 = around 0.033333</output>
<gadget id="calculator">1 / 45</gadget>
<output>1/45 = around 0.022222</output>
<gadget id="calculator">(1/30) + (1/45)</gadget>
<output>1/18 = around 0.055556</output>
<gadget id="calculator">7 * (1/18)</gadget>
<output>7/18 = around 0.388889</output>
<result>B</result>
|
B
| 0.388889 |
Two persons A and B can complete a piece of work in 30 days and 45 days respectively. If they work together, what part of the work will be completed in 7 days?
|
{
"A": "2 / 5",
"B": "7 / 18",
"C": "1 / 4",
"D": "1 / 9",
"E": "2 / 6"
}
|
multiply(7, add(divide(const_1, 30), divide(const_1, 45)))
|
divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|multiply(n2,#2)|
|
"a ' s one day ' s work = 1 / 30 b ' s one day ' s work = 1 / 45 ( a + b ) ' s one day ' s work = 1 / 30 + 1 / 45 = 1 / 18 the part of the work completed in 7 days = 7 ( 1 / 18 ) = 7 / 18 . answer b"
|
physics
|
math_qa__sb2OmKH064DCTTNq
|
24 men working 8 hours a day can finish a work in 10 days. Working at the rate of 10 hours a day, the number of men required to finish the same work in 6 days is Answers: A) 30 B) 36 C) 34 D) 32 E) none of these
|
<gadget id="calculator">24 * 8</gadget>
<output>192</output>
<gadget id="calculator">10 * 192</gadget>
<output>1_920</output>
<gadget id="calculator">10 * 6</gadget>
<output>60</output>
<gadget id="calculator">1_920 / 60</gadget>
<output>32</output>
<result>D</result>
|
D
| 32 |
24 men working 8 hours a day can finish a work in 10 days. Working at the rate of 10 hours a day, the number of men required to finish the same work in 6 days is
|
{
"A": "30",
"B": "36",
"C": "34",
"D": "32",
"E": "none of these"
}
|
divide(multiply(10, multiply(24, 8)), multiply(10, 6))
|
multiply(n0,n1)|multiply(n2,n4)|multiply(n2,#0)|divide(#2,#1)
|
m 1 × d 1 × t 1 × w 2 = m 2 × d 2 × t 2 × w 1 24 × 10 × 8 × 1 = m 2 × 6 × 10 × 1 ⇒ m 2 = 24 × 10 × 8 / 6 × 10 = 32 men answer d
|
physics
|
math_qa__ToO8cTwXwFdTtQXn
|
A jogger running at 9 km/hr along side a railway track is 190 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger? Pick one:
A) 88 B) 27 C) 36 D) 31 E) 12
|
<gadget id="calculator">190 + 120</gadget>
<output>310</output>
<gadget id="calculator">45 - 9</gadget>
<output>36</output>
<gadget id="calculator">10 / 2</gadget>
<output>5</output>
<gadget id="calculator">36 / 2</gadget>
<output>18</output>
<gadget id="calculator">5 / 18</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">36 * (5/18)</gadget>
<output>10</output>
<gadget id="calculator">310 / 10</gadget>
<output>31</output>
<result>D</result>
|
D
| 31 |
A jogger running at 9 km/hr along side a railway track is 190 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
|
{
"A": "88",
"B": "27",
"C": "36",
"D": "31",
"E": "12"
}
|
divide(add(190, 120), multiply(subtract(45, 9), divide(divide(const_10, const_2), divide(subtract(45, 9), const_2))))
|
add(n1,n2)|divide(const_10,const_2)|subtract(n3,n0)|divide(#2,const_2)|divide(#1,#3)|multiply(#4,#2)|divide(#0,#5)|
|
"speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 190 + 120 = 310 m . time taken = 310 / 10 = 31 sec . answer : d"
|
general
|
math_qa__DtPPx97b80nZ6f1b
|
A fruit seller sells mangoes at the rate of Rs.11 per kg and thereby loses 10%. At what price per kg, he should have sold them to make a profit of 10%? Options:
A) rs . 13.44
B) rs . 12
C) rs . 12.25
D) rs . 12.31
E) none
|
<gadget id="calculator">100 + 10</gadget>
<output>110</output>
<gadget id="calculator">11 * 110</gadget>
<output>1_210</output>
<gadget id="calculator">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">1_210 / 90</gadget>
<output>121/9 = around 13.444444</output>
<result>A</result>
|
A
| 13.44 |
A fruit seller sells mangoes at the rate of Rs.11 per kg and thereby loses 10%. At what price per kg, he should have sold them to make a profit of 10%?
|
{
"A": "rs . 13.44",
"B": "rs . 12",
"C": "rs . 12.25",
"D": "rs . 12.31",
"E": "none"
}
|
divide(multiply(11, add(const_100, 10)), subtract(const_100, 10))
|
add(n2,const_100)|subtract(const_100,n1)|multiply(n0,#0)|divide(#2,#1)|
|
"solution 90 : 11 = 110 : x x = ( 11 ã — 110 / 90 ) = rs . 13.44 hence , s . p per kg = rs . 13.44 answer a"
|
gain
|
math_qa__R6Ku0twQARYp3v8k
|
A contractor is engaged for 30days on the condition thathe receives Rs.25 for each day he works &is fined Rs.7.50 for each day is absent. He gets Rs.620 in all. For how many days was he absent? Choose the correct choice from the following choices
A) 8
B) 10
C) 15
D) 7
E) 4
|
<gadget id="calculator">7.5 * 30</gadget>
<output>225</output>
<gadget id="calculator">225 + 620</gadget>
<output>845</output>
<gadget id="calculator">7.5 + 25</gadget>
<output>32.5</output>
<gadget id="calculator">845 / 32.5</gadget>
<output>26</output>
<gadget id="calculator">30 - 26</gadget>
<output>4</output>
<result>E</result>
|
E
| 4 |
A contractor is engaged for 30days on the condition thathe receives Rs.25 for each day he works &is fined Rs.7.50 for each day is absent. He gets Rs.620 in all. For how many days was he absent?
|
{
"A": "8",
"B": "10",
"C": "15",
"D": "7",
"E": "4"
}
|
subtract(30, divide(add(multiply(7.50, 30), 620), add(7.50, 25)))
|
add(n1,n2)|multiply(n0,n2)|add(n3,#1)|divide(#2,#0)|subtract(n0,#3)|
|
"30 * 25 = 750 620 - - - - - - - - - - - 130 25 + 7.50 = 32.5 130 / 32.5 = 4 e"
|
physics
|
math_qa__r2WZknBTh8xI0pCD
|
The simple interest and the true discount on a certain sum for a given time and at a given rate are Rs. 85 and Rs. 80 respectively. The sum is:
Choose the correct option:
A) rs . 1800 B) rs . 1450 C) rs . 1360 D) rs . 6800 E) none
|
<gadget id="calculator">85 * 80</gadget>
<output>6_800</output>
<gadget id="calculator">85 - 80</gadget>
<output>5</output>
<gadget id="calculator">6_800 / 5</gadget>
<output>1_360</output>
<result>C</result>
|
C
| 1,360 |
The simple interest and the true discount on a certain sum for a given time and at a given rate are Rs. 85 and Rs. 80 respectively. The sum is:
|
{
"A": "rs . 1800",
"B": "rs . 1450",
"C": "rs . 1360",
"D": "rs . 6800",
"E": "none"
}
|
divide(multiply(85, 80), subtract(85, 80))
|
multiply(n0,n1)|subtract(n0,n1)|divide(#0,#1)|
|
"solution sum = s . i xt . d / ( s . i ) - ( t . d ) = 85 x 80 / 85 - 80 = rs . 1360 . answer c"
|
gain
|
math_qa__IgdDCPQMvwrkAthy
|
A business executive and his client are charging their dinner tab on the executive's expense account.The company will only allow them to spend a total of 75$ for the meal.Assuming that they will pay 7% in sales tax for the meal and leave a 15% tip,what is the most their food can cost? Options
A) 69.55 $ B) 50.63 $ C) 60.95 $ D) 52.15 $ E) 53.15 $
|
<gadget id="calculator">7 + 15</gadget>
<output>22</output>
<gadget id="calculator">22 / 100</gadget>
<output>11/50 = around 0.22</output>
<gadget id="calculator">(11/50) + 1</gadget>
<output>61/50 = around 1.22</output>
<gadget id="calculator">75 / (61/50)</gadget>
<output>3_750/61 = around 61.47541</output>
<result>C</result>
|
C
| 60.95 |
A business executive and his client are charging their dinner tab on the executive's expense account.The company will only allow them to spend a total of 75$ for the meal.Assuming that they will pay 7% in sales tax for the meal and leave a 15% tip,what is the most their food can cost?
|
{
"A": "69.55 $",
"B": "50.63 $",
"C": "60.95 $",
"D": "52.15 $",
"E": "53.15 $"
}
|
divide(75, add(divide(add(7, 15), const_100), const_1))
|
add(n1,n2)|divide(#0,const_100)|add(#1,const_1)|divide(n0,#2)|
|
"let x is the cost of the food 1.07 x is the gross bill after including sales tax 1.15 * 1.07 x = 75 x = 60.95 hence , the correct option is c"
|
general
|
math_qa__zLkrU24AmWWXdq9L
|
the age of father 5 years ago was 4 times the age of his son . 5 years hence , father ' s age will be twice that of his son . the ratio of their present ages is :
Choose the correct choice from the following answers: A) 5 : 4 B) 7 : 4 C) 5 : 2 D) 5 : 3 E) 7 : 5
|
<gadget id="calculator">4 * 5</gadget>
<output>20</output>
<gadget id="calculator">20 + 5</gadget>
<output>25</output>
<gadget id="calculator">5 + 5</gadget>
<output>10</output>
<gadget id="calculator">25 / 10</gadget>
<output>5/2 = around 2.5</output>
<result>C</result>
|
C
| 2.5 |
the age of father 5 years ago was 4 times the age of his son . 5 years hence , father ' s age will be twice that of his son . the ratio of their present ages is :
|
{
"A": "5 : 4",
"B": "7 : 4",
"C": "5 : 2",
"D": "5 : 3",
"E": "7 : 5"
}
|
divide(add(multiply(4, 5), 5), add(5, 5))
|
add(n0,n0)|multiply(n0,n1)|add(n0,#1)|divide(#2,#0)
|
let the ages of father and son 5 years ago be 4 x and x years respectively . then , ( 4 x + 5 ) + 5 = 2 [ ( x + 5 ) + 5 ] 4 x + 10 = 2 x + 20 x = 5 . required ratio = ( 4 x + 5 ) : ( x + 5 ) = 25 : 10 = 5 : 2 . answer : option c
|
general
|
math_qa__4gXdqc1hyvjeEWtP
|
The average of 11numbers is 50. Out of 11numbers the average of first 6no. is 58, and last 6numbers is 65 then find 6th number?
Choose the most appropriate option
A) 188 B) 65 C) 58 D) 62 E) 48
|
<gadget id="calculator">6 * 58</gadget>
<output>348</output>
<gadget id="calculator">6 * 65</gadget>
<output>390</output>
<gadget id="calculator">348 + 390</gadget>
<output>738</output>
<gadget id="calculator">11 * 50</gadget>
<output>550</output>
<gadget id="calculator">738 - 550</gadget>
<output>188</output>
<result>A</result>
|
A
| 188 |
The average of 11numbers is 50. Out of 11numbers the average of first 6no. is 58, and last 6numbers is 65 then find 6th number?
|
{
"A": "188",
"B": "65",
"C": "58",
"D": "62",
"E": "48"
}
|
subtract(add(multiply(6, 58), multiply(6, 65)), multiply(11, 50))
|
multiply(n3,n4)|multiply(n3,n6)|multiply(n0,n1)|add(#0,#1)|subtract(#3,#2)|
|
"6 th number = sum of 1 st 6 no . s + sum of last 6 no . s - sum of 11 no . s answer = 6 * 58 + 6 * 65 - 11 * 50 = 188 answer is a"
|
general
|
math_qa__PM9O7SRyBMr0Wr6i
|
The population of a town is 20000. It decreases annually at the rate of 20% p.a. What will be its population after 2 years?
Choose the correct choice from the following options.
A) 4300
B) 4500
C) 5120
D) 5230
E) 12800
|
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">20_000 * (1/5)</gadget>
<output>4_000</output>
<gadget id="calculator">20_000 - 4_000</gadget>
<output>16_000</output>
<gadget id="calculator">16_000 * (1/5)</gadget>
<output>3_200</output>
<gadget id="calculator">16_000 - 3_200</gadget>
<output>12_800</output>
<result>E</result>
|
E
| 12,800 |
The population of a town is 20000. It decreases annually at the rate of 20% p.a. What will be its population after 2 years?
|
{
"A": "4300",
"B": "4500",
"C": "5120",
"D": "5230",
"E": "12800"
}
|
subtract(subtract(20000, multiply(20000, divide(20, const_100))), multiply(subtract(20000, multiply(20000, divide(20, const_100))), divide(20, const_100)))
|
divide(n1,const_100)|multiply(n0,#0)|subtract(n0,#1)|multiply(#0,#2)|subtract(#2,#3)|
|
"20000 × 80 / 100 × 80 / 100 = 12800 answer : e"
|
gain
|
math_qa__cVa77SqUNvCvwJsS
|
The population of a village is 15540. It increases annually at the rate of 28% p.a. What will be its population after 2 years? Select the correct option:
A) 10000 B) 25460 C) 26709 D) 14000 E) 14400
|
<gadget id="calculator">28 / 100</gadget>
<output>7/25 = around 0.28</output>
<gadget id="calculator">1 + (7/25)</gadget>
<output>32/25 = around 1.28</output>
<gadget id="calculator">(32/25) ** 2</gadget>
<output>1_024/625 = around 1.6384</output>
<gadget id="calculator">15_540 * (1_024/625)</gadget>
<output>3_182_592/125 = around 25_460.736</output>
<result>B</result>
|
B
| 25,460 |
The population of a village is 15540. It increases annually at the rate of 28% p.a. What will be its population after 2 years?
|
{
"A": "10000",
"B": "25460",
"C": "26709",
"D": "14000",
"E": "14400"
}
|
multiply(15540, power(add(const_1, divide(28, const_100)), 2))
|
divide(n1,const_100)|add(#0,const_1)|power(#1,n2)|multiply(n0,#2)|
|
"formula : ( after = 100 denominator ago = 100 numerator ) 15540 × 128 / 100 × 128 / 100 = 25460 b"
|
gain
|
math_qa__ydxLORx0YC8ATrJ2
|
The sum of money will be double itself in 10 years and simple interest find rate of interest? Pick one.
A) 10 % B) 15 % C) 20 % D) 25 % E) 30 %
|
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/10) * 100</gadget>
<output>10</output>
<result>A</result>
|
A
| 10 |
The sum of money will be double itself in 10 years and simple interest find rate of interest?
|
{
"A": "10 %",
"B": "15 %",
"C": "20 %",
"D": "25 %",
"E": "30 %"
}
|
multiply(divide(10, const_100), const_100)
|
divide(n0,const_100)|multiply(#0,const_100)
|
t = 10 years p = principle amount = x a = total amount = 2 x si = simple interest = a - p = 2 x - x = x r = 100 si / pt = 100 x / 10 x = 10 % answer is a
|
gain
|
math_qa__Q7gkgrzqpUTYOBQv
|
A runner runs the 40 miles from Marathon to Athens at a constant speed. Halfway through the run she injures her foot, and continues to run at half her previous speed. If the second half takes her 11 hours longer than the first half, how many hours did it take the runner to run the second half? Select.
A) 14 B) 15 C) 18 D) 22 E) 33
|
<gadget id="calculator">40 / 2</gadget>
<output>20</output>
<gadget id="calculator">20 / 11</gadget>
<output>20/11 = around 1.818182</output>
<gadget id="calculator">40 / (20/11)</gadget>
<output>22</output>
<result>D</result>
|
D
| 22 |
A runner runs the 40 miles from Marathon to Athens at a constant speed. Halfway through the run she injures her foot, and continues to run at half her previous speed. If the second half takes her 11 hours longer than the first half, how many hours did it take the runner to run the second half?
|
{
"A": "14",
"B": "15",
"C": "18",
"D": "22",
"E": "33"
}
|
divide(40, divide(divide(40, const_2), 11))
|
divide(n0,const_2)|divide(#0,n1)|divide(n0,#1)|
|
"the runner runs the first 20 miles at speed v and the second 20 miles at speed v / 2 . the time t 2 to run the second half must be twice the time t 1 to run the first half . t 2 = 2 * t 1 = t 1 + 11 t 1 = 11 and so t 2 = 22 . the answer is d ."
|
physics
|
math_qa__E3PoRayWgfiG5ACi
|
The cost price of a radio is Rs.4500 and it was sold for Rs.3200, find the loss %? Choose one
A) 28.9 % B) 22 % C) 28 % D) 45 % E) 32 %
|
<gadget id="calculator">4_500 - 3_200</gadget>
<output>1_300</output>
<gadget id="calculator">1_300 / 4_500</gadget>
<output>13/45 = around 0.288889</output>
<gadget id="calculator">(13/45) * 100</gadget>
<output>260/9 = around 28.888889</output>
<result>A</result>
|
A
| 28.9 |
The cost price of a radio is Rs.4500 and it was sold for Rs.3200, find the loss %?
|
{
"A": "28.9 %",
"B": "22 %",
"C": "28 %",
"D": "45 %",
"E": "32 %"
}
|
multiply(divide(subtract(4500, 3200), 4500), const_100)
|
subtract(n0,n1)|divide(#0,n0)|multiply(#1,const_100)|
|
"4500 - - - - 1300 100 - - - - ? = > 28.9 % answer : a"
|
gain
|
math_qa__bh7lT127aVeqr8eN
|
A gardener grows cabbages in her garden that is in the shape of a square. Each cabbage takes 1 square feet of area in her garden. This year, she has increased her output by 197 cabbages as compared to last year. The shape of the area used for growing the cabbages has remained a square in both these years. How many cabbages did she produce this year? Answers
A) 9801 B) 10,000 C) 14,400 D) 12,696 E) can not be determined
|
<gadget id="calculator">197 / 2</gadget>
<output>197/2 = around 98.5</output>
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) + (1/4)</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(197/2) + (1/2)</gadget>
<output>99</output>
<gadget id="calculator">99 ** 2</gadget>
<output>9_801</output>
<result>A</result>
|
A
| 9,801 |
A gardener grows cabbages in her garden that is in the shape of a square. Each cabbage takes 1 square feet of area in her garden. This year, she has increased her output by 197 cabbages as compared to last year. The shape of the area used for growing the cabbages has remained a square in both these years. How many cabbages did she produce this year?
|
{
"A": "9801",
"B": "10,000",
"C": "14,400",
"D": "12,696",
"E": "can not be determined"
}
|
power(add(divide(197, const_2), add(const_0_25, const_0_25)), const_2)
|
add(const_0_25,const_0_25)|divide(n1,const_2)|add(#0,#1)|power(#2,const_2)|
|
"let the side for growing cabbages this year be x ft . thus the area is x ^ 2 . let the side for growing cabbages last year be y ft . thus , the area was y ^ 2 . the area would have increased by 197 sq ft as each cabbage takes 1 sq ft space . x ^ 2 - y ^ 2 = 197 ( x + y ) ( x - y ) = 197 197 is a prime number and thus it will be ( 99 + 98 ) * ( 99 - 98 ) . thus x = 99 and y = 98 x ^ 2 = 99 ^ 2 = 9801 the answer is a ."
|
geometry
|
math_qa__GjiE7FSZ2cpHqLnT
|
a special municipal payroll tax charges not tax on a payroll less than $ 200000 and only 0.2 % on a company ’ s payroll above $ 200000 . if belfried industries paid $ 200 in this special municipal payroll tax , then they must have had a payroll of ? Select the correct option:
A) $ 180,000 B) $ 202,000 C) $ 220,000 D) $ 300,000 E) $ 2 , 200,000
|
<gadget id="calculator">0.2 / 100</gadget>
<output>0.002</output>
<gadget id="calculator">200 / 0.002</gadget>
<output>100_000</output>
<gadget id="calculator">200_000 + 100_000</gadget>
<output>300_000</output>
<result>D</result>
|
D
| 300,000 |
a special municipal payroll tax charges not tax on a payroll less than $ 200000 and only 0.2 % on a company ’ s payroll above $ 200000 . if belfried industries paid $ 200 in this special municipal payroll tax , then they must have had a payroll of ?
|
{
"A": "$ 180,000",
"B": "$ 202,000",
"C": "$ 220,000",
"D": "$ 300,000",
"E": "$ 2 , 200,000"
}
|
add(200000, divide(200, divide(0.2, const_100)))
|
divide(n1,const_100)|divide(n3,#0)|add(n0,#1)
|
answer : d , ( with different approach ) : the 200 paid is 0.2 % of the additional amount above 200,000 . let it be x now 0.2 % of x = 200 therefore x = 100,000 total = 200,000 + x = 300,000
|
general
|
math_qa__hM4iJJTLGmrPX756
|
A man bought an article and sold it at a gain of 5 %. If he had bought it at 5% less and sold it for Re 4 less, he would have made a profit of 10%. The C.P. of the article was Options: A) 344 B) 600 C) 200 D) 800 E) 700
|
<gadget id="calculator">5 * 4</gadget>
<output>20</output>
<gadget id="calculator">20 * 10</gadget>
<output>200</output>
<gadget id="calculator">200 * 4</gadget>
<output>800</output>
<result>D</result>
|
D
| 800 |
A man bought an article and sold it at a gain of 5 %. If he had bought it at 5% less and sold it for Re 4 less, he would have made a profit of 10%. The C.P. of the article was
|
{
"A": "344",
"B": "600",
"C": "200",
"D": "800",
"E": "700"
}
|
multiply(multiply(multiply(5, 4), 10), 4)
|
multiply(n0,n2)|multiply(n3,#0)|multiply(n2,#1)
|
explanation : let original cost price is x its selling price = ( 105 / 100 ) * x = 21 x / 20 new cost price = ( 95 / 100 ) * x = 19 x / 20 new selling price = ( 110 / 100 ) * ( 19 x / 20 ) = 209 x / 200 [ ( 21 x / 20 ) - ( 209 x / 200 ) ] = 4 = > x = 800 answer : d ) rs 800
|
gain
|
math_qa__kscUuwWAMLfftbsV
|
In a group of people, if 30 people were made to stand in each column, 16 columns could be formed. If 40 people were made to stand in a column, how many columns could be formed? Pick one:
A) 12 B) 14 C) 16 D) 18 E) 20
|
<gadget id="calculator">40 / 16</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">30 / (5/2)</gadget>
<output>12</output>
<result>A</result>
|
A
| 12 |
In a group of people, if 30 people were made to stand in each column, 16 columns could be formed. If 40 people were made to stand in a column, how many columns could be formed?
|
{
"A": "12",
"B": "14",
"C": "16",
"D": "18",
"E": "20"
}
|
divide(30, divide(40, 16))
|
divide(n2,n1)|divide(n0,#0)|
|
"16 * 30 = 40 * n n = 12 the answer is a ."
|
other
|
math_qa__titEaxe0SP0dPSgM
|
Find large number from below question The difference of two numbers is 1200. On dividing the larger number by the smaller, we get 5 as quotient and the 4 as remainder
Choose the correct choice: A) 1234 B) 1345 C) 1456 D) 1567 E) 1499
|
<gadget id="calculator">1_200 - 4</gadget>
<output>1_196</output>
<gadget id="calculator">5 - 1</gadget>
<output>4</output>
<gadget id="calculator">1_196 / 4</gadget>
<output>299</output>
<gadget id="calculator">299 * 5</gadget>
<output>1_495</output>
<result>E</result>
|
E
| 1,499 |
Find large number from below question The difference of two numbers is 1200. On dividing the larger number by the smaller, we get 5 as quotient and the 4 as remainder
|
{
"A": "1234",
"B": "1345",
"C": "1456",
"D": "1567",
"E": "1499"
}
|
multiply(divide(subtract(1200, 4), subtract(5, const_1)), 5)
|
subtract(n0,n2)|subtract(n1,const_1)|divide(#0,#1)|multiply(n1,#2)|
|
"let the smaller number be x . then larger number = ( x + 1200 ) . x + 1200 = 5 x + 4 4 x = 1196 x = 299 large number = 299 + 1200 = 1499 e"
|
general
|
math_qa__NjRHoA0qddCh1p5t
|
The area of a rectangular field is equal to 50 square meters. Its perimeter is equal to 30 meters. Find the width of this rectangle. Select the correct option:
A) 5
B) 10
C) 15
D) 20
E) 25
|
<gadget id="calculator">30 / 2</gadget>
<output>15</output>
<gadget id="calculator">15 * 15</gadget>
<output>225</output>
<gadget id="calculator">4 * 50</gadget>
<output>200</output>
<gadget id="calculator">225 - 200</gadget>
<output>25</output>
<gadget id="calculator">25 ** (1/2)</gadget>
<output>5</output>
<gadget id="calculator">15 - 5</gadget>
<output>10</output>
<gadget id="calculator">10 / 2</gadget>
<output>5</output>
<result>A</result>
|
A
| 5 |
The area of a rectangular field is equal to 50 square meters. Its perimeter is equal to 30 meters. Find the width of this rectangle.
|
{
"A": "5",
"B": "10",
"C": "15",
"D": "20",
"E": "25"
}
|
divide(subtract(divide(30, const_2), sqrt(subtract(multiply(divide(30, const_2), divide(30, const_2)), multiply(const_4, 50)))), const_2)
|
divide(n1,const_2)|multiply(n0,const_4)|multiply(#0,#0)|subtract(#2,#1)|sqrt(#3)|subtract(#0,#4)|divide(#5,const_2)|
|
"l * w = 50 : area , l is the length and w is the width . 2 l + 2 w = 30 : perimeter l = 15 - w : solve for l ( 15 - w ) * w = 30 : substitute in the area equation w = 5 and l = 10 correct answer a"
|
geometry
|
math_qa__kaHxYvrke2c5HUIt
|
A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 35%? Select the correct option: A) 600 B) 887 C) 256 D) 654 E) 675
|
<gadget id="calculator">35 / 100</gadget>
<output>7/20 = around 0.35</output>
<gadget id="calculator">500 * (7/20)</gadget>
<output>175</output>
<gadget id="calculator">500 + 175</gadget>
<output>675</output>
<result>E</result>
|
E
| 675 |
A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 35%?
|
{
"A": "600",
"B": "887",
"C": "256",
"D": "654",
"E": "675"
}
|
add(500, multiply(500, divide(35, const_100)))
|
divide(n1,const_100)|multiply(n0,#0)|add(n0,#1)|
|
"cost price = rs . 500 profit = 35 % of 500 = rs . 175 selling price = cost price + profit = 500 + 175 = 675 answer : e"
|
gain
|
math_qa__LyMMVncqyrWVcLjz
|
65 boys can complete a work in 30 days.how many men need to complete twice the work in 20 days
Choose the correct answer
A) 160 B) 170 C) 180 D) 195 E) 200
|
<gadget id="calculator">30 * 2</gadget>
<output>60</output>
<gadget id="calculator">65 * 60</gadget>
<output>3_900</output>
<gadget id="calculator">3_900 / 20</gadget>
<output>195</output>
<result>D</result>
|
D
| 195 |
65 boys can complete a work in 30 days.how many men need to complete twice the work in 20 days
|
{
"A": "160",
"B": "170",
"C": "180",
"D": "195",
"E": "200"
}
|
divide(multiply(65, multiply(30, const_2)), 20)
|
multiply(n1,const_2)|multiply(n0,#0)|divide(#1,n2)|
|
"one man can complete the work in 30 * 65 = 1950 days = one time work to complete the work twice it will be completed in let m be the no . of worker assign for this therefore the eqn becomes m * 20 = 2 * 1950 m = 195 workers answer : d"
|
physics
|
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