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stringlengths 7
6.48k
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|---|---|---|---|---|---|---|---|---|---|---|
math_qa__Jsh4hKewD2LLGMYF | Find the cost of fencing around a circular field of diameter 70 m at the rate of Rs.1 a meter? Choose the correct choice
A) 288 B) 132 C) 220 D) 592 E) 261 | <gadget id="calculator">70 / 2</gadget>
<output>35</output>
<gadget id="calculator">2 * pi * 35</gadget>
<output>70*pi = around 219.911486</output>
<gadget id="calculator">(70*pi) * 1</gadget>
<output>70*pi = around 219.911486</output>
<result>C</result> | C | 220 | Find the cost of fencing around a circular field of diameter 70 m at the rate of Rs.1 a meter? | {
"A": "288",
"B": "132",
"C": "220",
"D": "592",
"E": "261"
} | multiply(circumface(divide(70, const_2)), 1) | divide(n0,const_2)|circumface(#0)|multiply(n1,#1)| | "2 * 22 / 7 * 35 = 220 220 * 1 = rs . 220 answer : c" | physics |
math_qa__PBnBDq1vvq8m7RxN | A train takes 10 sec to pass a signal post and covers a distance of 10 km in 15 min. Find the length of train? Choose the correct answer:
A) 100.1 m B) 223.1 m C) 111.1 m D) 120.3 m E) 133.4 m | <gadget id="calculator">1_000 * 10</gadget>
<output>10_000</output>
<gadget id="calculator">60 * 15</gadget>
<output>900</output>
<gadget id="calculator">10_000 / 900</gadget>
<output>100/9 = around 11.111111</output>
<gadget id="calculator">(100/9) * 10</gadget>
<output>1_000/9 = around 111.111111</output>
<result>C</result> | C | 111.1 | A train takes 10 sec to pass a signal post and covers a distance of 10 km in 15 min. Find the length of train? | {
"A": "100.1 m",
"B": "223.1 m",
"C": "111.1 m",
"D": "120.3 m",
"E": "133.4 m"
} | multiply(divide(multiply(const_1000, 10), multiply(const_60, 15)), 10) | multiply(n0,const_1000)|multiply(n2,const_60)|divide(#0,#1)|multiply(n0,#2) | explanation : we know , speed = distance / time speed = 10 / 50 x 60 = 40 x 5 / 18 m / sec = 11.1 m / sec length of train = ( speed x time ) = ( 11.11 x 10 ) = 111.1 m answer is c | physics |
math_qa__CU7WnV2cbF6Dmz7W | An amount of money is to be distributed among Faruk, Vasim and Ranjith in the ratio 3 : 5 : 6. If Vasims share is Rs. 1500, what is the difference between Faruk's and Ranjith's shares? Choices: A) s 1200 B) s 1500 C) s 1600 D) s 1900 E) s 900 | <gadget id="calculator">1_500 / 5</gadget>
<output>300</output>
<gadget id="calculator">6 - 3</gadget>
<output>3</output>
<gadget id="calculator">300 * 3</gadget>
<output>900</output>
<result>E</result> | E | 900 | An amount of money is to be distributed among Faruk, Vasim and Ranjith in the ratio 3 : 5 : 6. If Vasims share is Rs. 1500, what is the difference between Faruk's and Ranjith's shares? | {
"A": "s 1200",
"B": "s 1500",
"C": "s 1600",
"D": "s 1900",
"E": "s 900"
} | multiply(divide(1500, 5), subtract(6, 3)) | divide(n3,n1)|subtract(n2,n0)|multiply(#0,#1) | explanation : let p = faruk , q = vasim , r = ranjith let p = 3 x , q = 5 x and r = 6 x . then , 5 x = 1500 ? x = 300 . p = 900 , q = 1500 and r = 1800 . hence , ( r - p ) = ( 1800 - 900 ) = 900 answer : e | other |
math_qa__xxWFYiPGd3OKw54s | A sum of Rs.312 was divided among 100 boys and girls in such
a way that each boy gets Rs.3.60 and each girl Rs.2.40. Choose the most appropriate option: A) 45 B) 49 C) 52 D) 60 E) 74 | <gadget id="calculator">2.4 * 100</gadget>
<output>240</output>
<gadget id="calculator">312 - 240</gadget>
<output>72</output>
<gadget id="calculator">3.6 - 2.4</gadget>
<output>1.2</output>
<gadget id="calculator">72 / 1.2</gadget>
<output>60</output>
<result>D</result> | D | 60 | A sum of Rs.312 was divided among 100 boys and girls in such
a way that each boy gets Rs.3.60 and each girl Rs.2.40. | {
"A": "45",
"B": "49",
"C": "52",
"D": "60",
"E": "74"
} | divide(subtract(312, multiply(2.4, const_100)), subtract(3.6, 2.4)) | multiply(n3,const_100)|subtract(n2,n3)|subtract(n0,#0)|divide(#2,#1) | let number of boys = x then number of girls = ( 100 - x ) 3.60 x + 2.40 ( 100 - x ) = 312 ¡ ê 1.2 x = 312 - 240 = 72 ¡ ê x = 60 answer : d | general |
math_qa__qciRth3bdySwpOE3 | If the average (arithmetic mean) of a and b is 30 and the average of b and c is 60, what is the value of c − a? Choose the correct choice from the following answers.
A) 25
B) 60
C) 90
D) 140
E) it can not be determined from the information given . | <gadget id="calculator">60 * 2</gadget>
<output>120</output>
<gadget id="calculator">30 * 2</gadget>
<output>60</output>
<gadget id="calculator">120 - 60</gadget>
<output>60</output>
<result>B</result> | B | 60 | If the average (arithmetic mean) of a and b is 30 and the average of b and c is 60, what is the value of c − a? | {
"A": "25",
"B": "60",
"C": "90",
"D": "140",
"E": "it can not be determined from the information given ."
} | subtract(multiply(60, const_2), multiply(30, const_2)) | multiply(n1,const_2)|multiply(n0,const_2)|subtract(#0,#1) | - ( a + b = 60 ) b + c = 120 c - a = 60 b . 60 | general |
math_qa__I1JY4YRkvUJFCdXQ | What is the minimum percentage increase in the mean of set F {-4, -1, 0, 6, 9} if its two smallest elements are replaced with two different primes? Choose the most appropriate option: A) 25 % B) 50 % C) 75 % D) 100 % E) 200 % | <gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">5 + 6</gadget>
<output>11</output>
<gadget id="calculator">11 + 9</gadget>
<output>20</output>
<gadget id="calculator">1 + 4</gadget>
<output>5</output>
<gadget id="calculator">20 / 5</gadget>
<output>4</output>
<gadget id="calculator">-4</gadget>
<output>-4</output>
<gadget id="calculator">-1</gadget>
<output>-1</output>
<gadget id="calculator">(-4) + (-1)</gadget>
<output>-5</output>
<gadget id="calculator">(-5) + 6</gadget>
<output>1</output>
<gadget id="calculator">1 + 9</gadget>
<output>10</output>
<gadget id="calculator">10 / 5</gadget>
<output>2</output>
<gadget id="calculator">4 - 2</gadget>
<output>2</output>
<gadget id="calculator">2 / 2</gadget>
<output>1</output>
<gadget id="calculator">1 * 100</gadget>
<output>100</output>
<result>D</result> | D | 100 | What is the minimum percentage increase in the mean of set F {-4, -1, 0, 6, 9} if its two smallest elements are replaced with two different primes? | {
"A": "25 %",
"B": "50 %",
"C": "75 %",
"D": "100 %",
"E": "200 %"
} | multiply(divide(subtract(divide(add(add(add(const_2, const_3), 6), 9), add(1, 4)), divide(add(add(add(negate(4), negate(1)), 6), 9), add(1, 4))), divide(add(add(add(negate(4), negate(1)), 6), 9), add(1, 4))), const_100) | add(const_2,const_3)|add(n0,n1)|negate(n0)|negate(n1)|add(n3,#0)|add(#2,#3)|add(n4,#4)|add(n3,#5)|add(n4,#7)|divide(#6,#1)|divide(#8,#1)|subtract(#9,#10)|divide(#11,#10)|multiply(#12,const_100) | mean of f is ( - 4 - 1 + 0 + 6 + 9 ) / 5 = 2 ; in order the increase to be minimal we should replace two smallest elements of f , which are - 4 and - 1 , with two smallest primes , which are 2 and 3 . hence our new set will be { 2 , 3 , 0 , 6 , 9 } - - > new mean is ( 2 + 3 + 0 + 6 + 9 ) / 5 = 4 . percent increase = ( 4 - 2 ) / 2 * 100 = 100 % . answer : d . | general |
math_qa__Pl8sYlmOYuPX0oZa | The volumes of two cones are in the ratio 1 : 12 and the radii of the cones are in the ratio of 1 : 3. What is the ratio of their heights?
Select the correct option.
A) 3 : 4 B) 2 : 7 C) 2 : 2 D) 2 : 1 E) 2 : 9 | <gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>
<result>A</result> | A | 0.75 | The volumes of two cones are in the ratio 1 : 12 and the radii of the cones are in the ratio of 1 : 3. What is the ratio of their heights? | {
"A": "3 : 4",
"B": "2 : 7",
"C": "2 : 2",
"D": "2 : 1",
"E": "2 : 9"
} | divide(3, const_4) | divide(n3,const_4) | the volume of the cone = ( 1 / 3 ) π r 2 h only radius ( r ) and height ( h ) are varying . hence , ( 1 / 3 ) π may be ignored . v 1 / v 2 = r 12 h 1 / r 22 h 2 = > 1 / 12 = ( 1 ) 2 h 1 / ( 3 ) 2 h 2 = > h 1 / h 2 = 3 / 4 i . e . h 1 : h 2 = 3 : 4 answer : a | geometry |
math_qa__2RZgtjHRASP6GYAZ | Two numbers are 35% and 42% are less than a third number .How much percent is the second number less than the first ? Answers
A) 11.769 % B) 10.769 % C) 12.769 % D) 11.69 % E) 11.89 % | <gadget id="calculator">100 - 35</gadget>
<output>65</output>
<gadget id="calculator">100 - 42</gadget>
<output>58</output>
<gadget id="calculator">65 - 58</gadget>
<output>7</output>
<gadget id="calculator">7 / 65</gadget>
<output>7/65 = around 0.107692</output>
<gadget id="calculator">(7/65) * 100</gadget>
<output>140/13 = around 10.769231</output>
<result>B</result> | B | 10.769 | Two numbers are 35% and 42% are less than a third number .How much percent is the second number less than the first ? | {
"A": "11.769 %",
"B": "10.769 %",
"C": "12.769 %",
"D": "11.69 %",
"E": "11.89 %"
} | multiply(divide(subtract(subtract(const_100, 35), subtract(const_100, 42)), subtract(const_100, 35)), const_100) | subtract(const_100,n0)|subtract(const_100,n1)|subtract(#0,#1)|divide(#2,#0)|multiply(#3,const_100)| | "explanation : i ii iii 65 58 100 65 - - - - - - - - 7 100 - - - - - - ? = > 10.769 % answer b" | gain |
math_qa__lXZhvrkPx5RyAuYg | JOHN and Roger can finish the work 24 days if they work together. They worked together for 16 days and then Roger left. JOHN finished the remaining work in another 16 days. In how many days JOHN alone can finish the work? Pick one:
A) 30 days B) 48 days C) 70 days D) 80 days E) 90 days | <gadget id="calculator">16 / 24</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">1 - (2/3)</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">16 / (1/3)</gadget>
<output>48</output>
<result>B</result> | B | 48 | JOHN and Roger can finish the work 24 days if they work together. They worked together for 16 days and then Roger left. JOHN finished the remaining work in another 16 days. In how many days JOHN alone can finish the work? | {
"A": "30 days",
"B": "48 days",
"C": "70 days",
"D": "80 days",
"E": "90 days"
} | divide(16, subtract(const_1, divide(16, 24))) | divide(n1,n0)|subtract(const_1,#0)|divide(n1,#1) | amount of work done by john and roger in 1 day = 1 / 24 amount of work done by john and roger in 16 days = 16 ã — ( 1 / 24 ) = 2 / 3 remaining work â € “ 1 â € “ 2 / 3 = 1 / 3 john completes 1 / 3 work in 16 days amount of work john can do in 1 day = ( 1 / 3 ) / 16 = 1 / 48 = > john can complete the work in 48 days answer : b | physics |
math_qa__PuuYM8Q1RFNUF86D | There are 43 stations between Ernakulam and Chennai. How many second class tickets have to be printed, so that a passenger can travel from one station to any other station? Pick.
A) 1980 B) 1920 C) 1990 D) 1890 E) 1900 | <gadget id="calculator">43 + 2</gadget>
<output>45</output>
<gadget id="calculator">45 - 1</gadget>
<output>44</output>
<gadget id="calculator">45 * 44</gadget>
<output>1_980</output>
<result>A</result> | A | 1,980 | There are 43 stations between Ernakulam and Chennai. How many second class tickets have to be printed, so that a passenger can travel from one station to any other station? | {
"A": "1980",
"B": "1920",
"C": "1990",
"D": "1890",
"E": "1900"
} | multiply(add(43, const_2), subtract(add(43, const_2), const_1)) | add(n0,const_2)|subtract(#0,const_1)|multiply(#0,#1)| | "the total number of stations = 45 from 45 stations we have to choose any two stations and the direction of travel ( ernakulam to chennai is different from chennai to ernakulam ) in 45 p 2 ways . 45 p 2 = 45 * 44 = 870 answer : a" | physics |
math_qa__5dNbjdYNBUCEpAeR | If X and Y are sets of integers, X # Y denotes the set of integers that belong to set X or set Y, but not both. If X consists of 12 integers, Y consists of 18 integers, and 6 of the integers are in both X and Y, then X # Y consists of how many integers? Choose one: A) 6 B) 16 C) 18 D) 30 E) 174 | <gadget id="calculator">18 - 6</gadget>
<output>12</output>
<gadget id="calculator">12 - 6</gadget>
<output>6</output>
<gadget id="calculator">12 + 6</gadget>
<output>18</output>
<result>C</result> | C | 18 | If X and Y are sets of integers, X # Y denotes the set of integers that belong to set X or set Y, but not both. If X consists of 12 integers, Y consists of 18 integers, and 6 of the integers are in both X and Y, then X # Y consists of how many integers? | {
"A": "6",
"B": "16",
"C": "18",
"D": "30",
"E": "174"
} | add(subtract(18, 6), subtract(12, 6)) | subtract(n1,n2)|subtract(n0,n2)|add(#0,#1)| | "the number of integers that belong to set x only is 12 - 6 = 6 ; the number of integers that belong to set y only is 18 - 6 = 12 ; the number of integers that belong to set x or set y , but not both is 6 + 12 = 18 . answer : c ." | other |
math_qa__1PepQdlp2TvvbNdB | When a certain tree was first planted, it was 4 feet tall, and the height of the tree increased by a constant amount each year for the next 6 years. At the end of the 6th year, the tree was 1/6 taller than it was at the end of the 4th year. By how many feet did the height of the tree increase each year? Pick:
A) 3 / 10 B) 2 / 5 C) 1 / 2 D) 2 / 3 E) 6 / 5 | <gadget id="calculator">6 - 4</gadget>
<output>2</output>
<gadget id="calculator">2 * 6</gadget>
<output>12</output>
<gadget id="calculator">12 - 4</gadget>
<output>8</output>
<gadget id="calculator">4 / 8</gadget>
<output>1/2 = around 0.5</output>
<result>C</result> | C | 0.5 | When a certain tree was first planted, it was 4 feet tall, and the height of the tree increased by a constant amount each year for the next 6 years. At the end of the 6th year, the tree was 1/6 taller than it was at the end of the 4th year. By how many feet did the height of the tree increase each year? | {
"A": "3 / 10",
"B": "2 / 5",
"C": "1 / 2",
"D": "2 / 3",
"E": "6 / 5"
} | divide(4, subtract(multiply(subtract(6, 4), 6), 4)) | subtract(n1,n0)|multiply(n4,#0)|subtract(#1,n0)|divide(n0,#2)| | "say , the tree grows by x feet every year . then , 4 + 6 x = ( 1 + 1 / 6 ) ( 4 + 4 x ) or , x = 1 / 2 answer c" | general |
math_qa__NGVlKCbxnmzh2uGJ | A dishonest dealer professes to sell goods at the cost price but uses a weight of 500 grams per kg, what is his percent? Choose the correct choice from the following options
A) 20 % B) 25 % C) 29 % D) 55 % E) 100 % | <gadget id="calculator">100 / 500</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">100 * 10</gadget>
<output>1_000</output>
<gadget id="calculator">(1/5) * 1_000</gadget>
<output>200</output>
<gadget id="calculator">200 - 100</gadget>
<output>100</output>
<result>E</result> | E | 100 | A dishonest dealer professes to sell goods at the cost price but uses a weight of 500 grams per kg, what is his percent? | {
"A": "20 %",
"B": "25 %",
"C": "29 %",
"D": "55 %",
"E": "100 %"
} | subtract(multiply(divide(const_100, 500), multiply(const_100, multiply(add(const_3, const_2), const_2))), const_100) | add(const_2,const_3)|divide(const_100,n0)|multiply(#0,const_2)|multiply(#2,const_100)|multiply(#1,#3)|subtract(#4,const_100)| | "500 - - - 500 100 - - - ? = > 100 % answer : e" | gain |
math_qa__t6cv8qeDAHZTYg6Y | A waitress's income consists of her salary and tips.During one week ,her tips were 9/4 of her salary.What fraction of her income for the week came from tips? Choose the correct choice from the following answers:
A) 9 / 13 B) 1 / 6 C) 1 / 3 D) 4 / 9 E) 5 / 9 | <gadget id="calculator">9 + 4</gadget>
<output>13</output>
<gadget id="calculator">9 / 13</gadget>
<output>9/13 = around 0.692308</output>
<result>A</result> | A | 0.692308 | A waitress's income consists of her salary and tips.During one week ,her tips were 9/4 of her salary.What fraction of her income for the week came from tips? | {
"A": "9 / 13",
"B": "1 / 6",
"C": "1 / 3",
"D": "4 / 9",
"E": "5 / 9"
} | divide(9, add(9, 4)) | add(n0,n1)|divide(n0,#0) | her tips were 9 / 4 of her salary . let ' s say her salary = $ 4 this mean her tips = ( 9 / 4 ) ( $ 4 ) = $ 9 so , her total income = $ 4 + $ 9 = $ 13 what fraction of her income for the week came from tips $ 9 $ 13 = 9 / 13 = a | general |
math_qa__RZ85Zk07qVWYorMr | A can do a piece of work in 8 days. B can do it in 12 days. With the assistance of C they completed the work in 4 days. Find in how many days can C alone do it? Choose the most appropriate option:
A) 87 days
B) 20 days
C) 16 days
D) 24 days
E) 36 days | <gadget id="calculator">8 * 12</gadget>
<output>96</output>
<gadget id="calculator">96 / 8</gadget>
<output>12</output>
<gadget id="calculator">96 / 12</gadget>
<output>8</output>
<gadget id="calculator">12 + 8</gadget>
<output>20</output>
<gadget id="calculator">20 * 4</gadget>
<output>80</output>
<gadget id="calculator">96 - 80</gadget>
<output>16</output>
<gadget id="calculator">16 / 4</gadget>
<output>4</output>
<gadget id="calculator">96 / 4</gadget>
<output>24</output>
<result>D</result> | D | 24 | A can do a piece of work in 8 days. B can do it in 12 days. With the assistance of C they completed the work in 4 days. Find in how many days can C alone do it? | {
"A": "87 days",
"B": "20 days",
"C": "16 days",
"D": "24 days",
"E": "36 days"
} | divide(multiply(8, 12), divide(subtract(multiply(8, 12), multiply(add(divide(multiply(8, 12), 8), divide(multiply(8, 12), 12)), 4)), 4)) | multiply(n0,n1)|divide(#0,n0)|divide(#0,n1)|add(#1,#2)|multiply(n2,#3)|subtract(#0,#4)|divide(#5,n2)|divide(#0,#6)| | "c = 1 / 4 - 1 / 8 - 1 / 12 = 1 / 24 = > 24 days answer : d" | physics |
math_qa__89mArjDYhBbgZpvY | Find the value of m 62519 x 9999 = m? Choose the correct choice from the following choices:
A) 724533811
B) 625127481
C) 545463251
D) 725117481
E) 677899932 | <gadget id="calculator">9_999 - 4</gadget>
<output>9_995</output>
<gadget id="calculator">9_995 * 62_519</gadget>
<output>624_877_405</output>
<result>B</result> | B | 625,127,481 | Find the value of m 62519 x 9999 = m? | {
"A": "724533811",
"B": "625127481",
"C": "545463251",
"D": "725117481",
"E": "677899932"
} | multiply(subtract(9999, const_4), 62519) | subtract(n1,const_4)|multiply(#0,n0)| | "62519 x 9999 = 62519 x ( 10000 - 1 ) = 62519 x 10000 - 62519 x 1 = 625190000 - 62519 = 625127481 b" | general |
math_qa__7Z1813UABg4n2LIo | An Italian sausage is 8 inches long. How many pieces of sausage can be cut from the 8-inch piece of sausage if each piece is to be 2/3 of an inch ? Choose the most appropriate option:
A) 12
B) 32
C) 22
D) 15
E) 20 | <gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">8 / (2/3)</gadget>
<output>12</output>
<result>A</result> | A | 12 | An Italian sausage is 8 inches long. How many pieces of sausage can be cut from the 8-inch piece of sausage if each piece is to be 2/3 of an inch ? | {
"A": "12",
"B": "32",
"C": "22",
"D": "15",
"E": "20"
} | divide(8, divide(2, 3)) | divide(n2,n3)|divide(n0,#0) | number of pieces = italian sausage ÷ 2 / 3 of an inch = 8 ÷ 2 / 3 = 8 / 1 ÷ 2 / 3 = 8 / 1 * 3 / 2 = 24 / 2 = 12 . answer is a . | general |
math_qa__V8R5CmuVexDnEv2G | A is a working partner and B is a sleeping partner in the business. A puts in Rs.3500 and B Rs.2500, A receives 10% of the profit for managing the business the rest being divided in proportion of their capitals. Out of a total profit of Rs.9600, money received by A is?
Choose the correct choice from the following choices
A) 1978 B) 2707 C) 7728 D) 4200 E) 6000 | <gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 - (1/10)</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">9_600 * (9/10)</gadget>
<output>8_640</output>
<gadget id="calculator">3_500 + 2_500</gadget>
<output>6_000</output>
<gadget id="calculator">2_500 / 6_000</gadget>
<output>5/12 = around 0.416667</output>
<gadget id="calculator">8_640 * (5/12)</gadget>
<output>3_600</output>
<gadget id="calculator">9_600 - 3_600</gadget>
<output>6_000</output>
<result>E</result> | E | 6,000 | A is a working partner and B is a sleeping partner in the business. A puts in Rs.3500 and B Rs.2500, A receives 10% of the profit for managing the business the rest being divided in proportion of their capitals. Out of a total profit of Rs.9600, money received by A is? | {
"A": "1978",
"B": "2707",
"C": "7728",
"D": "4200",
"E": "6000"
} | subtract(9600, multiply(multiply(9600, subtract(const_1, divide(10, const_100))), divide(2500, add(3500, 2500)))) | add(n0,n1)|divide(n2,const_100)|divide(n1,#0)|subtract(const_1,#1)|multiply(n3,#3)|multiply(#2,#4)|subtract(n3,#5)| | "35 : 25 = > 7 : 5 9600 * 10 / 100 = 960 9600 - 960 = 8640 8640 * 7 / 12 = 5040 + 960 = 6000 answer : e" | gain |
math_qa__ecbDNFTHO7NhFljy | What is the dividend. divisor 20, the quotient is 8 and the remainder is 6 Select.
A) 145
B) 148
C) 150
D) 153
E) 166 | <gadget id="calculator">20 * 8</gadget>
<output>160</output>
<gadget id="calculator">160 + 6</gadget>
<output>166</output>
<result>E</result> | E | 166 | What is the dividend. divisor 20, the quotient is 8 and the remainder is 6 | {
"A": "145",
"B": "148",
"C": "150",
"D": "153",
"E": "166"
} | add(multiply(20, 8), 6) | multiply(n0,n1)|add(n2,#0)| | "d = d * q + r d = 20 * 8 + 6 d = 160 + 6 d = 166 answer : e" | general |
math_qa__DTTlcSQOm9wGuTRQ | A train 550 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going? Choose the correct choice from the following choices
A) 30 B) 60 C) 25 D) 40 E) 10 | <gadget id="calculator">550 / 1_000</gadget>
<output>11/20 = around 0.55</output>
<gadget id="calculator">60 + 6</gadget>
<output>66</output>
<gadget id="calculator">(11/20) / 66</gadget>
<output>1/120 = around 0.008333</output>
<gadget id="calculator">3_600 * (1/120)</gadget>
<output>30</output>
<result>A</result> | A | 30 | A train 550 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going? | {
"A": "30",
"B": "60",
"C": "25",
"D": "40",
"E": "10"
} | multiply(const_3600, divide(divide(550, const_1000), add(60, 6))) | add(n1,n2)|divide(n0,const_1000)|divide(#1,#0)|multiply(#2,const_3600) | speed of train relative to man = ( 60 + 6 ) km / hr = 66 km / hr [ 66 * 5 / 18 ] m / sec = [ 55 / 3 ] m / sec . time taken to pass the man = [ 550 * 3 / 55 ] sec = 30 sec answer : a | physics |
math_qa__33cXG0TiieZ5bmVt | Given that 268x74= 19732, find the value of 2.68x.74. Select
A) 1.9732
B) 1.0025
C) 1.5693
D) 1.0266
E) none | <gadget id="calculator">268 / 100</gadget>
<output>67/25 = around 2.68</output>
<gadget id="calculator">74 / 100</gadget>
<output>37/50 = around 0.74</output>
<gadget id="calculator">(67/25) * (37/50)</gadget>
<output>2_479/1_250 = around 1.9832</output>
<result>A</result> | A | 1.9732 | Given that 268x74= 19732, find the value of 2.68x.74. | {
"A": "1.9732",
"B": "1.0025",
"C": "1.5693",
"D": "1.0266",
"E": "none"
} | multiply(divide(268, const_100), divide(74, const_100)) | divide(n0,const_100)|divide(n1,const_100)|multiply(#0,#1)| | "solution sum of decimals places = ( 2 + 2 ) = 4 . therefore , = 2.68 × . 74 = 1.9732 answer a" | general |
math_qa__uOVjdNDgfPyAc0HU | Bill made a profit of 10% by selling a product. If he had purchased that product for 10% less and sold it at a profit of 30%, he would have received $ 70 more. What was his original selling price? Pick one:
A) $ 770 B) $ 660 C) $ 700 D) $ 1100 E) $ 840 | <gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 - (1/10)</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">1 + (3/10)</gadget>
<output>13/10 = around 1.3</output>
<gadget id="calculator">(9/10) * (13/10)</gadget>
<output>117/100 = around 1.17</output>
<gadget id="calculator">1 + (1/10)</gadget>
<output>11/10 = around 1.1</output>
<gadget id="calculator">(117/100) - (11/10)</gadget>
<output>7/100 = around 0.07</output>
<gadget id="calculator">70 / (7/100)</gadget>
<output>1_000</output>
<gadget id="calculator">1_000 * (11/10)</gadget>
<output>1_100</output>
<result>D</result> | D | 1,100 | Bill made a profit of 10% by selling a product. If he had purchased that product for 10% less and sold it at a profit of 30%, he would have received $ 70 more. What was his original selling price? | {
"A": "$ 770",
"B": "$ 660",
"C": "$ 700",
"D": "$ 1100",
"E": "$ 840"
} | multiply(divide(70, subtract(multiply(subtract(const_1, divide(10, const_100)), add(const_1, divide(30, const_100))), add(const_1, divide(10, const_100)))), add(const_1, divide(10, const_100))) | divide(n0,const_100)|divide(n2,const_100)|add(#0,const_1)|add(#1,const_1)|subtract(const_1,#0)|multiply(#3,#4)|subtract(#5,#2)|divide(n3,#6)|multiply(#2,#7)| | "let the original purchase price be x so original selling price at 10 % profit = 1.1 x if product is purchased at 10 % less of original = 0.9 x profit of 30 % on this price = 1.3 ( 0.9 x ) he would have received $ 70 more in second scenario = > 1.3 ( 0.9 x ) - 1.1 x = 70 = > 0.07 x = 70 = > x = $ 1000 original purchase price = $ 1000 hence , original selling price ( at 10 % of profit ) = 1.1 ( 1000 ) = $ 1100 option d" | general |
math_qa__WkadHKisNdDhnyWF | George baked a total of 50 pizzas for 5 straight days, beginning on Saturday. He baked 3/5 of the pizzas the first day, and 3/5 of the remaining pizzas the second day. If each successive day he baked fewer pizzas than the previous day, what is the maximum number of pizzas he could have baked on Wednesday? Pick: A) 5 B) 4 C) 3 D) 2 E) 1 | <gadget id="calculator">3 / 5</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">50 * (3/5)</gadget>
<output>30</output>
<gadget id="calculator">50 - 30</gadget>
<output>20</output>
<gadget id="calculator">20 * (3/5)</gadget>
<output>12</output>
<gadget id="calculator">20 - 12</gadget>
<output>8</output>
<gadget id="calculator">8 - 3</gadget>
<output>5</output>
<gadget id="calculator">5 / 5</gadget>
<output>1</output>
<result>E</result> | E | 1 | George baked a total of 50 pizzas for 5 straight days, beginning on Saturday. He baked 3/5 of the pizzas the first day, and 3/5 of the remaining pizzas the second day. If each successive day he baked fewer pizzas than the previous day, what is the maximum number of pizzas he could have baked on Wednesday? | {
"A": "5",
"B": "4",
"C": "3",
"D": "2",
"E": "1"
} | divide(subtract(subtract(subtract(50, multiply(50, divide(3, 5))), multiply(subtract(50, multiply(50, divide(3, 5))), divide(3, 5))), 3), subtract(subtract(subtract(50, multiply(50, divide(3, 5))), multiply(subtract(50, multiply(50, divide(3, 5))), divide(3, 5))), 3)) | divide(n2,n1)|multiply(n0,#0)|subtract(n0,#1)|multiply(#0,#2)|subtract(#2,#3)|subtract(#4,n2)|divide(#5,#5)| | 3 / 5 of the 50 pizzas cooked on saturday = 30 pizzas 3 / 5 of the remaining pizzas on sunday = 12 pizzas we ' re left with ( 50 - 30 - 12 ) = 8 pizzas for the remaining 3 days . the prompt tells us that each day has fewer pizzas than the day before it , so we ca n ' t have duplicate numbers . m t w 5 2 1 = 8 w = 1 e | general |
math_qa__ikZ5p9508HiiaGeD | The difference between the value of a number increased by 12.5% and the value of the original number decreased by 25% is 30. What is the original number?
Choose the correct option:
A) 60 B) 80 C) 40 D) 120 E) 160 | <gadget id="calculator">12.5 / 100</gadget>
<output>0.125</output>
<gadget id="calculator">1 + 0.125</gadget>
<output>1.125</output>
<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 - (1/4)</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">1.125 - (3/4)</gadget>
<output>0.375</output>
<gadget id="calculator">30 / 0.375</gadget>
<output>80</output>
<result>B</result> | B | 80 | The difference between the value of a number increased by 12.5% and the value of the original number decreased by 25% is 30. What is the original number? | {
"A": "60",
"B": "80",
"C": "40",
"D": "120",
"E": "160"
} | divide(30, subtract(add(const_1, divide(12.5, const_100)), subtract(const_1, divide(25, const_100)))) | divide(n0,const_100)|divide(n1,const_100)|add(#0,const_1)|subtract(const_1,#1)|subtract(#2,#3)|divide(n2,#4)| | "explanatory answer let the original number be x . let a be the value obtained when x is increased by 12.5 % . therefore , a = x + 12.5 % of x let b be the value obtained when x is decreased by 25 % . therefore , b = x - 25 % of x the question states that a - b = 30 i . e . , x + 12.5 % of x - ( x - 25 % of x ) = 30 x + 12.5 % of x - x + 25 % of x = 30 37.5 % of x = 30 x = 30 / 37.5 * 100 = 80 the correct choice is ( b )" | general |
math_qa__RQZJu3PFgMwkCrj9 | A man walking at a rate of 10km/hr crosses a bridge in 15 minutes. The length of the bridge is?
Pick one: A) 1521 B) 1492 C) 1667 D) 2500 E) 1112 | <gadget id="calculator">10 * 1_000</gadget>
<output>10_000</output>
<gadget id="calculator">10_000 / 60</gadget>
<output>500/3 = around 166.666667</output>
<gadget id="calculator">(500/3) * 15</gadget>
<output>2_500</output>
<result>D</result> | D | 2,500 | A man walking at a rate of 10km/hr crosses a bridge in 15 minutes. The length of the bridge is? | {
"A": "1521",
"B": "1492",
"C": "1667",
"D": "2500",
"E": "1112"
} | multiply(divide(multiply(10, const_1000), const_60), 15) | multiply(n0,const_1000)|divide(#0,const_60)|multiply(n1,#1)| | "speed = 10 * 5 / 18 = 50 / 18 m / sec distance covered in 15 minutes = 50 / 18 * 15 * 60 = 2500 m answer is d" | gain |
math_qa__05EDB74zyhIgdNsr | Dames school has 2000 boys and 5000 girls. What is the percentage increase from boys to total attendance and girls to total attendance? Choose the correct answer: A) 40 % B) 10 % C) . 4 % D) 50 % E) 12 % | <gadget id="calculator">2_000 / 5_000</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) * 100</gadget>
<output>40</output>
<result>A</result> | A | 40 | Dames school has 2000 boys and 5000 girls. What is the percentage increase from boys to total attendance and girls to total attendance? | {
"A": "40 %",
"B": "10 %",
"C": ". 4 %",
"D": "50 %",
"E": "12 %"
} | multiply(divide(2000, 5000), const_100) | divide(n0,n1)|multiply(#0,const_100) | ratio of boys to total attendance ( 2 / 7 ) ratio of girls to total attendance ( 5 / 7 ) percentage increase is ( difference / initial quantity ) * 100 ( 2 / 7 ) / ( 5 / 7 ) * 100 = 40 % correct answer is a | general |
math_qa__cXzKy4MOqGAYjKi0 | The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 16000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is Select:
A) 20
B) 21
C) 35
D) 23
E) 24 | <gadget id="calculator">16_000 - 8_000</gadget>
<output>8_000</output>
<gadget id="calculator">7 * 8_000</gadget>
<output>56_000</output>
<gadget id="calculator">8_000 - 6_000</gadget>
<output>2_000</output>
<gadget id="calculator">56_000 / 2_000</gadget>
<output>28</output>
<gadget id="calculator">7 + 28</gadget>
<output>35</output>
<result>C</result> | C | 35 | The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 16000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is | {
"A": "20",
"B": "21",
"C": "35",
"D": "23",
"E": "24"
} | add(7, divide(multiply(7, subtract(16000, 8000)), subtract(8000, 6000))) | subtract(n2,n0)|subtract(n0,n3)|multiply(n1,#0)|divide(#2,#1)|add(n1,#3)| | "solution let the toatl number of workers be x . then 8000 x = ( 16000 x 7 ) + 6000 ( x - 7 ) x = 35 . answer c" | general |
math_qa__01GHE215Tbi0bRiP | N = 1/3 + 1/4
What is the value of N? Choose the correct choice from the following choices
A) 7 / 12
B) 1 / 6
C) 1 / 8
D) 5 / 17
E) 12 / 7 | <gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/3) + (1/4)</gadget>
<output>7/12 = around 0.583333</output>
<result>A</result> | A | 0.583333 | N = 1/3 + 1/4
What is the value of N? | {
"A": "7 / 12",
"B": "1 / 6",
"C": "1 / 8",
"D": "5 / 17",
"E": "12 / 7"
} | add(divide(1, 3), divide(1, 4)) | divide(n0,n1)|divide(n0,n3)|add(#0,#1) | to sum 1 / 3 and 1 / 4 multiply both sides by 12 12 * n = 12 * 1 / 3 + 12 * 1 / 4 12 * n = 4 + 3 n = 7 / 12 ans : a | general |
math_qa__pQGkD7EugSn8NU2Y | How many even multiples of 55 are there between 549 and 1101?
Answers
A) 5
B) 6
C) 9
D) 10
E) 11 | <gadget id="calculator">1_101 - 549</gadget>
<output>552</output>
<gadget id="calculator">55 * 2</gadget>
<output>110</output>
<gadget id="calculator">552 / 110</gadget>
<output>276/55 = around 5.018182</output>
<gadget id="calculator">(276/55) + 1</gadget>
<output>331/55 = around 6.018182</output>
<result>B</result> | B | 6 | How many even multiples of 55 are there between 549 and 1101? | {
"A": "5",
"B": "6",
"C": "9",
"D": "10",
"E": "11"
} | add(divide(subtract(1101, 549), multiply(55, const_2)), const_1) | multiply(n0,const_2)|subtract(n2,n1)|divide(#1,#0)|add(#2,const_1)| | "550 = 10 * 55 1100 = 20 * 55 the even multiples are 55 multiplied by 10 , 12 , 14 , 16 , 18 , and 20 for a total of 6 . the answer is b ." | general |
math_qa__rBvLYGx9XQUCRPFc | Before leaving home for the town of Madison, Pete checks a map which shows that Madison is 5 inches from his current location, Gardensquare. Pete arrives in Madison 5 hours later and drove at an average speed of 60 miles per hour. At what scale, in inches per mile, is the map drawn? Choose the correct choice:
A) 1 / 3
B) 1 / 30
C) 1 / 10
D) 1 / 45
E) 1 / 60 | <gadget id="calculator">5 / 5</gadget>
<output>1</output>
<gadget id="calculator">1 * 60</gadget>
<output>60</output>
<gadget id="calculator">1 / 60</gadget>
<output>1/60 = around 0.016667</output>
<result>E</result> | E | 0.016667 | Before leaving home for the town of Madison, Pete checks a map which shows that Madison is 5 inches from his current location, Gardensquare. Pete arrives in Madison 5 hours later and drove at an average speed of 60 miles per hour. At what scale, in inches per mile, is the map drawn? | {
"A": "1 / 3",
"B": "1 / 30",
"C": "1 / 10",
"D": "1 / 45",
"E": "1 / 60"
} | divide(const_1, multiply(divide(5, 5), 60)) | divide(n1,n0)|multiply(#0,n2)|divide(const_1,#1)| | "pete covered 5 * 60 = 300 miles which correspond to 5 inches on the map - - > scale in inches per mile is 5 / 300 = 1 / 60 . answer : e ." | physics |
math_qa__1jzdaNHnBAW0HoRl | 25.25/2000 is equal to:
Choose the correct choice
A) 1.012526
B) 0.012625
C) 0.12526
D) 0.12625
E) 0.12725 | <gadget id="calculator">25.25 / 2_000</gadget>
<output>0.012625</output>
<result>B</result> | B | 0.012625 | 25.25/2000 is equal to: | {
"A": "1.012526",
"B": "0.012625",
"C": "0.12526",
"D": "0.12625",
"E": "0.12725"
} | divide(25.25, 2000) | divide(n0,n1)| | "25.25 / 2000 = 2525 / 200000 = 0.012625 answer : b" | general |
math_qa__eKgscNuPSXlvO7nR | On a sum of money, the simple interest for 2 years is Rs. 660,while the compound interest is Rs.696.30,the rate of interest being the same in both the cases. The rate of interest is Choose the correct choice from the following options
A) 10 % B) 11 % C) 12 % D) 10.5 % E) none | <gadget id="calculator">660 / 2</gadget>
<output>330</output>
<gadget id="calculator">696.3 - 330</gadget>
<output>366.3</output>
<gadget id="calculator">366.3 - 330</gadget>
<output>36.3</output>
<gadget id="calculator">100 * 36.3</gadget>
<output>3_630</output>
<gadget id="calculator">3_630 / 330</gadget>
<output>11</output>
<result>B</result> | B | 11 | On a sum of money, the simple interest for 2 years is Rs. 660,while the compound interest is Rs.696.30,the rate of interest being the same in both the cases. The rate of interest is | {
"A": "10 %",
"B": "11 %",
"C": "12 %",
"D": "10.5 %",
"E": "none"
} | divide(multiply(const_100, subtract(subtract(696.30, divide(660, 2)), divide(660, 2))), divide(660, 2)) | divide(n1,n0)|subtract(n2,#0)|subtract(#1,#0)|multiply(#2,const_100)|divide(#3,#0)| | "solution difference in c . i and s . i for 2 years = rs ( 696.30 - 660 ) = rs . 36.30 . s . i for one years = rs 330 . s . i on rs . 330 for 1 year = rs . 36.30 rate = ( 100 x 36.30 / 330 x 1 ) % = 11 % . answer b" | gain |
math_qa__RvnMrjZh0yZkeDBn | a certain tire company can produce tires at a cost of $ 22500 per batch plus $ 8 per tire . the company can sell tires to the wholesaler at a cost of $ 20 per tire . if a batch of 15000 tires is produced and sold , what is the company ’ s profit per tire ? Choose the correct choice from the following
A) $ 9.00
B) $ 9.50
C) $ 10.50
D) $ 13.50
E) $ 20.00 | <gadget id="calculator">15_000 * 20</gadget>
<output>300_000</output>
<gadget id="calculator">8 * 15_000</gadget>
<output>120_000</output>
<gadget id="calculator">22_500 + 120_000</gadget>
<output>142_500</output>
<gadget id="calculator">300_000 - 142_500</gadget>
<output>157_500</output>
<gadget id="calculator">157_500 / 15_000</gadget>
<output>21/2 = around 10.5</output>
<result>C</result> | C | 10.5 | a certain tire company can produce tires at a cost of $ 22500 per batch plus $ 8 per tire . the company can sell tires to the wholesaler at a cost of $ 20 per tire . if a batch of 15000 tires is produced and sold , what is the company ’ s profit per tire ? | {
"A": "$ 9.00",
"B": "$ 9.50",
"C": "$ 10.50",
"D": "$ 13.50",
"E": "$ 20.00"
} | divide(subtract(multiply(15000, 20), add(22500, multiply(8, 15000))), 15000) | multiply(n2,n3)|multiply(n1,n3)|add(n0,#1)|subtract(#0,#2)|divide(#3,n3) | cp ( 15000 tires ) = $ 22500 + ( $ 8 × 15000 ) = $ 142500 sp ( 15000 tires ) = $ 20 × 15000 = $ 300000 profit = sp - cp = $ 300000 - $ 142500 = $ 157500 profit / tire = $ 157500 / 15000 = $ 10.50 answer c | gain |
math_qa__O8zKq7r8GyMzWHp3 | At a certain company, two-thirds of the employees had cell phones and two-fifths had pagers. If one-third of the employees had neither cell phones nor pagers then what fraction of the employees had both cell phones and pagers? Select the correct option:
A) 7 / 5 B) 6 / 11 C) 2 / 5 D) 1 / 3 E) 4 / 15 | <gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 - (1/3)</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">1 + 4</gadget>
<output>5</output>
<gadget id="calculator">2 / 5</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/3) + (2/5)</gadget>
<output>16/15 = around 1.066667</output>
<gadget id="calculator">(16/15) - (2/3)</gadget>
<output>2/5 = around 0.4</output>
<result>C</result> | C | 0.4 | At a certain company, two-thirds of the employees had cell phones and two-fifths had pagers. If one-third of the employees had neither cell phones nor pagers then what fraction of the employees had both cell phones and pagers? | {
"A": "7 / 5",
"B": "6 / 11",
"C": "2 / 5",
"D": "1 / 3",
"E": "4 / 15"
} | subtract(add(subtract(const_1, divide(const_1, const_3)), divide(const_2, add(const_1, const_4))), subtract(const_1, divide(const_1, const_3))) | add(const_1,const_4)|divide(const_1,const_3)|divide(const_2,#0)|subtract(const_1,#1)|add(#2,#3)|subtract(#4,#3) | let there be 15 employees cell phone = 10 pagers = 6 neither pager nor cell phone = 5 so , 10 = 10 + 6 - x or , x = 6 so , fraction of the employees had both cell phones and pagers = 6 / 15 = > 2 / 5 answer : c | other |
math_qa__3plicbQ9VvIfoAzn | The original price of a suit is $200. The price increased 30%, and after this increase, the store published a 30% off coupon for a one-day sale. Given that the consumers who used the coupon on sale day were getting 30% off the increased price, how much did these consumers pay for the suit? Pick:
A) $ 182
B) $ 191
C) $ 200
D) $ 209
E) $ 219 | <gadget id="calculator">200 * 30</gadget>
<output>6_000</output>
<gadget id="calculator">6_000 / 100</gadget>
<output>60</output>
<gadget id="calculator">200 + 60</gadget>
<output>260</output>
<gadget id="calculator">260 * 30</gadget>
<output>7_800</output>
<gadget id="calculator">7_800 / 100</gadget>
<output>78</output>
<gadget id="calculator">260 - 78</gadget>
<output>182</output>
<result>A</result> | A | 182 | The original price of a suit is $200. The price increased 30%, and after this increase, the store published a 30% off coupon for a one-day sale. Given that the consumers who used the coupon on sale day were getting 30% off the increased price, how much did these consumers pay for the suit? | {
"A": "$ 182",
"B": "$ 191",
"C": "$ 200",
"D": "$ 209",
"E": "$ 219"
} | subtract(add(200, divide(multiply(200, 30), const_100)), divide(multiply(add(200, divide(multiply(200, 30), const_100)), 30), const_100)) | multiply(n0,n1)|divide(#0,const_100)|add(n0,#1)|multiply(n1,#2)|divide(#3,const_100)|subtract(#2,#4)| | "given the foregoing discussion , it may be obvious now the trap - mistake answer is ( c ) . even if you can ’ t remember the correct thing to do , at the very least , learn to spot the trap ! the multiplier for a 30 % increases is 1 + 0.30 = 1.3 , and the multiplier for a 30 % decrease is 1 – 0.30 = 0.70 , so the combined change is 1.3 * 0.7 = 0.91 , 91 % percent of the original , or a 9 % decreases . now , multiply $ 200 * 0.91 = $ 182 . answer = ( a ) ." | general |
math_qa__WtNsJQJ68KTznlwg | A boat can travel with a speed of 22 km/hr in still water. If the speed of the stream is 5 km/hr, find the time taken by the boat to go 81 km downstream Choose the correct choice:
A) 5 hours B) 4 hours C) 3 hours D) 2 hours E) none of these | <gadget id="calculator">22 + 5</gadget>
<output>27</output>
<gadget id="calculator">81 / 27</gadget>
<output>3</output>
<result>C</result> | C | 3 | A boat can travel with a speed of 22 km/hr in still water. If the speed of the stream is 5 km/hr, find the time taken by the boat to go 81 km downstream | {
"A": "5 hours",
"B": "4 hours",
"C": "3 hours",
"D": "2 hours",
"E": "none of these"
} | divide(81, add(22, 5)) | add(n0,n1)|divide(n2,#0)| | "explanation : speed of the boat in still water = 22 km / hr speed of the stream = 5 km / hr speed downstream = ( 22 + 5 ) = 27 km / hr distance travelled downstream = 81 km time taken = distance / speed = 81 / 27 = 3 hours . answer : option c" | physics |
math_qa__pYO6S0Q7kKQLFibD | A man can do a piece of work in 5 days, but with the help of his son he can do it in 4 days. In what time can the son do it alone ?
Choose the correct choice from the following: A) 2 days B) 6 days C) 12 days D) 20 days E) none of these | <gadget id="calculator">5 * 4</gadget>
<output>20</output>
<gadget id="calculator">5 - 4</gadget>
<output>1</output>
<gadget id="calculator">20 / 1</gadget>
<output>20</output>
<result>D</result> | D | 20 | A man can do a piece of work in 5 days, but with the help of his son he can do it in 4 days. In what time can the son do it alone ? | {
"A": "2 days",
"B": "6 days",
"C": "12 days",
"D": "20 days",
"E": "none of these"
} | divide(multiply(5, 4), subtract(5, 4)) | multiply(n0,n1)|subtract(n0,n1)|divide(#0,#1)| | "explanation : in this type of question , where we have one person work and together work done . then we can easily get the other person work just by subtracting them . as son ' s one day work = ( 1 / 4 − 1 / 5 ) = ( 5 − 4 ) / 20 = 1 / 20 so son will do whole work in 20 days answer : d" | physics |
math_qa__daib0a1KfP0Q1zoL | A dealer offers a cash discount of 15% and still makes a profit of 36% when he further allows 25 articles to be sold at the cost price of 20 articles to a particular sticky bargainer. How much percent above the cost price were his articles listed? Choose the correct choice from the following choices:
A) 60 % B) 80 % C) 100 % D) 120 % E) 150 % | <gadget id="calculator">100 + 36</gadget>
<output>136</output>
<gadget id="calculator">136 / 100</gadget>
<output>34/25 = around 1.36</output>
<gadget id="calculator">25 - 20</gadget>
<output>5</output>
<gadget id="calculator">5 / 25</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(34/25) / (4/5)</gadget>
<output>17/10 = around 1.7</output>
<gadget id="calculator">100 - 15</gadget>
<output>85</output>
<gadget id="calculator">85 / 100</gadget>
<output>17/20 = around 0.85</output>
<gadget id="calculator">(17/10) / (17/20)</gadget>
<output>2</output>
<gadget id="calculator">2 - 1</gadget>
<output>1</output>
<gadget id="calculator">1 * 100</gadget>
<output>100</output>
<result>C</result> | C | 100 | A dealer offers a cash discount of 15% and still makes a profit of 36% when he further allows 25 articles to be sold at the cost price of 20 articles to a particular sticky bargainer. How much percent above the cost price were his articles listed? | {
"A": "60 %",
"B": "80 %",
"C": "100 %",
"D": "120 %",
"E": "150 %"
} | multiply(subtract(divide(divide(divide(add(const_100, 36), const_100), subtract(const_1, divide(subtract(25, 20), 25))), divide(subtract(const_100, 15), const_100)), const_1), const_100) | add(n1,const_100)|subtract(n2,n3)|subtract(const_100,n0)|divide(#0,const_100)|divide(#1,n2)|divide(#2,const_100)|subtract(const_1,#4)|divide(#3,#6)|divide(#7,#5)|subtract(#8,const_1)|multiply(#9,const_100) | given cash discount - 15 % profit - 36 % items sold - 25 price sold at = list price of 20 assume list price = $ 10 total invoice = $ 200 - 15 % cash discount = $ 170 let cost price of 25 items be x so total cost = 25 * x given the shopkeeper had a profit of 36 % 25 * x * 136 / 100 = 170 or x = $ 5 which means his products were listed at $ 10 which is a 100 % markup over $ 5 answer c | gain |
math_qa__iAseSoAFsk78RC1j | If x+y=2 and x2y3 + y2x3=32, what is the value of xy? Choose one:
A) 1
B) 2
C) 3
D) 4
E) 5 | <gadget id="calculator">32 / 2</gadget>
<output>16</output>
<gadget id="calculator">16 ** (1/2)</gadget>
<output>4</output>
<result>D</result> | D | 4 | If x+y=2 and x2y3 + y2x3=32, what is the value of xy? | {
"A": "1",
"B": "2",
"C": "3",
"D": "4",
"E": "5"
} | sqrt(divide(32, 2)) | divide(n5,n0)|sqrt(#0)| | "xy = 4 as x + y = 2 x 2 y 3 + y 2 x 3 = 32 x 2 y 2 ( y + x ) = 32 substituting x + y x 2 y 2 = 16 xy = 4 answer : d" | general |
math_qa__IahsJQBvZBwMm58D | if the price of a book is first decreased by 20% and then increased by 10%, then the net change in the price will be : Choose the correct choice from the following answers.
A) 10 B) 12 C) 37 D) 29 E) 22 | <gadget id="calculator">100 * 20</gadget>
<output>2_000</output>
<gadget id="calculator">2_000 / 100</gadget>
<output>20</output>
<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">100 * 10</gadget>
<output>1_000</output>
<gadget id="calculator">1_000 / 100</gadget>
<output>10</output>
<gadget id="calculator">100 + 10</gadget>
<output>110</output>
<gadget id="calculator">110 / 100</gadget>
<output>11/10 = around 1.1</output>
<gadget id="calculator">(4/5) * (11/10)</gadget>
<output>22/25 = around 0.88</output>
<gadget id="calculator">(22/25) * 100</gadget>
<output>88</output>
<gadget id="calculator">100 - 88</gadget>
<output>12</output>
<result>B</result> | B | 12 | if the price of a book is first decreased by 20% and then increased by 10%, then the net change in the price will be : | {
"A": "10",
"B": "12",
"C": "37",
"D": "29",
"E": "22"
} | subtract(const_100, multiply(multiply(divide(subtract(const_100, divide(multiply(const_100, 20), const_100)), const_100), divide(add(const_100, divide(multiply(const_100, 10), const_100)), const_100)), const_100)) | multiply(n0,const_100)|multiply(n1,const_100)|divide(#0,const_100)|divide(#1,const_100)|add(#3,const_100)|subtract(const_100,#2)|divide(#5,const_100)|divide(#4,const_100)|multiply(#6,#7)|multiply(#8,const_100)|subtract(const_100,#9) | explanation : let the original price be rs . 100 . decreased by 20 % = 80 then increased 10 % on rs 80 = 80 + 8 = 88 net change in price = 100 - 88 = 12 answer : b | general |
math_qa__dEZN59osfyz18rdY | The regular price per can of a certain brand of soda is $0.60. If the regular price per can is discounted 20 percent when the soda is purchased in 24-can cases, what is the price of 72 cans of this brand of soda purchased in 24-can cases? Choose the correct choice from the following answers:
A) $ 16.32 B) $ 18.00 C) $ 21.60 D) $ 34.56 E) $ 28.80 | <gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">0.6 * 72</gadget>
<output>43.2</output>
<gadget id="calculator">(4/5) * 43.2</gadget>
<output>34.56</output>
<result>D</result> | D | 34.56 | The regular price per can of a certain brand of soda is $0.60. If the regular price per can is discounted 20 percent when the soda is purchased in 24-can cases, what is the price of 72 cans of this brand of soda purchased in 24-can cases? | {
"A": "$ 16.32",
"B": "$ 18.00",
"C": "$ 21.60",
"D": "$ 34.56",
"E": "$ 28.80"
} | multiply(divide(subtract(const_100, 20), const_100), multiply(0.60, 72)) | multiply(n0,n3)|subtract(const_100,n1)|divide(#1,const_100)|multiply(#2,#0)| | "the discounted price of one can of soda is ( 0.8 ) ( $ 0.60 ) , or $ 0.48 therefore , the price of 72 cans of soda at the discounted price would be ( 72 ) ( $ 0.48 ) = 34.56 answer : d ." | gain |
math_qa__uBhoJJ0YFwVD3MZk | The cost price of an article is 36% of the marked price. Calculate the gain percent after allowing a discount of 20%. Choices.
A) 22.2 %
B) 36 %
C) 80 %
D) 122.2 %
E) none | <gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">80 / 36</gadget>
<output>20/9 = around 2.222222</output>
<gadget id="calculator">(20/9) - 1</gadget>
<output>11/9 = around 1.222222</output>
<gadget id="calculator">(11/9) * 100</gadget>
<output>1_100/9 = around 122.222222</output>
<result>D</result> | D | 122.2 | The cost price of an article is 36% of the marked price. Calculate the gain percent after allowing a discount of 20%. | {
"A": "22.2 %",
"B": "36 %",
"C": "80 %",
"D": "122.2 %",
"E": "none"
} | multiply(subtract(divide(subtract(const_100, 20), 36), const_1), const_100) | subtract(const_100,n1)|divide(#0,n0)|subtract(#1,const_1)|multiply(#2,const_100)| | "sol . let marked price = rs . 100 . then , c . p . = rs . 36 . s . p = rs . 80 . â ˆ ´ gain % = [ 44 / 36 * 100 ] % = 122.2 % . answer d" | gain |
math_qa__pKMNFmjnPmXxk9F3 | Mr Yadav spends 60% of his monthly salary on consumable items and 50% of the remaining on clothes and transport. He saves the remaining amount. If his savings at the end of the year were 19008, how much amount per month would he have spent on clothes and transport?
Choose the most appropriate option
A) 4038
B) 8076
C) 9691.2
D) 1584
E) 1625 | <gadget id="calculator">100 - 60</gadget>
<output>40</output>
<gadget id="calculator">40 * 50</gadget>
<output>2_000</output>
<gadget id="calculator">2_000 / 100</gadget>
<output>20</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">19_008 / (1/5)</gadget>
<output>95_040</output>
<gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">95_040 / 12</gadget>
<output>7_920</output>
<gadget id="calculator">7_920 * (1/5)</gadget>
<output>1_584</output>
<result>D</result> | D | 1,584 | Mr Yadav spends 60% of his monthly salary on consumable items and 50% of the remaining on clothes and transport. He saves the remaining amount. If his savings at the end of the year were 19008, how much amount per month would he have spent on clothes and transport? | {
"A": "4038",
"B": "8076",
"C": "9691.2",
"D": "1584",
"E": "1625"
} | multiply(divide(divide(19008, divide(divide(multiply(subtract(const_100, 60), 50), const_100), const_100)), multiply(const_3, const_4)), divide(divide(multiply(subtract(const_100, 60), 50), const_100), const_100)) | multiply(const_3,const_4)|subtract(const_100,n0)|multiply(n1,#1)|divide(#2,const_100)|divide(#3,const_100)|divide(n2,#4)|divide(#5,#0)|multiply(#6,#4)| | "∵ amount , he have spent in 1 month on clothes transport = amount spent on saving per month ∵ amount , spent on clothes and transport = 19008 ⁄ 12 = 1584 answer d" | general |
math_qa__VxlzdVJcejV19Hrv | Express 15 mps in kmph? Pick one: A) 22 B) 88 C) 90 D) 21 E) 54 | <gadget id="calculator">15 / 1_000</gadget>
<output>3/200 = around 0.015</output>
<gadget id="calculator">(3/200) * 3_600</gadget>
<output>54</output>
<result>E</result> | E | 54 | Express 15 mps in kmph? | {
"A": "22",
"B": "88",
"C": "90",
"D": "21",
"E": "54"
} | multiply(divide(15, const_1000), const_3600) | divide(n0,const_1000)|multiply(#0,const_3600)| | "15 * 18 / 5 = 54 kmph answer : e" | physics |
math_qa__JY94iThzE7HDPHaO | A man buy a book in Rs50 & sale it Rs80. What is the rate of profit ??? Choose the correct answer: A) 10 % B) 60 % C) 30 % D) 25 % E) 28 % | <gadget id="calculator">80 - 50</gadget>
<output>30</output>
<gadget id="calculator">30 / 50</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(3/5) * 100</gadget>
<output>60</output>
<result>B</result> | B | 60 | A man buy a book in Rs50 & sale it Rs80. What is the rate of profit ??? | {
"A": "10 %",
"B": "60 %",
"C": "30 %",
"D": "25 %",
"E": "28 %"
} | multiply(divide(subtract(80, 50), 50), const_100) | subtract(n1,n0)|divide(#0,n0)|multiply(#1,const_100)| | "cp = 50 sp = 80 profit = 80 - 50 = 30 % = 30 / 50 * 100 = 60 % answer : b" | gain |
math_qa__a2ZGjcAd1kHO8iJe | Find the simple interest on Rs. 71,200 at 16 2/3% per annum for 9 months. Choose the correct option.
A) s . 8500 B) s . 8900 C) s . 7500 D) s . 7000 E) s . 6500 | <gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">6 * 100</gadget>
<output>600</output>
<gadget id="calculator">600 * 100</gadget>
<output>60_000</output>
<gadget id="calculator">3 * 3</gadget>
<output>9</output>
<gadget id="calculator">9 * 100</gadget>
<output>900</output>
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">900 * 10</gadget>
<output>9_000</output>
<gadget id="calculator">60_000 + 9_000</gadget>
<output>69_000</output>
<gadget id="calculator">16 * 3</gadget>
<output>48</output>
<gadget id="calculator">48 + 2</gadget>
<output>50</output>
<gadget id="calculator">50 / 3</gadget>
<output>50/3 = around 16.666667</output>
<gadget id="calculator">69_000 * (50/3)</gadget>
<output>1_150_000</output>
<gadget id="calculator">2 * 6</gadget>
<output>12</output>
<gadget id="calculator">9 / 12</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">1_150_000 * (3/4)</gadget>
<output>862_500</output>
<gadget id="calculator">1 / 100</gadget>
<output>1/100 = around 0.01</output>
<gadget id="calculator">862_500 * (1/100)</gadget>
<output>8_625</output>
<result>B</result> | B | 8,900 | Find the simple interest on Rs. 71,200 at 16 2/3% per annum for 9 months. | {
"A": "s . 8500",
"B": "s . 8900",
"C": "s . 7500",
"D": "s . 7000",
"E": "s . 6500"
} | multiply(multiply(multiply(add(multiply(multiply(multiply(2, 3), const_100), const_100), multiply(multiply(multiply(3, 3), const_100), multiply(add(3, 2), 2))), divide(add(multiply(16, 3), 2), 3)), divide(multiply(3, 3), multiply(2, multiply(2, 3)))), divide(const_1, const_100)) | add(n2,n3)|divide(const_1,const_100)|multiply(n3,n3)|multiply(n2,n3)|multiply(n1,n3)|add(n2,#4)|multiply(n2,#3)|multiply(#3,const_100)|multiply(#2,const_100)|multiply(#0,n2)|divide(#2,#6)|divide(#5,n3)|multiply(#7,const_100)|multiply(#8,#9)|add(#12,#13)|multiply(#14,#11)|multiply(#10,#15)|multiply(#1,#16)| | "p = rs . 71200 , r = 50 / 3 % p . a and t = 9 / 12 years = 3 / 4 years . s . i . = ( p * r * t ) / 100 = rs . ( 71,200 * ( 50 / 3 ) * ( 3 / 4 ) * ( 1 / 100 ) ) = rs . 8900 answer is b ." | gain |
math_qa__EBIlyTWg0i9prTz5 | A number is doubled and 9 is added. If resultant is trebled, it becomes 51. What is that number
Answers:
A) 4
B) 10
C) 12
D) 14
E) 15 | <gadget id="calculator">3 * 9</gadget>
<output>27</output>
<gadget id="calculator">51 - 27</gadget>
<output>24</output>
<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">24 / 6</gadget>
<output>4</output>
<result>A</result> | A | 4 | A number is doubled and 9 is added. If resultant is trebled, it becomes 51. What is that number | {
"A": "4",
"B": "10",
"C": "12",
"D": "14",
"E": "15"
} | divide(subtract(51, multiply(const_3, 9)), multiply(const_3, const_2)) | multiply(n0,const_3)|multiply(const_2,const_3)|subtract(n1,#0)|divide(#2,#1)| | "explanation : = > 3 ( 2 x + 9 ) = 51 = > 2 x + 9 = 17 = > x = 4 answer : option a" | general |
math_qa__KUVPxNA6BDdmkKzW | Bill spends two days driving from Point A to Point B . On the first day, he drove 2 hours longer and at an average speed 5 miles per hour faster than he drove on the second day. If during the two days he drove a total of 680 miles over the course of 18 hours, what was his average speed on the second day, in miles per hour? Options.
A) 20
B) 25
C) 28
D) 30
E) 35 | <gadget id="calculator">2 * 5</gadget>
<output>10</output>
<gadget id="calculator">10 * 5</gadget>
<output>50</output>
<gadget id="calculator">680 - 50</gadget>
<output>630</output>
<gadget id="calculator">2 * 4</gadget>
<output>8</output>
<gadget id="calculator">10 + 8</gadget>
<output>18</output>
<gadget id="calculator">630 / 18</gadget>
<output>35</output>
<result>E</result> | E | 35 | Bill spends two days driving from Point A to Point B . On the first day, he drove 2 hours longer and at an average speed 5 miles per hour faster than he drove on the second day. If during the two days he drove a total of 680 miles over the course of 18 hours, what was his average speed on the second day, in miles per hour? | {
"A": "20",
"B": "25",
"C": "28",
"D": "30",
"E": "35"
} | divide(subtract(680, multiply(multiply(2, 5), 5)), add(multiply(2, 5), multiply(const_2, const_4))) | multiply(n0,n1)|multiply(const_2,const_4)|add(#0,#1)|multiply(n1,#0)|subtract(n2,#3)|divide(#4,#2) | first recognize that we have two pieces of information regarding the time bill spent driving each day . on day 1 , bill drove 2 hours longer than he drove on day 2 . so , let x = # of driving hours on day 2 then x + 2 = # of driving hours on day 1 bill drove a total of 18 hours so , x + ( x + 2 ) = 18 simplify : 2 x + 2 = 18 solve , x = 8 so , bill drove 10 hours on day 1 and he drove 8 hours on day 2 now let ' s solve the question by starting with a word equation . let x = speed driven on day 2 so , x + 5 = speed driven on day 1 ( distance traveled on day 1 ) + ( distance traveled on day 2 ) = 680 distance = ( rate ) ( time ) we get : ( x + 5 ) ( 10 ) + ( x ) ( 8 ) = 680 expand : 10 x + 50 + 8 x = 680 simplify : 18 x + 50 = 680 18 x = 630 x = 35 ( mph ) answer : e | physics |
math_qa__7XcmM6rvk1Chuzpa | The Expenditure of an woman increase consistently by 30% per year. If her present expenditure is Rs. 1000 then what will her expenditure be after 3 years ? Choose the correct choice: A) 2107 B) 2197 C) 2187 D) 2177 E) 2167 | <gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">1 + (3/10)</gadget>
<output>13/10 = around 1.3</output>
<gadget id="calculator">(13/10) ** 3</gadget>
<output>2_197/1_000 = around 2.197</output>
<gadget id="calculator">(2_197/1_000) * 1_000</gadget>
<output>2_197</output>
<result>B</result> | B | 2,197 | The Expenditure of an woman increase consistently by 30% per year. If her present expenditure is Rs. 1000 then what will her expenditure be after 3 years ? | {
"A": "2107",
"B": "2197",
"C": "2187",
"D": "2177",
"E": "2167"
} | multiply(power(add(const_1, divide(30, const_100)), 3), 1000) | divide(n0,const_100)|add(#0,const_1)|power(#1,n2)|multiply(n1,#2) | explanation : expenditure = 1000 x 1.3 x 1.3 x 1.3 = 2197 answer : option b | general |
math_qa__DjftLCYv53iK3tn6 | A rectangular floor is covered by a rug except for a strip 4 meters wide along each of the four edge. If the floor is 25 meters by 20 meters, what is the area of the rug in square meters? Choose the correct answer: A) 256 B) 266 C) 204 D) 224 E) 324 | <gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">25 - 8</gadget>
<output>17</output>
<gadget id="calculator">20 - 8</gadget>
<output>12</output>
<gadget id="calculator">17 * 12</gadget>
<output>204</output>
<result>C</result> | C | 204 | A rectangular floor is covered by a rug except for a strip 4 meters wide along each of the four edge. If the floor is 25 meters by 20 meters, what is the area of the rug in square meters? | {
"A": "256",
"B": "266",
"C": "204",
"D": "224",
"E": "324"
} | rectangle_area(subtract(25, multiply(4, const_2)), subtract(20, multiply(4, const_2))) | multiply(n0,const_2)|subtract(n1,#0)|subtract(n2,#0)|rectangle_area(#1,#2) | a strip of 4 meters is covering the inner rectangular rug for all 4 sides . length of inner rug = 25 - ( 2 * 4 ) breadth of inner rug = 20 - ( 2 * 4 ) area of rug = 17 * 12 = 204 sq . mt â nswer : c | geometry |
math_qa__yxar7k8lIr3AGdgt | At what rate percent per annum will a sum of money double in 5 years.
Choose the correct choice:
A) 20.0 %
B) 13.5 %
C) 11.5 %
D) 14.5 %
E) 21.5 % | <gadget id="calculator">100 / 5</gadget>
<output>20</output>
<result>A</result> | A | 20 | At what rate percent per annum will a sum of money double in 5 years. | {
"A": "20.0 %",
"B": "13.5 %",
"C": "11.5 %",
"D": "14.5 %",
"E": "21.5 %"
} | divide(const_100, 5) | divide(const_100,n0) | let principal = p , then , s . i . = p and time = 8 years rate = [ ( 100 x p ) / ( p x 5 ) ] % = 20.0 % per annum . answer : a | gain |
math_qa__ubxVf4fiwZGzDOfJ | The percentage increase in the area of rectangle , if each of its side is increased by 20% is? Choose the most appropriate option: A) 30 % B) 44 % C) 50 % D) 55 % E) 60 % | <gadget id="calculator">100 + 20</gadget>
<output>120</output>
<gadget id="calculator">120 / 100</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">(6/5) * (6/5)</gadget>
<output>36/25 = around 1.44</output>
<gadget id="calculator">(36/25) - 1</gadget>
<output>11/25 = around 0.44</output>
<gadget id="calculator">(11/25) * 100</gadget>
<output>44</output>
<result>B</result> | B | 44 | The percentage increase in the area of rectangle , if each of its side is increased by 20% is? | {
"A": "30 %",
"B": "44 %",
"C": "50 %",
"D": "55 %",
"E": "60 %"
} | multiply(subtract(multiply(divide(add(const_100, 20), const_100), divide(add(const_100, 20), const_100)), const_1), const_100) | add(n0,const_100)|divide(#0,const_100)|multiply(#1,#1)|subtract(#2,const_1)|multiply(#3,const_100)| | "let original length = x meters original breadth = y meters original area = xy m ^ 2 new length = 120 x / 100 new breadth = 120 y / 100 = 6 y / 5 new area = 6 x / 5 * 6 y / 5 = 36 xy / 25 m ^ 2 increase percent = 11 xy / 25 * 1 / xy * 100 = 44 % answer is b" | geometry |
math_qa__0yBCcUqZx28ZNDhz | A cube is painted such that one pair of surfaces is painted brown and the other pair of surfaces is painted orange. The cube is cut in to 64 small cubes of equal size. Find how many cubes have both the color brown and orange? Choose the correct choice from the following options
A) 22 B) 16 C) 11 D) 12 E) 10 | <gadget id="calculator">64 / 2</gadget>
<output>32</output>
<gadget id="calculator">32 / 2</gadget>
<output>16</output>
<result>B</result> | B | 16 | A cube is painted such that one pair of surfaces is painted brown and the other pair of surfaces is painted orange. The cube is cut in to 64 small cubes of equal size. Find how many cubes have both the color brown and orange? | {
"A": "22",
"B": "16",
"C": "11",
"D": "12",
"E": "10"
} | divide(divide(64, const_2), const_2) | divide(n0,const_2)|divide(#0,const_2) | there are 6 surfaces to the cube . in which opposite surfaces are painted brown and other 2 opposite surfaces are painted orange . then 4 edges of the cube have both the colors . since the big cube cut in to 64 smaller cubes , the 4 edges of the cube have both the colors . since the big cube cut into 64 smaller cubes , the 4 edges of the big cube has 4 × 4 = 16 smaller cubes have both brown and orange colors . answer = 16 answer : b | geometry |
math_qa__oVEK8NyyOSK7C0Gs | A bag contains 4 red, 4 blue and 2 green balls. If 2 ballsare picked at random, what is the probability that both are red? Choices:
A) 2 / 15 B) 2 / 21 C) 5 / 26 D) 3 / 29 E) 4 / 27 | <gadget id="calculator">binomial(4, 2)</gadget>
<output>6</output>
<gadget id="calculator">4 + 4</gadget>
<output>8</output>
<gadget id="calculator">8 + 2</gadget>
<output>10</output>
<gadget id="calculator">binomial(10, 2)</gadget>
<output>45</output>
<gadget id="calculator">6 / 45</gadget>
<output>2/15 = around 0.133333</output>
<result>A</result> | A | 0.133333 | A bag contains 4 red, 4 blue and 2 green balls. If 2 ballsare picked at random, what is the probability that both are red? | {
"A": "2 / 15",
"B": "2 / 21",
"C": "5 / 26",
"D": "3 / 29",
"E": "4 / 27"
} | divide(choose(4, 2), choose(add(add(4, 4), 2), 2)) | add(n0,n1)|choose(n0,n3)|add(n2,#0)|choose(#2,n3)|divide(#1,#3)| | "p ( both are red ) , = 4 c 210 c 2 = 4 c 210 c 2 = 6 / 45 = 2 / 15 a" | other |
math_qa__VJyZEdgNdL14LChL | In the xy-coordinate system, if (m, n) and (m + 3, n + k) are two points on the line with the equation x = 2y + 5, then k = Choose the correct choice from the following options:
A) 1 / 2 B) 1 C) 2 D) 3 / 2 E) 4 | <gadget id="calculator">5 + 3</gadget>
<output>8</output>
<gadget id="calculator">8 - 5</gadget>
<output>3</output>
<gadget id="calculator">3 / 2</gadget>
<output>3/2 = around 1.5</output>
<result>D</result> | D | 1.5 | In the xy-coordinate system, if (m, n) and (m + 3, n + k) are two points on the line with the equation x = 2y + 5, then k = | {
"A": "1 / 2",
"B": "1",
"C": "2",
"D": "3 / 2",
"E": "4"
} | divide(subtract(add(5, 3), 5), const_2) | add(n0,n2)|subtract(#0,n2)|divide(#1,const_2) | since ( m , n ) and ( m + 2 , n + k ) are two points on the line with the equation x = 2 y + 5 they should satisfy m = 2 n + 5 and m + 3 = 2 * ( n + k ) + 5 . by 1 st equation we have m - 2 n = 5 and by 2 nd equation m - 2 n = 2 k + 2 - - - > 5 = 2 k + 2 - - - > k = 3 / 2 . the answer is , therefore , ( d ) . | general |
math_qa__6EalbHh3J262jLME | In a garden, 26 trees are planted at equal distances along a yard 300 metres long, one tree being at each end of the yard. What is the distance between two consecutive trees?
Choose the correct option.
A) 10 metres B) 20 metres C) 14 metres D) 12 metres E) 13 metres | <gadget id="calculator">26 - 1</gadget>
<output>25</output>
<gadget id="calculator">300 / 25</gadget>
<output>12</output>
<result>D</result> | D | 12 | In a garden, 26 trees are planted at equal distances along a yard 300 metres long, one tree being at each end of the yard. What is the distance between two consecutive trees? | {
"A": "10 metres",
"B": "20 metres",
"C": "14 metres",
"D": "12 metres",
"E": "13 metres"
} | divide(300, subtract(26, const_1)) | subtract(n0,const_1)|divide(n1,#0)| | "between 26 trees , there are 25 gaps length of each gap = 300 / 25 = 12 i . e . , distance between two consecutive trees = 12 answer : d" | physics |
math_qa__3SSkHS70z3QxbZSy | The product of 4 consecutive even numbers is always divisible by: Choose one: A) 384 B) 350 C) 400 D) 200 E) 250 | <gadget id="calculator">2 ** 4</gadget>
<output>16</output>
<gadget id="calculator">factorial(4)</gadget>
<output>24</output>
<gadget id="calculator">16 * 24</gadget>
<output>384</output>
<result>A</result> | A | 384 | The product of 4 consecutive even numbers is always divisible by: | {
"A": "384",
"B": "350",
"C": "400",
"D": "200",
"E": "250"
} | multiply(power(const_2, 4), factorial(const_4)) | factorial(const_4)|power(const_2,n0)|multiply(#0,#1) | the product of 4 consecutive numbers is always divisible by 4 ! . since , we have 4 even numbers , we have an additional 2 available with each number . now , using both the facts , we can say that the product of 4 consecutive even numbers is always divisible by , 2 ^ 4 * 4 ! 16 * 24 = 384 answer a | general |
math_qa__UK34NknoMdpHJwDf | Workers at a campaign office have 2500 fliers to send out. If they send out 1/5 of them in the morning and 1/4 of the remaining ones out during the afternoon, how many are left for the next day? Choose the correct choice from the following answers.
A) 300 B) 800 C) 1500 D) 1200 E) 1900 | <gadget id="calculator">2_500 / 5</gadget>
<output>500</output>
<gadget id="calculator">2_500 - 500</gadget>
<output>2_000</output>
<gadget id="calculator">2_000 / 4</gadget>
<output>500</output>
<gadget id="calculator">2_000 - 500</gadget>
<output>1_500</output>
<result>C</result> | C | 1,500 | Workers at a campaign office have 2500 fliers to send out. If they send out 1/5 of them in the morning and 1/4 of the remaining ones out during the afternoon, how many are left for the next day? | {
"A": "300",
"B": "800",
"C": "1500",
"D": "1200",
"E": "1900"
} | subtract(subtract(2500, divide(2500, 5)), divide(subtract(2500, divide(2500, 5)), 4)) | divide(n0,n2)|subtract(n0,#0)|divide(#1,n4)|subtract(#1,#2) | ( 1 / 5 ) * 2500 = 500 remaining = 2500 - 500 = 2000 ( 1 / 4 ) of remaining = ( 1 / 4 ) * 2000 = 500 remaining now = 2000 - 500 = 1500 answer : option c | physics |
math_qa__tHjaa2VdTWdIYvWZ | Two numbers N and 24 have LCM = 48 and GCF = 8. Find N. Choose the most appropriate option
A) 16 B) 56 C) 76 D) 87 E) 24 | <gadget id="calculator">48 * 8</gadget>
<output>384</output>
<gadget id="calculator">384 / 24</gadget>
<output>16</output>
<result>A</result> | A | 16 | Two numbers N and 24 have LCM = 48 and GCF = 8. Find N. | {
"A": "16",
"B": "56",
"C": "76",
"D": "87",
"E": "24"
} | divide(multiply(48, 8), 24) | multiply(n1,n2)|divide(#0,n0)| | "the product of two integers is equal to the product of their lcm and gcf . hence . 24 * n = 48 * 8 n = 48 * 8 / 24 = 16 correct answer a" | physics |
math_qa__z6FFrRzYT4q5z72K | A trailer carries 3, 4 and 5 crates on a trip. Each crate weighs no less than 1250 kg. What is the maximum weight of the crates on a single trip? Choose the correct answer:
A) 1250
B) 6250
C) 600
D) 7500
E) 375 | <gadget id="calculator">5 * 1_250</gadget>
<output>6_250</output>
<result>B</result> | B | 6,250 | A trailer carries 3, 4 and 5 crates on a trip. Each crate weighs no less than 1250 kg. What is the maximum weight of the crates on a single trip? | {
"A": "1250",
"B": "6250",
"C": "600",
"D": "7500",
"E": "375"
} | multiply(5, 1250) | multiply(n2,n3)| | "max no . of crates = 5 . max weight = 1250 kg max . weight carried = 5 * 1250 = 6250 kg = b" | general |
math_qa__zznJuH7rmkLQjLtJ | What will be the difference between simple and compound interest @10% per annum on a sum of $1000 after 4 years? Choose the correct choice from the following answers.
A) $ 48.12 B) $ 52.64 C) $ 64.10 D) $ 72.85 E) $ 60.10 | <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">(11/10) ** 4</gadget>
<output>14_641/10_000 = around 1.4641</output>
<gadget id="calculator">1_000 * (14_641/10_000)</gadget>
<output>14_641/10 = around 1_464.1</output>
<gadget id="calculator">(14_641/10) - 1_000</gadget>
<output>4_641/10 = around 464.1</output>
<gadget id="calculator">1_000 * (1/10)</gadget>
<output>100</output>
<gadget id="calculator">100 * 4</gadget>
<output>400</output>
<gadget id="calculator">(4_641/10) - 400</gadget>
<output>641/10 = around 64.1</output>
<result>C</result> | C | 64.1 | What will be the difference between simple and compound interest @10% per annum on a sum of $1000 after 4 years? | {
"A": "$ 48.12",
"B": "$ 52.64",
"C": "$ 64.10",
"D": "$ 72.85",
"E": "$ 60.10"
} | subtract(subtract(multiply(1000, power(add(divide(10, const_100), const_1), 4)), 1000), multiply(multiply(1000, divide(10, const_100)), 4)) | divide(n0,const_100)|add(#0,const_1)|multiply(n1,#0)|multiply(n2,#2)|power(#1,n2)|multiply(n1,#4)|subtract(#5,n1)|subtract(#6,#3)| | "s . i . = 1000 * 10 * 4 / 100 = $ 400 c . i . = 1000 * ( 1 + 10 / 100 ) ^ 4 - 1000 = $ 464.10 difference = 464.10 - 400 = $ 64.10 answer is c" | gain |
math_qa__UryFm0R97nZjaEFf | The ages of Patrick and Michael are in the ratio of 3 : 5 and that of Michael and Monica are in the ratio of 3 : 5. If the sum of their ages is 196, what is the difference between the ages of Patrick and Monica? Choose the correct option
A) 27 B) 64 C) 45 D) 72 E) 18 | <gadget id="calculator">5 * 5</gadget>
<output>25</output>
<gadget id="calculator">3 * 3</gadget>
<output>9</output>
<gadget id="calculator">3 * 5</gadget>
<output>15</output>
<gadget id="calculator">9 + 15</gadget>
<output>24</output>
<gadget id="calculator">24 + 25</gadget>
<output>49</output>
<gadget id="calculator">196 / 49</gadget>
<output>4</output>
<gadget id="calculator">25 * 4</gadget>
<output>100</output>
<gadget id="calculator">9 * 4</gadget>
<output>36</output>
<gadget id="calculator">100 - 36</gadget>
<output>64</output>
<result>B</result> | B | 64 | The ages of Patrick and Michael are in the ratio of 3 : 5 and that of Michael and Monica are in the ratio of 3 : 5. If the sum of their ages is 196, what is the difference between the ages of Patrick and Monica? | {
"A": "27",
"B": "64",
"C": "45",
"D": "72",
"E": "18"
} | subtract(multiply(multiply(5, 5), divide(196, add(add(multiply(3, 3), multiply(3, 5)), multiply(5, 5)))), multiply(multiply(3, 3), divide(196, add(add(multiply(3, 3), multiply(3, 5)), multiply(5, 5))))) | multiply(n0,n0)|multiply(n1,n0)|multiply(n1,n3)|add(#0,#1)|add(#3,#2)|divide(n4,#4)|multiply(#5,#2)|multiply(#5,#0)|subtract(#6,#7)| | "ages of p and mi = 3 x : 5 x ages of mi and mo = 3 x : 5 x rationalizing their ages . ratio of their ages will be 9 x : 15 x : 25 x sum = 49 x = 196 x = 4 difference if ages of pa and mo = 25 x - 9 x = 16 x = 16 * 4 = 64 answer b" | general |
math_qa__LLa3oDSrU4yK1OsI | If Tim had lunch at $50.50 and he gave 20% tip, how much did he spend? Options:
A) $ 30.60 B) $ 60.60 C) $ 70.60 D) $ 40.60 E) $ 50.60 | <gadget id="calculator">50.5 * 20</gadget>
<output>1_010</output>
<gadget id="calculator">1_010 / 100</gadget>
<output>101/10 = around 10.1</output>
<gadget id="calculator">50.5 + (101/10)</gadget>
<output>60.6</output>
<result>B</result> | B | 60.6 | If Tim had lunch at $50.50 and he gave 20% tip, how much did he spend? | {
"A": "$ 30.60",
"B": "$ 60.60",
"C": "$ 70.60",
"D": "$ 40.60",
"E": "$ 50.60"
} | add(50.50, divide(multiply(50.50, 20), const_100)) | multiply(n0,n1)|divide(#0,const_100)|add(n0,#1)| | "the tip is 20 % of what he paid for lunch . hence tip = 20 % of 50.50 = ( 20 / 100 ) * 50.50 = 101 / 100 = $ 10.10 total spent 50.50 + 10.10 = $ 60.60 correct answer b" | gain |
math_qa__aVBM1RCAlOKqvmi4 | 20 . a certain church bell rings the bell twice at half past the hour and 4 times at the hour plus an additional number of rings equal to what ever time it is . how many rings will the clock make from 6 : 20 in the morning to 09 : 50 in the morning ?
Select the correct option:
A) 44 .
B) 36 .
C) 42 .
D) 46 .
E) 50 . | <gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">4 * 4</gadget>
<output>16</output>
<gadget id="calculator">8 + 16</gadget>
<output>24</output>
<gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">7 + 5</gadget>
<output>12</output>
<gadget id="calculator">12 + 6</gadget>
<output>18</output>
<gadget id="calculator">24 + 18</gadget>
<output>42</output>
<result>A</result> | A | 44 | 20 . a certain church bell rings the bell twice at half past the hour and 4 times at the hour plus an additional number of rings equal to what ever time it is . how many rings will the clock make from 6 : 20 in the morning to 09 : 50 in the morning ? | {
"A": "44 .",
"B": "36 .",
"C": "42 .",
"D": "46 .",
"E": "50 ."
} | add(add(multiply(4, const_2), multiply(4, 4)), add(add(add(const_3, const_4), add(const_4, const_1)), 6)) | add(const_3,const_4)|add(const_1,const_4)|multiply(n1,const_2)|multiply(n1,n1)|add(#2,#3)|add(#0,#1)|add(n2,#5)|add(#4,#6) | unless i understood the problem correctly , i get 58 @ 6 : 30 - 2 @ 7 - 4 + 7 = 11 @ 7 : 30 - 2 @ 8 - 12 @ 8 : 30 - 2 @ 9 - 13 @ 9 : 30 - 2 totals to a = 44 | general |
math_qa__l1gJkPcoV7rGUhoh | Mahesh marks an article 15% above the cost price of Rs. 540. What must be his discount percentage if he sells it at Rs. 460? Choose the correct choice from the following answers:
A) 18 % B) 21 % C) 25.9 % D) 19 % E) none of these | <gadget id="calculator">100 + 15</gadget>
<output>115</output>
<gadget id="calculator">115 / 100</gadget>
<output>23/20 = around 1.15</output>
<gadget id="calculator">540 * (23/20)</gadget>
<output>621</output>
<gadget id="calculator">621 - 460</gadget>
<output>161</output>
<gadget id="calculator">161 * 100</gadget>
<output>16_100</output>
<gadget id="calculator">16_100 / 621</gadget>
<output>700/27 = around 25.925926</output>
<result>C</result> | C | 25.9 | Mahesh marks an article 15% above the cost price of Rs. 540. What must be his discount percentage if he sells it at Rs. 460? | {
"A": "18 %",
"B": "21 %",
"C": "25.9 %",
"D": "19 %",
"E": "none of these"
} | divide(multiply(subtract(multiply(540, divide(add(const_100, 15), const_100)), 460), const_100), multiply(540, divide(add(const_100, 15), const_100))) | add(n0,const_100)|divide(#0,const_100)|multiply(n1,#1)|subtract(#2,n2)|multiply(#3,const_100)|divide(#4,#2) | cp = rs . 540 , mp = 540 + 15 % of 540 = rs . 621 sp = rs . 460 , discount = 621 - 460 = 161 discount % = 161 / 621 * 100 = 25.9 % answer : c | gain |
math_qa__gu89diEextOcG0DF | s(n) is a n-digit number formed by attaching the first n perfect squares, in order, into one integer. For example, s(1) = 1, s(2) = 14, s(3) = 149, s(4) = 14916, s(5) = 1491625, etc. How many digits Y are in s(99)? Pick:
A) y = 350
B) y = 353
C) y = 354
D) y = 356
E) y = 357 | <gadget id="calculator">60 + 4</gadget>
<output>64</output>
<gadget id="calculator">64 + 4</gadget>
<output>68</output>
<gadget id="calculator">68 * 4</gadget>
<output>272</output>
<gadget id="calculator">68 + 272</gadget>
<output>340</output>
<gadget id="calculator">3 * 1</gadget>
<output>3</output>
<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">6 * 2</gadget>
<output>12</output>
<gadget id="calculator">3 + 12</gadget>
<output>15</output>
<gadget id="calculator">340 + 15</gadget>
<output>355</output>
<result>B</result> | B | 353 | s(n) is a n-digit number formed by attaching the first n perfect squares, in order, into one integer. For example, s(1) = 1, s(2) = 14, s(3) = 149, s(4) = 14916, s(5) = 1491625, etc. How many digits Y are in s(99)? | {
"A": "y = 350",
"B": "y = 353",
"C": "y = 354",
"D": "y = 356",
"E": "y = 357"
} | add(add(add(add(const_60, 4), 4), multiply(add(add(const_60, 4), 4), 4)), add(multiply(3, 1), multiply(multiply(3, 2), 2))) | add(n6,const_60)|multiply(n0,n4)|multiply(n2,n4)|add(n6,#0)|multiply(n2,#2)|add(#1,#4)|multiply(n6,#3)|add(#3,#6)|add(#7,#5)| | "focus on the points where the number of digits in squares change : 1 , 2 , 3 - single digit squares . first 2 digit number is 10 . 4 , 5 , . . . 9 - two digit squares . to get 9 , the last number with two digit square , think that first 3 digit number is 100 which is 10 ^ 2 . so 9 ^ 2 must be the last 2 digit square . 10 , 11 , 12 , . . . 31 - three digit squares . to get 31 , think of 1000 - the first 4 digit number . it is not a perfect square but 900 is 30 ^ 2 . 32 ^ 2 = 2 ^ 10 = 1024 , the first 4 digit square . 32 - 99 - four digit squares . to get 99 , think of 10,000 - the first 5 digit number which is 100 ^ 2 . so number of digits in s ( 99 ) = 3 * 1 + 6 * 2 + 22 * 3 + 68 * 4 = 3 + 12 + 66 + 272 = 353 . b" | general |
math_qa__r969uXBgTrjS9GCo | A can do a piece of work in 12 days and B can do a piece of work in 18 days how many days will the work be completed if both of them work together? Select.
A) 15 B) 7.2 C) 7.7 D) 7.4 E) 8 | <gadget id="calculator">1 / 12</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">1 / 18</gadget>
<output>1/18 = around 0.055556</output>
<gadget id="calculator">(1/12) + (1/18)</gadget>
<output>5/36 = around 0.138889</output>
<gadget id="calculator">1 / (5/36)</gadget>
<output>36/5 = around 7.2</output>
<result>B</result> | B | 7.2 | A can do a piece of work in 12 days and B can do a piece of work in 18 days how many days will the work be completed if both of them work together? | {
"A": "15",
"B": "7.2",
"C": "7.7",
"D": "7.4",
"E": "8"
} | inverse(add(inverse(12), inverse(18))) | inverse(n0)|inverse(n1)|add(#0,#1)|inverse(#2)| | "a ' s 1 day work = 1 / 12 , b ' s 1 day work = 1 / 18 ; ( a + b ) 1 day work = 1 / 12 + 1 / 18 = 5 / 36 ; they can finish the work in = 36 / 5 = 7.2 answer : b" | physics |
math_qa__ZtvDk0CTFE10SU61 | In track last week, the boys ran 34 laps. The girls ran 20 more
laps. Each lap is a 1/6th of a mile. How many miles did the girls run?
Select the correct option.
A) 9 miles
B) 10 miles
C) 11 miles
D) 12 miles
E) 13 miles | <gadget id="calculator">34 + 20</gadget>
<output>54</output>
<gadget id="calculator">54 / 6</gadget>
<output>9</output>
<result>A</result> | A | 9 | In track last week, the boys ran 34 laps. The girls ran 20 more
laps. Each lap is a 1/6th of a mile. How many miles did the girls run? | {
"A": "9 miles",
"B": "10 miles",
"C": "11 miles",
"D": "12 miles",
"E": "13 miles"
} | divide(add(34, 20), 6) | add(n0,n1)|divide(#0,n3) | the girls ran 34 + 20 = 54 laps . 54 x 1 / 6 = 54 / 6 , which reduces to 9 . the girls ran 9 miles correct answer a | general |
math_qa__eIF3shre2wu2TbXa | In a garment industry, 12 men working 8 hours per day complete a piece of work in 10 days. To complete the same work in 8 days, working 20 hours a day, the number of men required is: Choose the correct answer: A) 4 B) 5 C) 6 D) 8 E) 9 | <gadget id="calculator">12 * 8</gadget>
<output>96</output>
<gadget id="calculator">96 * 10</gadget>
<output>960</output>
<gadget id="calculator">960 / 20</gadget>
<output>48</output>
<gadget id="calculator">48 / 8</gadget>
<output>6</output>
<result>C</result> | C | 6 | In a garment industry, 12 men working 8 hours per day complete a piece of work in 10 days. To complete the same work in 8 days, working 20 hours a day, the number of men required is: | {
"A": "4",
"B": "5",
"C": "6",
"D": "8",
"E": "9"
} | divide(divide(multiply(multiply(12, 8), 10), 20), 8) | multiply(n0,n1)|multiply(n2,#0)|divide(#1,n4)|divide(#2,n1) | explanation : let the required number of men be x . less days , more men ( indirect proportion ) more working hrs per day , less men ( indirect proportion ) days 8 : 10 working hrs 20 : 8 : : 12 : x = > 8 x 20 x x = 10 x 8 x 12 = > x = 10 x 8 x 12 / ( 8 x 20 ) = > x = 6 answer : c | physics |
math_qa__Lx8rSPeho5DIciAM | Find the minimum value of n such that 50! is perfectly divisible by 2520^n. Choose the correct option
A) 0
B) 1
C) 2
D) 3
E) 4 | <gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) * 2</gadget>
<output>1</output>
<result>B</result> | B | 1 | Find the minimum value of n such that 50! is perfectly divisible by 2520^n. | {
"A": "0",
"B": "1",
"C": "2",
"D": "3",
"E": "4"
} | multiply(divide(50, const_100), const_2) | divide(n0,const_100)|multiply(#0,const_2) | 50 ! / 2520 ^ n 2520 - > 2 ^ 3 * 3 ^ 2 * 5 ^ 1 * 7 ^ 1 here 7 is the largest prime factor . . . so in order to find the minimum value of ` ` n ' ' , it is enough to find the minimum power of ` ` 7 ' ' . . . nd for maximum value of ` ` n ' ' , find max power of 7 . . . for max . value of n , find 50 / 7 ^ 1 + 50 / 7 ^ 2 = 7 + 1 = 8 [ quotient only ] max . value of n which is perfectly divisible by 2520 ^ n is ( 8 ) min . value is 1 max value : 8 min value : 1 answer : b | general |
math_qa__aOsuwk0IUtGcKmWB | A can finish a work in 10 days and B can do same work in half the time taken by A. then working together, what part of same work they can finish in a day? Answers:
A) 1 / 5 B) 1 / 6 C) 1 / 7 D) 3 / 10 E) none of these | <gadget id="calculator">1 / 10</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/10) * 2</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/10) + (1/5)</gadget>
<output>3/10 = around 0.3</output>
<result>D</result> | D | 0.3 | A can finish a work in 10 days and B can do same work in half the time taken by A. then working together, what part of same work they can finish in a day? | {
"A": "1 / 5",
"B": "1 / 6",
"C": "1 / 7",
"D": "3 / 10",
"E": "none of these"
} | add(divide(const_1, 10), multiply(divide(const_1, 10), const_2)) | divide(const_1,n0)|multiply(#0,const_2)|add(#0,#1)| | "explanation : please note in this question , we need to answer part of work for a day rather than complete work . it was worth mentioning here because many do mistake at this point in hurry to solve the question so lets solve now , a ' s 1 day work = 1 / 10 b ' s 1 day work = 1 / 5 [ because b take half the time than a ] ( a + b ) ' s one day work = ( 1 / 10 + 1 / 5 ) = 3 / 10 so in one day 3 / 10 work will be done answer : d" | physics |
math_qa__RfZh6Mxz2YHfJEtP | 81 men working 8 hours per day dig 30 m deep. How many extra men should be put to dig to a depth of 50 m working 6 hours per day? Select the correct option.
A) 99 B) 77 C) 66 D) 55 E) 88 | <gadget id="calculator">81 * 8</gadget>
<output>648</output>
<gadget id="calculator">648 / 30</gadget>
<output>108/5 = around 21.6</output>
<gadget id="calculator">(108/5) * 50</gadget>
<output>1_080</output>
<gadget id="calculator">1_080 / 6</gadget>
<output>180</output>
<gadget id="calculator">180 - 81</gadget>
<output>99</output>
<result>A</result> | A | 99 | 81 men working 8 hours per day dig 30 m deep. How many extra men should be put to dig to a depth of 50 m working 6 hours per day? | {
"A": "99",
"B": "77",
"C": "66",
"D": "55",
"E": "88"
} | subtract(divide(multiply(divide(multiply(81, 8), 30), 50), 6), 81) | multiply(n0,n1)|divide(#0,n2)|multiply(n3,#1)|divide(#2,n4)|subtract(#3,n0)| | "( 81 * 8 ) / 30 = ( x * 6 ) / 50 = > x = 180 180 – 81 = 99 answer : a" | physics |
math_qa__Eo8zPdPPyojORYAN | fog + fog + fog + fog = 1464 . if f , o and g are digits in a 3 - digit number in the preceding equation the f + o + g = ? Options: A) 11 B) 12 C) 13 D) 14 E) 15 | <gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">3 + 6</gadget>
<output>9</output>
<gadget id="calculator">9 + 6</gadget>
<output>15</output>
<result>E</result> | E | 15 | fog + fog + fog + fog = 1464 . if f , o and g are digits in a 3 - digit number in the preceding equation the f + o + g = ? | {
"A": "11",
"B": "12",
"C": "13",
"D": "14",
"E": "15"
} | add(add(3, multiply(const_3, const_2)), multiply(const_3, const_2)) | multiply(const_2,const_3)|add(n1,#0)|add(#1,#0) | given , fog + fog + fog + fog = 1464 4 ( fog ) = 1464 = > fog = 366 face value of f is : 3 face value of o is : 6 face value of g is : 6 so f + o + g = 3 + 6 + 6 = 15 answer : e | general |
math_qa__XxOL3PboMRDnNuC1 | a is an integer greater than 39 but less than 51, b is an integer greater than 49 but less than 61, what is the range of a/b? Choices
A) 1 / 4 B) 1 / 3 C) 3 / 4 D) 1 E) 5 / 4 | <gadget id="calculator">51 - 1</gadget>
<output>50</output>
<gadget id="calculator">49 + 1</gadget>
<output>50</output>
<gadget id="calculator">50 / 50</gadget>
<output>1</output>
<gadget id="calculator">39 + 1</gadget>
<output>40</output>
<gadget id="calculator">61 - 1</gadget>
<output>60</output>
<gadget id="calculator">40 / 60</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">1 - (2/3)</gadget>
<output>1/3 = around 0.333333</output>
<result>B</result> | B | 0.333333 | a is an integer greater than 39 but less than 51, b is an integer greater than 49 but less than 61, what is the range of a/b? | {
"A": "1 / 4",
"B": "1 / 3",
"C": "3 / 4",
"D": "1",
"E": "5 / 4"
} | subtract(divide(subtract(51, const_1), add(49, const_1)), divide(add(39, const_1), subtract(61, const_1))) | add(n2,const_1)|add(n0,const_1)|subtract(n1,const_1)|subtract(n3,const_1)|divide(#2,#0)|divide(#1,#3)|subtract(#4,#5)| | "min value of a / b will be when b is highest and a is lowest - - - > a = 40 and b = 60 so , a / b = 2 / 3 max value of a / b will be when b is lowest and a is highest - - - > a = 50 and b = 50 so , a / b = 1 range is 1 - ( 2 / 3 ) = 1 / 3 . answer should be b ." | general |
math_qa__denucIKau7CTkGTh | How many paying stones, each measuring 2 1/2 m * 2 m are required to pave a rectangular court yard 50 m long and 16 1/2 m board? Pick
A) 99 B) 18 C) 165 D) 10 E) 15 | <gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">16 + (1/2)</gadget>
<output>33/2 = around 16.5</output>
<gadget id="calculator">50 * (33/2)</gadget>
<output>825</output>
<gadget id="calculator">2 + (1/2)</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">(5/2) * 2</gadget>
<output>5</output>
<gadget id="calculator">825 / 5</gadget>
<output>165</output>
<result>C</result> | C | 165 | How many paying stones, each measuring 2 1/2 m * 2 m are required to pave a rectangular court yard 50 m long and 16 1/2 m board? | {
"A": "99",
"B": "18",
"C": "165",
"D": "10",
"E": "15"
} | divide(multiply(50, add(16, divide(1, 2))), multiply(add(2, divide(1, 2)), 2)) | divide(n1,n0)|add(n5,#0)|add(n0,#0)|multiply(n4,#1)|multiply(n0,#2)|divide(#3,#4) | 50 * 33 / 2 = 5 / 2 * 2 * x = > x = 165 answer : c | general |
math_qa__8G2Lo2NVXJZ89gop | How many digits are required to number a book containing 260 pages? Choose one.
A) 784 B) 672 C) 492 D) 372 E) 300 | <gadget id="calculator">10 - 1</gadget>
<output>9</output>
<gadget id="calculator">9 * 10</gadget>
<output>90</output>
<gadget id="calculator">90 * 2</gadget>
<output>180</output>
<gadget id="calculator">9 + 180</gadget>
<output>189</output>
<gadget id="calculator">260 - 100</gadget>
<output>160</output>
<gadget id="calculator">160 + 1</gadget>
<output>161</output>
<gadget id="calculator">161 * 3</gadget>
<output>483</output>
<gadget id="calculator">189 + 483</gadget>
<output>672</output>
<result>B</result> | B | 672 | How many digits are required to number a book containing 260 pages? | {
"A": "784",
"B": "672",
"C": "492",
"D": "372",
"E": "300"
} | add(add(subtract(const_10, const_1), multiply(multiply(subtract(const_10, const_1), const_10), const_2)), multiply(add(subtract(260, const_100), const_1), const_3)) | subtract(const_10,const_1)|subtract(n0,const_100)|add(#1,const_1)|multiply(#0,const_10)|multiply(#3,const_2)|multiply(#2,const_3)|add(#4,#0)|add(#6,#5)| | "9 pages from 1 to 9 will require 9 digits . 90 pages from 10 to 99 will require 90 * 2 = 180 digits . 260 - ( 90 + 9 ) = 161 pages will require 161 * 3 = 483 digits . the total number of digits is 9 + 180 + 483 = 672 . the answer is b ." | general |
math_qa__Kgqp6nHfP5ZvZMpZ | log3 N+log15 N what is 3 digit number N that will be whole number Pick
A) 3375
B) 7292
C) 8291
D) 3929
E) 2727 | <gadget id="calculator">15 ** 3</gadget>
<output>3_375</output>
<result>A</result> | A | 3,375 | log3 N+log15 N what is 3 digit number N that will be whole number | {
"A": "3375",
"B": "7292",
"C": "8291",
"D": "3929",
"E": "2727"
} | power(15, 3) | power(n1,n0)| | "no of values n can take is 1 15 ^ 3 = 3375 answer : a" | other |
math_qa__qarjgSf0RS0ADTFX | the sum of squares of 3 numbers is 764 and sum of their products taken two at a time is 500 . what is their sum ? Choose the correct answer: A) 48 B) 42 C) 52 D) 32 E) 33 | <gadget id="calculator">500 / 3</gadget>
<output>500/3 = around 166.666667</output>
<gadget id="calculator">(500/3) / 3</gadget>
<output>500/9 = around 55.555556</output>
<gadget id="calculator">(500/9) - 10</gadget>
<output>410/9 = around 45.555556</output>
<gadget id="calculator">(410/9) - 3</gadget>
<output>383/9 = around 42.555556</output>
<result>B</result> | B | 42 | the sum of squares of 3 numbers is 764 and sum of their products taken two at a time is 500 . what is their sum ? | {
"A": "48",
"B": "42",
"C": "52",
"D": "32",
"E": "33"
} | subtract(subtract(divide(divide(500, 3), 3), const_10), const_3) | divide(n2,n0)|divide(#0,n0)|subtract(#1,const_10)|subtract(#2,const_3) | description : let the numbers be x , y , z . = > x 2 + y 2 + z 2 = 764 = > 2 ( xy + yz + xz ) = 2 * 500 = 1000 = > ( x + y + z ) 2 = ( x 2 + y 2 + z 2 ) + 2 ( xy + yz + xz ) = 1764 = > ( x + y + z ) = sqrt ( 1764 ) = 42 answer b | general |
math_qa__649DnmxQPh3uopKz | The maximum number of students among them 1340 pens and 1280 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils?
Choose one
A) 25
B) 30
C) 20
D) 45
E) 90 | <gadget id="calculator">gcd(1_340, 1_280)</gadget>
<output>20</output>
<result>C</result> | C | 20 | The maximum number of students among them 1340 pens and 1280 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils? | {
"A": "25",
"B": "30",
"C": "20",
"D": "45",
"E": "90"
} | gcd(1340, 1280) | gcd(n0,n1)| | "number of pens = 1340 number of pencils = 1280 required number of students = h . c . f . of 1340 and 1280 = 20 answer is c" | general |
math_qa__Lok8m4c1ovAuzhTv | If the remainder is 10 when the integer n is divided by 18, what is the remainder when 2n is divided by 9? Choose the correct choice from the following choices
A) 0 B) 1 C) 2 D) 3 E) 4 | <gadget id="calculator">10 * 2</gadget>
<output>20</output>
<gadget id="calculator">20 - 18</gadget>
<output>2</output>
<result>C</result> | C | 2 | If the remainder is 10 when the integer n is divided by 18, what is the remainder when 2n is divided by 9? | {
"A": "0",
"B": "1",
"C": "2",
"D": "3",
"E": "4"
} | subtract(multiply(10, 2), 18) | multiply(n0,n2)|subtract(#0,n1)| | "n = 18 k + 10 2 n = 2 ( 18 k + 10 ) = 4 k * 9 + 20 = 4 k * 9 + 2 * 9 + 2 = 9 j + 2 the answer is c ." | general |
math_qa__rMdLWSskXR3mmDxu | In the Land of Oz only one or two-letter words are used. The local language has 67 different letters. The parliament decided to forbid the use of the seventh letter. How many words have the people of Oz lost because of the prohibition? Options
A) 65 B) 66 C) 67 D) 131 E) 134 | <gadget id="calculator">1 + 67</gadget>
<output>68</output>
<gadget id="calculator">68 + 67</gadget>
<output>135</output>
<result>E</result> | E | 134 | In the Land of Oz only one or two-letter words are used. The local language has 67 different letters. The parliament decided to forbid the use of the seventh letter. How many words have the people of Oz lost because of the prohibition? | {
"A": "65",
"B": "66",
"C": "67",
"D": "131",
"E": "134"
} | add(add(const_1, 67), 67) | add(n0,const_1)|add(n0,#0)| | "the answer to the question is indeed e . the problem with above solutions is that they do not consider words like aa , bb , . . . the number of 1 letter words ( x ) that can be made from 67 letters is 67 ; the number of 2 letter words ( xx ) that can be made from 67 letters is 67 * 67 , since each x can take 67 values . total : 67 + 67 * 67 . similarly : the number of 1 letter words ( x ) that can be made from 66 letters is 66 ; the number of 2 letter words ( xx ) that can be made from 66 letters is 66 * 66 , since each x can take 66 values . total : 66 + 66 * 66 . the difference is ( 67 + 67 * 67 ) - ( 66 + 66 * 66 ) = 134 . answer : e ." | general |
math_qa__EfOJwJOWAmCTcDRj | $500 is divided amongst A,B and C so that A may get 2/3 as much as B and C together, B may get 6/9 as much as A and C together, then the share of A is
Pick one:
A) $ 100
B) $ 150
C) $ 125
D) $ 200
E) $ 250 | <gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(2/3) + 1</gadget>
<output>5/3 = around 1.666667</output>
<gadget id="calculator">500 / (5/3)</gadget>
<output>300</output>
<gadget id="calculator">300 * (2/3)</gadget>
<output>200</output>
<result>D</result> | D | 200 | $500 is divided amongst A,B and C so that A may get 2/3 as much as B and C together, B may get 6/9 as much as A and C together, then the share of A is | {
"A": "$ 100",
"B": "$ 150",
"C": "$ 125",
"D": "$ 200",
"E": "$ 250"
} | multiply(divide(500, add(divide(2, 3), const_1)), divide(2, 3)) | divide(n1,n2)|add(#0,const_1)|divide(n0,#1)|multiply(#2,#0)| | "a : ( b + c ) = 2 : 3 a ' s share = 500 * 2 / 5 = $ 200 answer is d" | general |
math_qa__1OkBEzqWQ7F1HKxi | In an election between two candidates A and B, the number of valid votes received by A exceeds those received by B by 15% of the total number of votes polled. If 20% of the votes polled were invalid and a total of 5720 votes were polled, then how many valid votes did B get? Choose one:
A) 1859 B) 2999 C) 2834 D) 2777 E) 2991 | <gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(4/5) * 5_720</gadget>
<output>4_576</output>
<gadget id="calculator">15 * 5_720</gadget>
<output>85_800</output>
<gadget id="calculator">85_800 / 100</gadget>
<output>858</output>
<gadget id="calculator">4_576 - 858</gadget>
<output>3_718</output>
<gadget id="calculator">3_718 / 2</gadget>
<output>1_859</output>
<result>A</result> | A | 1,859 | In an election between two candidates A and B, the number of valid votes received by A exceeds those received by B by 15% of the total number of votes polled. If 20% of the votes polled were invalid and a total of 5720 votes were polled, then how many valid votes did B get? | {
"A": "1859",
"B": "2999",
"C": "2834",
"D": "2777",
"E": "2991"
} | divide(subtract(multiply(subtract(const_1, divide(20, const_100)), 5720), divide(multiply(15, 5720), const_100)), const_2) | divide(n1,const_100)|multiply(n0,n2)|divide(#1,const_100)|subtract(const_1,#0)|multiply(n2,#3)|subtract(#4,#2)|divide(#5,const_2)| | "let the total number of votes polled in the election be 100 k . number of valid votes = 100 k - 20 % ( 100 k ) = 80 k let the number of votes polled in favour of a and b be a and b respectively . a - b = 15 % ( 100 k ) = > a = b + 15 k = > a + b = b + 15 k + b now , 2 b + 15 k = 80 k and hence b = 32.5 k it is given that 100 k = 5720 32.5 k = 32.5 k / 100 k * 85720 = 1859 the number of valid votes polled in favour of b is 1859 . answer : a" | general |
math_qa__lJ6KGCeqsrIc7y1I | 10 x 1.8 - 2 x 1.5/0.3 = ? Choose one
A) 30 B) 20 C) 15 D) 44 E) 50 | <gadget id="calculator">10 * 1.8</gadget>
<output>18</output>
<gadget id="calculator">2 * 1.5</gadget>
<output>3</output>
<gadget id="calculator">18 - 3</gadget>
<output>15</output>
<gadget id="calculator">15 / 0.3</gadget>
<output>50</output>
<result>E</result> | E | 50 | 10 x 1.8 - 2 x 1.5/0.3 = ? | {
"A": "30",
"B": "20",
"C": "15",
"D": "44",
"E": "50"
} | divide(subtract(multiply(10, 1.8), multiply(2, 1.5)), 0.3) | multiply(n0,n1)|multiply(n2,n3)|subtract(#0,#1)|divide(#2,n4) | given expression = ( 18 - 3.0 ) / 0.3 = 15 / 0.3 = 150 / 3 = 50 answer is e . | general |
math_qa__krvMvE9WtwItjWdK | There are 1000 students in a school and among them 20% of them attends chess class. 10% of the students who are in the chess class are also enrolled for swimming. No other students are interested in swimming so how many will attend the swimming class if all enrolled attends?
Choose the most appropriate option.
A) 1 B) 10 C) 100 D) 50 E) 20 | <gadget id="calculator">20 * 1_000</gadget>
<output>20_000</output>
<gadget id="calculator">20_000 / 100</gadget>
<output>200</output>
<gadget id="calculator">200 * 10</gadget>
<output>2_000</output>
<gadget id="calculator">2_000 / 100</gadget>
<output>20</output>
<result>E</result> | E | 20 | There are 1000 students in a school and among them 20% of them attends chess class. 10% of the students who are in the chess class are also enrolled for swimming. No other students are interested in swimming so how many will attend the swimming class if all enrolled attends? | {
"A": "1",
"B": "10",
"C": "100",
"D": "50",
"E": "20"
} | divide(multiply(divide(multiply(20, 1000), const_100), 10), const_100) | multiply(n0,n1)|divide(#0,const_100)|multiply(n2,#1)|divide(#2,const_100)| | "20 % of 1000 gives 200 . so 200 attends chess and 10 % of 200 gives 20 . so 20 enrolled for swimming answer : e" | gain |
math_qa__7rzIH0IDB30YsbgC | An object thrown directly upward is at a height of h feet after t seconds, where h = -15 (t-2)^2 + 150. At what height, in feet, is the object 2 seconds after it reaches its maximum height? Answers.
A) 72 B) 90 C) 124 D) 132 E) 140 | <gadget id="calculator">-15</gadget>
<output>-15</output>
<gadget id="calculator">2 + 2</gadget>
<output>4</output>
<gadget id="calculator">4 - 2</gadget>
<output>2</output>
<gadget id="calculator">2 ** 2</gadget>
<output>4</output>
<gadget id="calculator">(-15) * 4</gadget>
<output>-60</output>
<gadget id="calculator">(-60) + 150</gadget>
<output>90</output>
<result>B</result> | B | 90 | An object thrown directly upward is at a height of h feet after t seconds, where h = -15 (t-2)^2 + 150. At what height, in feet, is the object 2 seconds after it reaches its maximum height? | {
"A": "72",
"B": "90",
"C": "124",
"D": "132",
"E": "140"
} | add(multiply(negate(15), power(subtract(add(2, 2), 2), 2)), 150) | add(n1,n2)|negate(n0)|subtract(#0,n1)|power(#2,n2)|multiply(#1,#3)|add(n3,#4)| | "we see that h will be a maximum h = 150 when t - 2 = 0 , that is when t = 2 . at t = 4 , h = - 15 ( 4 - 2 ) ^ 2 + 150 = - 15 ( 4 ) + 150 = 90 the answer is b ." | general |
math_qa__cJy0XIEjIwg77FRk | A trader sells 66 meters of cloth for Rs. 660 at the profit of Rs. 5 per metre of cloth. What is the cost price of one metre of cloth? Choose the correct choice from the following choices: A) 26 B) 88 C) 90 D) 42 E) 5 | <gadget id="calculator">660 / 66</gadget>
<output>10</output>
<gadget id="calculator">10 - 5</gadget>
<output>5</output>
<result>E</result> | E | 5 | A trader sells 66 meters of cloth for Rs. 660 at the profit of Rs. 5 per metre of cloth. What is the cost price of one metre of cloth? | {
"A": "26",
"B": "88",
"C": "90",
"D": "42",
"E": "5"
} | subtract(divide(660, 66), 5) | divide(n1,n0)|subtract(#0,n2)| | "sp of 1 m of cloth = 660 / 66 = rs . 10 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 10 - rs . 5 = rs . 5 answer : e" | physics |
math_qa__dnQYQ81pdDZRBl4L | What is the sum of the first 15 terms of an A.P whose 11 th and 7 th terms are 5.25 and 3.25 respectively Choices:
A) 56.25
B) 60
C) 52.5
D) 5.25
E) none of these | <gadget id="calculator">15 / 2</gadget>
<output>15/2 = around 7.5</output>
<gadget id="calculator">(15/2) * (15/2)</gadget>
<output>225/4 = around 56.25</output>
<result>A</result> | A | 56.25 | What is the sum of the first 15 terms of an A.P whose 11 th and 7 th terms are 5.25 and 3.25 respectively | {
"A": "56.25",
"B": "60",
"C": "52.5",
"D": "5.25",
"E": "none of these"
} | multiply(divide(15, const_2), divide(15, const_2)) | divide(n0,const_2)|multiply(#0,#0) | a + 10 d = 5.25 , a + 6 d = 3.25 , 4 d = 2 , d = ½ a + 5 = 5.25 , a = 0.25 = ¼ , s 15 = 15 / 2 ( 2 * ¼ + 14 * ½ ) = 15 / 2 ( 1 / 2 + 14 / 2 ) = 15 / 2 * 15 / 2 = 225 / 4 = 56.25 answer : a | general |
math_qa__DbZojbGHPSkuw0lS | The average marks of a class of 30 students is 40 and that of another class of 50 students is 70. Find the average marks of all the students? Choose the correct choice: A) 52.5 B) 52.9 C) 52.1 D) 58.75 E) 42.5 | <gadget id="calculator">30 * 40</gadget>
<output>1_200</output>
<gadget id="calculator">50 * 70</gadget>
<output>3_500</output>
<gadget id="calculator">1_200 + 3_500</gadget>
<output>4_700</output>
<gadget id="calculator">30 + 50</gadget>
<output>80</output>
<gadget id="calculator">4_700 / 80</gadget>
<output>235/4 = around 58.75</output>
<result>D</result> | D | 58.75 | The average marks of a class of 30 students is 40 and that of another class of 50 students is 70. Find the average marks of all the students? | {
"A": "52.5",
"B": "52.9",
"C": "52.1",
"D": "58.75",
"E": "42.5"
} | divide(add(multiply(30, 40), multiply(50, 70)), add(30, 50)) | add(n0,n2)|multiply(n0,n1)|multiply(n2,n3)|add(#1,#2)|divide(#3,#0)| | "sum of the marks for the class of 30 students = 30 * 40 = 1200 sum of the marks for the class of 50 students = 50 * 70 = 3500 sum of the marks for the class of 80 students = 1200 + 3500 = 4700 average marks of all the students = 4700 / 80 = 58.75 answer : d" | general |
math_qa__AAyATimjfVUrCeUU | The ratio of the length and the width of a rectangle is 4 : 3 and the area of the rectangle is 6348 sq cm. What is the ratio of the width and the area of the rectangle? Select: A) 1 : 96 B) 1 : 99 C) 1 : 94 D) 1 : 92 E) 1 : 91 | <gadget id="calculator">3 * 6_348</gadget>
<output>19_044</output>
<gadget id="calculator">19_044 ** (1/2)</gadget>
<output>138</output>
<gadget id="calculator">138 / 2</gadget>
<output>69</output>
<gadget id="calculator">69 / 6_348</gadget>
<output>1/92 = around 0.01087</output>
<result>D</result> | D | 0.01087 | The ratio of the length and the width of a rectangle is 4 : 3 and the area of the rectangle is 6348 sq cm. What is the ratio of the width and the area of the rectangle? | {
"A": "1 : 96",
"B": "1 : 99",
"C": "1 : 94",
"D": "1 : 92",
"E": "1 : 91"
} | divide(divide(sqrt(multiply(3, 6348)), const_2), 6348) | multiply(n2,n1)|sqrt(#0)|divide(#1,const_2)|divide(#2,n2)| | "let the length and the width be 4 x and 3 x respectively . area = ( 4 x ) ( 3 x ) = 6348 12 x ^ 2 = 6348 x ^ 2 = 529 x = 23 the ratio of the width and the area is 3 x : 12 x ^ 2 = 1 : 4 x = 1 : 92 the answer is d ." | geometry |
math_qa__HoEvT0ykxzMqOlVe | Rates for having a manuscript typed at a certain typing service are $5 per page for the first time a page is typed and $3 per page each time a page is revised. If a certain manuscript has 100 pages, of which 30 were revised only once, 20 were revised twice, and the rest required no revisions, what was the total cost of having the manuscript typed? Choose the correct choice: A) $ 430 B) $ 620 C) $ 650 D) $ 680 E) $ 710 | <gadget id="calculator">100 * 5</gadget>
<output>500</output>
<gadget id="calculator">30 * 3</gadget>
<output>90</output>
<gadget id="calculator">500 + 90</gadget>
<output>590</output>
<gadget id="calculator">20 * 3</gadget>
<output>60</output>
<gadget id="calculator">60 * 2</gadget>
<output>120</output>
<gadget id="calculator">590 + 120</gadget>
<output>710</output>
<result>E</result> | E | 710 | Rates for having a manuscript typed at a certain typing service are $5 per page for the first time a page is typed and $3 per page each time a page is revised. If a certain manuscript has 100 pages, of which 30 were revised only once, 20 were revised twice, and the rest required no revisions, what was the total cost of having the manuscript typed? | {
"A": "$ 430",
"B": "$ 620",
"C": "$ 650",
"D": "$ 680",
"E": "$ 710"
} | add(add(multiply(100, 5), multiply(30, 3)), multiply(multiply(20, 3), const_2)) | multiply(n0,n2)|multiply(n1,n3)|multiply(n1,n4)|add(#0,#1)|multiply(#2,const_2)|add(#3,#4)| | "for 100 - 30 - 20 = 50 pages only cost is 5 $ per page for the first time page is typed - 50 * 5 = 250 $ ; for 30 pages the cost is : first time 5 $ + 3 $ of the first revision - 30 * ( 5 + 3 ) = 240 $ ; for 20 pages the cost is : first time 5 $ + 3 $ of the first revision + 3 $ of the second revision - 20 ( 5 + 3 + 3 ) = 220 $ ; total : 250 + 240 + 220 = 710 $ . answer : e ." | general |
math_qa__16rbzmL85Ock59OQ | if josh , doug , and brad have a total of $ 68 between them , and josh has two times as much money as brad but only 3 - fourths as much as doug , how much money does brad have ? Choose the correct choice from the following answers:
A) $ 10 B) $ 24 C) $ 26 D) $ 12 E) $ 36 | <gadget id="calculator">1 + 2</gadget>
<output>3</output>
<gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">2 / (3/4)</gadget>
<output>8/3 = around 2.666667</output>
<gadget id="calculator">3 + (8/3)</gadget>
<output>17/3 = around 5.666667</output>
<gadget id="calculator">68 / (17/3)</gadget>
<output>12</output>
<result>D</result> | D | 12 | if josh , doug , and brad have a total of $ 68 between them , and josh has two times as much money as brad but only 3 - fourths as much as doug , how much money does brad have ? | {
"A": "$ 10",
"B": "$ 24",
"C": "$ 26",
"D": "$ 12",
"E": "$ 36"
} | divide(68, add(add(const_1, const_2), divide(const_2, divide(3, const_4)))) | add(const_1,const_2)|divide(n1,const_4)|divide(const_2,#1)|add(#0,#2)|divide(n0,#3) | josh + doug + brad = 68 ; josh = 2 brad , josh = 3 / 4 doug josh + 1 / 2 josh + 4 / 3 josh = 68 ( substituted the given values ) josh = 24 . 24 = 3 / 4 doug = > doug = 32 josh + doug + brad = 68 24 + 32 + brad = 68 brad = 12 answer is d . | general |
math_qa__PWZGas2ogzRbEclE | Mahesh can do a piece of work in 45days. He works at it for 20days and then Rajesh finished it in 30days. How long will Y take to complete the work?
Choose the correct choice:
A) 54 B) 25 C) 37 D) 41 E) 30 | <gadget id="calculator">1 / 45</gadget>
<output>1/45 = around 0.022222</output>
<gadget id="calculator">20 * (1/45)</gadget>
<output>4/9 = around 0.444444</output>
<gadget id="calculator">1 - (4/9)</gadget>
<output>5/9 = around 0.555556</output>
<gadget id="calculator">(5/9) / 30</gadget>
<output>1/54 = around 0.018519</output>
<gadget id="calculator">1 / (1/54)</gadget>
<output>54</output>
<result>A</result> | A | 54 | Mahesh can do a piece of work in 45days. He works at it for 20days and then Rajesh finished it in 30days. How long will Y take to complete the work? | {
"A": "54",
"B": "25",
"C": "37",
"D": "41",
"E": "30"
} | divide(const_1, divide(subtract(const_1, multiply(20, divide(const_1, 45))), 30)) | divide(const_1,n0)|multiply(n1,#0)|subtract(const_1,#1)|divide(#2,n2)|divide(const_1,#3) | work done by mahesh in 45 days = 20 * 1 / 45 = 4 / 9 remaining work = 1 - 4 / 9 = 5 / 9 5 / 9 work is done by rajesh in 30 days whole work will be done by rajesh is 30 * 9 / 5 = 54 days answer is a | physics |
math_qa__BPFVlH83pWAHQazp | The speed of a car is 100 km in the first hour and 30 km in the second hour. What is the average speed of the car?
Options.
A) 50 kmph B) 65 kmph C) 75 kmph D) 85 kmph E) 65 kmph | <gadget id="calculator">100 + 30</gadget>
<output>130</output>
<gadget id="calculator">130 / 2</gadget>
<output>65</output>
<result>E</result> | E | 65 | The speed of a car is 100 km in the first hour and 30 km in the second hour. What is the average speed of the car? | {
"A": "50 kmph",
"B": "65 kmph",
"C": "75 kmph",
"D": "85 kmph",
"E": "65 kmph"
} | divide(add(100, 30), const_2) | add(n0,n1)|divide(#0,const_2)| | "explanation : s = ( 100 + 30 ) / 2 = 65 kmph e )" | physics |
math_qa__UuBMn03XRPxnjrG9 | The hour hand of a watch rotates 30 degrees every hour. How many complete rotations does the hour hand make in 6 days? Choices
A) 8 B) 10 C) 12 D) 14 E) 16 | <gadget id="calculator">2 * 6</gadget>
<output>12</output>
<result>C</result> | C | 12 | The hour hand of a watch rotates 30 degrees every hour. How many complete rotations does the hour hand make in 6 days? | {
"A": "8",
"B": "10",
"C": "12",
"D": "14",
"E": "16"
} | multiply(const_2, 6) | multiply(n1,const_2) | explanation : there are 360 degrees in a complete circle , so 360 / 30 = 12 hours to make one full circle . in 6 days there are 24 hours x 6 = 144 hours total . the total number of rotations will be 144 / 12 = 12 . answer : ( c ) | physics |
math_qa__lQ7KGu1MDfONaOcn | Find the remainder when 6^23 is divided by 5 ? Choose the correct choice from the following: A) 3 B) 2 C) 1 D) 0 E) 4 | <gadget id="calculator">6 ** 23</gadget>
<output>789_730_223_053_602_816</output>
<gadget id="calculator">789_730_223_053_602_816 % 5</gadget>
<output>1</output>
<result>C</result> | C | 1 | Find the remainder when 6^23 is divided by 5 ? | {
"A": "3",
"B": "2",
"C": "1",
"D": "0",
"E": "4"
} | reminder(power(6, 23), 5) | power(n0,n1)|reminder(#0,n2)| | "6 ^ 23 = 6 ^ ( 4 * 5 + 3 ) = 6 ^ ( 20 ) * 6 ^ 3 last 3 digits = 216 216 / 5 remainder = 1 answer : c" | general |
math_qa__eprpl5sU7vLhxMQm | A vessel of capacity 75 litres is fully filled with pure milk. Nine litres of milk is removed from the vessel and replaced with water. Nine litres of the solution thus formed is removed and replaced with water. Find the quantity of pure milk in the final milk solution?
Options: A) 23.89 B) 72.9 C) 58.08 D) 78.3 E) 79.3 | <gadget id="calculator">3 * 3</gadget>
<output>9</output>
<gadget id="calculator">75 - 9</gadget>
<output>66</output>
<gadget id="calculator">66 / 75</gadget>
<output>22/25 = around 0.88</output>
<gadget id="calculator">(22/25) * 9</gadget>
<output>198/25 = around 7.92</output>
<gadget id="calculator">66 - (198/25)</gadget>
<output>1_452/25 = around 58.08</output>
<result>C</result> | C | 58.08 | A vessel of capacity 75 litres is fully filled with pure milk. Nine litres of milk is removed from the vessel and replaced with water. Nine litres of the solution thus formed is removed and replaced with water. Find the quantity of pure milk in the final milk solution? | {
"A": "23.89",
"B": "72.9",
"C": "58.08",
"D": "78.3",
"E": "79.3"
} | subtract(subtract(75, multiply(const_3, const_3)), multiply(divide(subtract(75, multiply(const_3, const_3)), 75), multiply(const_3, const_3))) | multiply(const_3,const_3)|subtract(n0,#0)|divide(#1,n0)|multiply(#2,#0)|subtract(#1,#3)| | "explanation : let the initial quantity of milk in vessel be t litres . let us say y litres of the mixture is taken out and replaced by water for n times , alternatively . quantity of milk finally in the vessel is then given by [ ( t - y ) / t ] n * t for the given problem , t = 75 , y = 9 and n = 2 . hence , quantity of milk finally in the vessel = [ ( 75 - 9 ) / 75 ] ^ 2 ( 75 ) = 58.08 litres . answer : option c" | physics |
math_qa__9i0NVZexW9MNiecx | Riya and Priya set on a journey. Riya moves eastward at a speed of 25kmph and Priya moves westward at a speed of 40 kmph.How far will be priya from Riya after 15 minutes Choose the correct choice from the following options.
A) 18 kms B) 16 kms C) 50 kms D) 30 kms E) 40 kms | <gadget id="calculator">25 + 40</gadget>
<output>65</output>
<gadget id="calculator">65 / 60</gadget>
<output>13/12 = around 1.083333</output>
<gadget id="calculator">(13/12) * 15</gadget>
<output>65/4 = around 16.25</output>
<result>B</result> | B | 16 | Riya and Priya set on a journey. Riya moves eastward at a speed of 25kmph and Priya moves westward at a speed of 40 kmph.How far will be priya from Riya after 15 minutes | {
"A": "18 kms",
"B": "16 kms",
"C": "50 kms",
"D": "30 kms",
"E": "40 kms"
} | multiply(speed(add(25, 40), const_60), 15) | add(n0,n1)|speed(#0,const_60)|multiply(n2,#1)| | "total eastward distance = 25 kmph * 1 / 4 hr = 6.25 km total westward distance = 40 kmph * 1 / 4 hr = 10 km total distn betn them = 6.25 + 10 = 16.25 km ans 16 km answer : b" | physics |
math_qa__VEsG7E0b6fA3SbhA | The product of two successive numbers is 9506. Which is the smaller of the two numbers? Choose the correct choice from the following answers
A) 78 B) 68 C) 88 D) 97 E) 37 | <gadget id="calculator">9_506 ** (1/2)</gadget>
<output>7*sqrt(194) = around 97.498718</output>
<result>D</result> | D | 97 | The product of two successive numbers is 9506. Which is the smaller of the two numbers? | {
"A": "78",
"B": "68",
"C": "88",
"D": "97",
"E": "37"
} | sqrt(9506) | sqrt(n0)| | "d 97 from the given alternatives , 97 × 98 = 9506 ∴ smaller number = 97" | general |
math_qa__Y5iA62QveI8O5yH7 | The difference between a positive proper fraction and its reciprocal is 9/20. The fraction is:
Options
A) 4 / 5 B) 5 / 4 C) 3 / 5 D) 2 / 5 E) 3 / 4 | <gadget id="calculator">9 - 4</gadget>
<output>5</output>
<gadget id="calculator">4 / 5</gadget>
<output>4/5 = around 0.8</output>
<result>A</result> | A | 0.8 | The difference between a positive proper fraction and its reciprocal is 9/20. The fraction is: | {
"A": "4 / 5",
"B": "5 / 4",
"C": "3 / 5",
"D": "2 / 5",
"E": "3 / 4"
} | divide(const_4, subtract(9, const_4)) | subtract(n0,const_4)|divide(const_4,#0)| | "let the required fraction be x . then 1 / x - x = 9 / 20 ( 1 - x ^ 2 ) / x = 9 / 20 = = > 20 - 20 x ^ 2 = 9 x 20 x ^ 2 + 9 x - 20 = 0 20 x ^ 2 + 25 x - 16 x - 20 = 0 5 x ( 4 x + 5 ) - 4 ( 4 x + 5 ) = 0 ( 4 x + 5 ) ( 5 x - 4 ) = 0 x = 4 / 5 ( neglecting - ve value ) answer a ) 4 / 5" | general |
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