id stringlengths 25 25 | question stringlengths 45 1.01k | chain stringlengths 75 4.11k | result stringclasses 5 values | result_float float64 -4,212 100B | question_without_options stringlengths 6 962 | options dict | annotated_formula stringlengths 7 6.48k | linear_formula stringlengths 8 925 | rationale stringlengths 1 2.74k | category stringclasses 6 values |
|---|---|---|---|---|---|---|---|---|---|---|
math_qa__wYAtw1GuLbmscFTI | A box contains 20 electric bulbs, out of which 4 are defective. Two bulbs are chosen at random form this box. The probability that at least one of these is defective is: Choose the correct answer
A) 8 / 19 B) 7 / 19 C) 10 / 19 D) 20 / 19 E) 22 / 19 | <gadget id="calculator">20 - 4</gadget>
<output>16</output>
<gadget id="calculator">binomial(16, 2)</gadget>
<output>120</output>
<gadget id="calculator">binomial(20, 2)</gadget>
<output>190</output>
<gadget id="calculator">120 / 190</gadget>
<output>12/19 = around 0.631579</output>
<gadget id="calculator">1 - (12/19)</gadget>
<output>7/19 = around 0.368421</output>
<result>B</result> | B | 0.368421 | A box contains 20 electric bulbs, out of which 4 are defective. Two bulbs are chosen at random form this box. The probability that at least one of these is defective is: | {
"A": "8 / 19",
"B": "7 / 19",
"C": "10 / 19",
"D": "20 / 19",
"E": "22 / 19"
} | subtract(const_1, divide(choose(subtract(20, 4), const_2), choose(20, const_2))) | choose(n0,const_2)|subtract(n0,n1)|choose(#1,const_2)|divide(#2,#0)|subtract(const_1,#3)| | "p ( none is defective ) = 16 c 2 / 20 c 2 = 12 / 19 p ( at least one is defective ) = 1 - 12 / 19 = 7 / 19 answer b" | probability |
math_qa__OiocAzakNfPJklXE | John and Amanda stand at opposite ends of a straight road and start running towards each other at the same moment. Their rates are randomly selected in advance so that John runs at a constant rate of 2, 3, 4, or 5 miles per hour and Amanda runs at a constant rate of 3, 4, 5, 6, or 7 miles per hour. What is the probability that John has traveled farther than Amanda by the time they meet?
Choose the correct option:
A) 1 / 5 B) 2 / 5 C) 3 / 10 D) 3 / 20 E) 7 / 20 | <gadget id="calculator">4 * 5</gadget>
<output>20</output>
<gadget id="calculator">3 / 20</gadget>
<output>3/20 = around 0.15</output>
<result>D</result> | D | 0.15 | John and Amanda stand at opposite ends of a straight road and start running towards each other at the same moment. Their rates are randomly selected in advance so that John runs at a constant rate of 2, 3, 4, or 5 miles per hour and Amanda runs at a constant rate of 3, 4, 5, 6, or 7 miles per hour. What is the probability that John has traveled farther than Amanda by the time they meet? | {
"A": "1 / 5",
"B": "2 / 5",
"C": "3 / 10",
"D": "3 / 20",
"E": "7 / 20"
} | divide(const_3, multiply(4, 5)) | multiply(n2,n3)|divide(const_3,#0) | john will run farther if he runs at 5 mph and amanda runs at 4 mph or 3 mph . in this case , p ( john runs farther ) = 1 / 4 * 2 / 5 = 2 / 20 john will run farther if he runs at 4 mph and amanda runs at 3 mph . in this case , p ( john runs farther ) = 1 / 4 * 1 / 5 = 1 / 20 p ( john runs farther ) = 2 / 20 + 1 / 20 = 3 / 20 the answer is d . | physics |
math_qa__ukqDHQMHU9S2RWLX | John invests $x at the semi-annual constant compounded rate of 2 percent and also does $40,000 at the quarterly constant compounded rate of 4 percent. If the interests are the same after 1 year, what is the value of x??
Choices
A) 50000 B) 55000 C) 60000 D) 70000 E) 80804 | <gadget id="calculator">4 * 100</gadget>
<output>400</output>
<gadget id="calculator">400 * 100</gadget>
<output>40_000</output>
<gadget id="calculator">4 / 100</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">(1/25) / 4</gadget>
<output>1/100 = around 0.01</output>
<gadget id="calculator">1 + (1/100)</gadget>
<output>101/100 = around 1.01</output>
<gadget id="calculator">(101/100) ** 4</gadget>
<output>104_060_401/100_000_000 = around 1.040604</output>
<gadget id="calculator">40_000 * (104_060_401/100_000_000)</gadget>
<output>104_060_401/2_500 = around 41_624.1604</output>
<gadget id="calculator">(104_060_401/2_500) - 40_000</gadget>
<output>4_060_401/2_500 = around 1_624.1604</output>
<gadget id="calculator">2 / 100</gadget>
<output>1/50 = around 0.02</output>
<gadget id="calculator">(1/50) / 2</gadget>
<output>1/100 = around 0.01</output>
<gadget id="calculator">(101/100) ** 2</gadget>
<output>10_201/10_000 = around 1.0201</output>
<gadget id="calculator">(10_201/10_000) - 1</gadget>
<output>201/10_000 = around 0.0201</output>
<gadget id="calculator">(4_060_401/2_500) / (201/10_000)</gadget>
<output>80_804</output>
<result>E</result> | E | 80,804 | John invests $x at the semi-annual constant compounded rate of 2 percent and also does $40,000 at the quarterly constant compounded rate of 4 percent. If the interests are the same after 1 year, what is the value of x?? | {
"A": "50000",
"B": "55000",
"C": "60000",
"D": "70000",
"E": "80804"
} | divide(subtract(multiply(multiply(multiply(const_4, const_100), const_100), power(add(const_1, divide(divide(4, const_100), const_4)), const_4)), multiply(multiply(const_4, const_100), const_100)), subtract(power(add(const_1, divide(divide(2, const_100), const_2)), const_2), const_1)) | divide(n2,const_100)|divide(n0,const_100)|multiply(const_100,const_4)|divide(#0,const_4)|divide(#1,const_2)|multiply(#2,const_100)|add(#3,const_1)|add(#4,const_1)|power(#6,const_4)|power(#7,const_2)|multiply(#5,#8)|subtract(#9,const_1)|subtract(#10,#5)|divide(#12,#11) | a = p ( 1 + r / n ) ^ nt a = total amount accrued p = principal deposited r = rate of interest in decimal form n = number of times per year , interest compounded t = time in number of years . . x ( 1 + 0.02 / 2 ) ^ 2 - x = 40,000 ( 1 + 0.04 / 4 ) ^ 4 - 40,000 [ when the principal is subtracted from the total amount accrued , the resulting difference is the interest portion and question states interests are equal ) = > x [ ( 1.01 ) ^ 2 - 1 ] = 40,000 [ ( 1.01 ) ^ 4 - 1 ] = > x [ ( 1.01 ) ^ 2 - 1 ] = 40,000 [ ( 1.01 ) ^ 2 + 1 ] [ ( 1.01 ) ^ 2 - 1 ] - - > using a ^ 2 - b ^ 2 = a + b x a - b formula and cancel common expression on both sides = > x = 40,000 ( 1.0201 + 1 ) = 80804 . hence answer is e . | gain |
math_qa__HUqXTOQADClbtnHi | If 7125¸1.25= 5700< the value of 712.5÷12.5 is: Choose the correct option.
A) 5.7
B) 57
C) 570
D) 0.57
E) 0.057 | <gadget id="calculator">712.5 / 12.5</gadget>
<output>57</output>
<result>B</result> | B | 57 | If 7125¸1.25= 5700< the value of 712.5÷12.5 is: | {
"A": "5.7",
"B": "57",
"C": "570",
"D": "0.57",
"E": "0.057"
} | divide(712.5, 12.5) | divide(n3,n4) | given 7125 / 1.25 = 5700 712.5 / 12.5 = 71.25 / 1.25 = 7125 * 1 / 1.25 * 100 = 5700 / 100 = 57 answer : b | general |
math_qa__ykweQnIAn4VP857c | Find the principle on a certain sum of money at 5% per annum for 6 years if the amount being Rs.1120? Select
A) 862 B) 1067 C) 1977 D) 1056 E) 1097 | <gadget id="calculator">5 * 6</gadget>
<output>30</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">1_120 / (13/10)</gadget>
<output>11_200/13 = around 861.538462</output>
<result>A</result> | A | 862 | Find the principle on a certain sum of money at 5% per annum for 6 years if the amount being Rs.1120? | {
"A": "862",
"B": "1067",
"C": "1977",
"D": "1056",
"E": "1097"
} | divide(1120, add(const_1, divide(multiply(5, 6), const_100))) | multiply(n0,n1)|divide(#0,const_100)|add(#1,const_1)|divide(n2,#2) | 1120 = p [ 1 + ( 5 * 6 ) / 100 ] p = 862 answer : a | gain |
math_qa__aHBhnsnQLd8bUn8v | A certain high school has 500 students. Of these students, 40 are taking music, 20 are taking art, and 10 are taking both music and art. How many students are taking neither music nor art? Pick one
A) 430
B) 440
C) 450
D) 460
E) 470 | <gadget id="calculator">40 + 20</gadget>
<output>60</output>
<gadget id="calculator">60 - 10</gadget>
<output>50</output>
<gadget id="calculator">500 - 50</gadget>
<output>450</output>
<result>C</result> | C | 450 | A certain high school has 500 students. Of these students, 40 are taking music, 20 are taking art, and 10 are taking both music and art. How many students are taking neither music nor art? | {
"A": "430",
"B": "440",
"C": "450",
"D": "460",
"E": "470"
} | subtract(500, subtract(add(40, 20), 10)) | add(n1,n2)|subtract(#0,n3)|subtract(n0,#1) | we ' re given a series of facts to work with : 1 ) a certain high school has 500 students . 2 ) of these students : x are taking music , y are taking art , and z are taking both music and art . we ' re asked how many students are taking neither music nor art ? let ' s test x = 40 y = 20 z = 10 so , we have 40 students taking music , 20 taking art and 10 taking both music and art . 30 student taking just music 10 student taking just art 10 student taking both music and art total = 50 students we ' re asked for the total number of students who are taking neither course . that is 500 - 50 = 450 . c | other |
math_qa__8mDDrRm6GaoT5D2D | When 1/10 percent of 7,000 is subtracted from 1/10 of 7,000, the difference is
Choose the correct choice from the following options:
A) 0 B) 50 C) 450 D) 693 E) 500 | <gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">7 * 1_000</gadget>
<output>7_000</output>
<gadget id="calculator">1 / 10</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">7_000 * (1/10)</gadget>
<output>700</output>
<gadget id="calculator">(1/10) / 100</gadget>
<output>1/1_000 = around 0.001</output>
<gadget id="calculator">(1/1_000) * 7_000</gadget>
<output>7</output>
<gadget id="calculator">700 - 7</gadget>
<output>693</output>
<result>D</result> | D | 693 | When 1/10 percent of 7,000 is subtracted from 1/10 of 7,000, the difference is | {
"A": "0",
"B": "50",
"C": "450",
"D": "693",
"E": "500"
} | subtract(multiply(multiply(add(const_3, const_4), const_1000), divide(1, 10)), multiply(divide(divide(1, 10), const_100), multiply(add(const_3, const_4), const_1000))) | add(const_3,const_4)|divide(n0,n1)|divide(#1,const_100)|multiply(#0,const_1000)|multiply(#1,#3)|multiply(#2,#3)|subtract(#4,#5) | we can break this problem into two parts : 1 ) what is 1 / 10 percent of 7,000 ? 2 ) what is 1 / 10 of 7,000 ? to calculate 1 / 10 percent of 7,000 we must first remember to divide 1 / 10 by 100 . so we have : ( 1 / 10 ) / ( 100 ) to divide a number by 100 means to multiply it by 1 / 100 , so we have : 1 / 10 x 1 / 100 = 1 / 1,000 thus , 1 / 10 percent of 7,000 = 1 / 1,000 x 7,000 = 7 . now let ' s concentrate on part 2 . we need to calculate 1 / 10 of 7,000 . to do this we simply multiply 1 / 10 by 7,000 . 1 / 10 x 7,000 = 700 the answer to part 1 is 7 , and the answer to part 2 is 700 . their difference is 700 – 7 = 693 . answer d . | general |
math_qa__OQoeKiOzIYK3GHCn | What sum of money will produce Rs.210 as simple interest in 4 years at 3 1/2 percent?
Choose the correct choice from the following: A) rs . 2500 B) rs . 1500 C) rs . 1400 D) rs . 1600 E) rs . 1300 | <gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">3 + (1/2)</gadget>
<output>7/2 = around 3.5</output>
<gadget id="calculator">4 * (7/2)</gadget>
<output>14</output>
<gadget id="calculator">14 / 100</gadget>
<output>7/50 = around 0.14</output>
<gadget id="calculator">210 / (7/50)</gadget>
<output>1_500</output>
<result>B</result> | B | 1,500 | What sum of money will produce Rs.210 as simple interest in 4 years at 3 1/2 percent? | {
"A": "rs . 2500",
"B": "rs . 1500",
"C": "rs . 1400",
"D": "rs . 1600",
"E": "rs . 1300"
} | divide(210, divide(multiply(4, add(3, divide(1, 2))), const_100)) | divide(n3,n4)|add(n2,#0)|multiply(n1,#1)|divide(#2,const_100)|divide(n0,#3) | 210 = ( p * 4 * 7 / 2 ) / 100 p = 1500 answer : b | gain |
math_qa__UjNrZL0nSoBiqSk9 | While driving from A-ville to B-town, Harriet drove at a constant speed of 90 kilometers per hour. Upon arriving in B-town, Harriet immediately turned and drove back to A-ville at a constant speed of 160 kilometers per hour. If the entire trip took 5 hours, how many minutes did it take Harriet to drive from A-ville to B-town? Select.
A) 138 B) 148 C) 150 D) 162 E) 192 | <gadget id="calculator">90 * 5</gadget>
<output>450</output>
<gadget id="calculator">90 + 160</gadget>
<output>250</output>
<gadget id="calculator">450 / 250</gadget>
<output>9/5 = around 1.8</output>
<gadget id="calculator">5 - (9/5)</gadget>
<output>16/5 = around 3.2</output>
<gadget id="calculator">(16/5) * 60</gadget>
<output>192</output>
<result>E</result> | E | 192 | While driving from A-ville to B-town, Harriet drove at a constant speed of 90 kilometers per hour. Upon arriving in B-town, Harriet immediately turned and drove back to A-ville at a constant speed of 160 kilometers per hour. If the entire trip took 5 hours, how many minutes did it take Harriet to drive from A-ville to B-town? | {
"A": "138",
"B": "148",
"C": "150",
"D": "162",
"E": "192"
} | multiply(subtract(5, divide(multiply(90, 5), add(90, 160))), const_60) | add(n0,n1)|multiply(n0,n2)|divide(#1,#0)|subtract(n2,#2)|multiply(#3,const_60) | 5 hr = 300 min . if harriet spend equal hrs on each leg she will spend 150 min on each . since speed a - b is less than speed b - a and distance on each leg is the same , time spent on a - b is more than 150 min , which mean we can eliminate ans . a , b and c . now let plug in ans . d or e and verify which one give same distance on each leg . d . t = 162 min * leg a - b - - - > d = 90.192 / 60 = 17280 / 60 * leg b - a - - - - > d = 160 * 108 / 60 = 17280 / 60 so the correct ans . ise | physics |
math_qa__TGNhGkB1d8slYGOK | The milk level in a rectangular box measuring 64 feet by 25 feet is to be lowered by 6 inches. How many gallons of milk must be removed? (1 cu ft = 7.5 gallons)
Choose the correct choice from the following: A) 100 B) 250 C) 750 D) 5625 E) 6000 | <gadget id="calculator">64 * 25</gadget>
<output>1_600</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1_600 * (1/2)</gadget>
<output>800</output>
<gadget id="calculator">800 * 7.5</gadget>
<output>6_000</output>
<result>E</result> | E | 6,000 | The milk level in a rectangular box measuring 64 feet by 25 feet is to be lowered by 6 inches. How many gallons of milk must be removed? (1 cu ft = 7.5 gallons) | {
"A": "100",
"B": "250",
"C": "750",
"D": "5625",
"E": "6000"
} | multiply(multiply(multiply(64, 25), divide(1, const_2)), 7.5) | divide(n3,const_2)|multiply(n0,n1)|multiply(#0,#1)|multiply(n4,#2) | 6 inches = 1 / 2 feet ( there are 12 inches in a foot . ) , so 64 * 25 * 1 / 2 = 800 feet ^ 3 of milk must be removed , which equals to 800 * 7.5 = 6000 gallons . answer : e . | general |
math_qa__7eyXwj3z5sHH32jR | I sold a book at a profit of 10%. Had I sold it for $90 more, 15% would have been gained. Find the cost price? Select:
A) $ 1800 B) $ 2500 C) $ 3000 D) $ 3120 E) $ 1540 | <gadget id="calculator">90 * 10</gadget>
<output>900</output>
<gadget id="calculator">15 - 10</gadget>
<output>5</output>
<gadget id="calculator">900 / 5</gadget>
<output>180</output>
<gadget id="calculator">180 * 100</gadget>
<output>18_000</output>
<gadget id="calculator">18_000 / 10</gadget>
<output>1_800</output>
<result>A</result> | A | 1,800 | I sold a book at a profit of 10%. Had I sold it for $90 more, 15% would have been gained. Find the cost price? | {
"A": "$ 1800",
"B": "$ 2500",
"C": "$ 3000",
"D": "$ 3120",
"E": "$ 1540"
} | divide(multiply(divide(multiply(90, 10), subtract(15, 10)), const_100), 10) | multiply(n0,n1)|subtract(n2,n0)|divide(#0,#1)|multiply(#2,const_100)|divide(#3,n0)| | "115 % of cost - 110 % of cost = $ 90 5 % of cost = $ 90 cost = 90 * 100 / 5 = $ 1800 answer is a" | gain |
math_qa__aCeD1V5haEFwLwpG | A dog takes 5 leaps for every 8 leaps of a hare. If one leap of the dog is equal to 4 leaps of the hare, the ratio of the speed of the dog to that of the hare is :
Options: A) 5 : 8 B) 5 : 3 C) 5 : 2 D) 5 : 9 E) 2 : 5 | <gadget id="calculator">5 * 4</gadget>
<output>20</output>
<gadget id="calculator">20 / 8</gadget>
<output>5/2 = around 2.5</output>
<result>C</result> | C | 2.5 | A dog takes 5 leaps for every 8 leaps of a hare. If one leap of the dog is equal to 4 leaps of the hare, the ratio of the speed of the dog to that of the hare is : | {
"A": "5 : 8",
"B": "5 : 3",
"C": "5 : 2",
"D": "5 : 9",
"E": "2 : 5"
} | divide(multiply(5, 4), 8) | multiply(n0,n2)|divide(#0,n1)| | "explanation : dog : hare = ( 5 * 4 ) leaps of hare : 8 leaps of hare = 20 : 8 - - > 10 : 4 - - > 5 : 2 answer : c" | other |
math_qa__lhpa6o4IErxgdq0A | By selling 200 apples, a fruit-seller gains the selling price of 50 apples. Find the gain percent? Choose the most appropriate option.
A) 33.33 %
B) 35 %
C) 27.75 %
D) 35.75 %
E) 32.25 % | <gadget id="calculator">200 - 50</gadget>
<output>150</output>
<gadget id="calculator">50 / 150</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(1/3) * 100</gadget>
<output>100/3 = around 33.333333</output>
<result>A</result> | A | 33.33 | By selling 200 apples, a fruit-seller gains the selling price of 50 apples. Find the gain percent? | {
"A": "33.33 %",
"B": "35 %",
"C": "27.75 %",
"D": "35.75 %",
"E": "32.25 %"
} | multiply(divide(50, subtract(200, 50)), const_100) | subtract(n0,n1)|divide(n1,#0)|multiply(#1,const_100) | sp = cp + g 200 sp = 200 cp + 50 sp 150 sp = 200 cp 150 - - - 50 cp 100 - - - ? = > 33.33 % answer : a | gain |
math_qa__1N6tHR1l7zrqqFUK | A, B and C can do a piece of work in 24 days, 30 days and 40 days respectively. They began the work together but C left 8 days before the completion of the work. In how many days was the work completed?
Select:
A) 12 days B) 16 days C) 18 days D) 11 days E) 38 days | <gadget id="calculator">1 / 24</gadget>
<output>1/24 = around 0.041667</output>
<gadget id="calculator">1 / 30</gadget>
<output>1/30 = around 0.033333</output>
<gadget id="calculator">(1/24) + (1/30)</gadget>
<output>3/40 = around 0.075</output>
<gadget id="calculator">(3/40) * 8</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">1 - (3/5)</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">2 * 8</gadget>
<output>16</output>
<gadget id="calculator">5 * 16</gadget>
<output>80</output>
<gadget id="calculator">1 / 80</gadget>
<output>1/80 = around 0.0125</output>
<gadget id="calculator">(1/80) + (3/40)</gadget>
<output>7/80 = around 0.0875</output>
<gadget id="calculator">(2/5) / (7/80)</gadget>
<output>32/7 = around 4.571429</output>
<gadget id="calculator">(32/7) + 8</gadget>
<output>88/7 = around 12.571429</output>
<result>A</result> | A | 12 | A, B and C can do a piece of work in 24 days, 30 days and 40 days respectively. They began the work together but C left 8 days before the completion of the work. In how many days was the work completed? | {
"A": "12 days",
"B": "16 days",
"C": "18 days",
"D": "11 days",
"E": "38 days"
} | add(divide(subtract(const_1, multiply(add(divide(const_1, 24), divide(const_1, 30)), 8)), add(divide(const_1, multiply(add(const_2, const_3), multiply(const_2, 8))), add(divide(const_1, 24), divide(const_1, 30)))), 8) | add(const_2,const_3)|divide(const_1,n0)|divide(const_1,n1)|multiply(const_2,n3)|add(#1,#2)|multiply(#0,#3)|divide(const_1,#5)|multiply(n3,#4)|add(#4,#6)|subtract(const_1,#7)|divide(#9,#8)|add(n3,#10)| | "one day work of a , b and c = 1 / 24 + 1 / 30 + 1 / 40 = 1 / 10 work done by a and b together in the last 8 days = 8 * ( 1 / 24 + 1 / 30 ) = 3 / 5 remaining work = 2 / 5 the number of days required for this initial work = 4 days . the total number of days required = 8 + 4 = 12 days . answer : a" | physics |
math_qa__RjY7PxTqWl0FpuVN | A man whose bowling average is 12.4, takes 4 wickets for 26 runs and there by decreases his average by 0.4. the number of wickets taken by him before his last match is? Choose one
A) 53 B) 54 C) 55 D) 56 E) 57 | <gadget id="calculator">floor(12.4)</gadget>
<output>12</output>
<gadget id="calculator">12 * 4</gadget>
<output>48</output>
<gadget id="calculator">48 - 26</gadget>
<output>22</output>
<gadget id="calculator">12.4 - 12</gadget>
<output>0.4</output>
<gadget id="calculator">22 / 0.4</gadget>
<output>55</output>
<result>C</result> | C | 55 | A man whose bowling average is 12.4, takes 4 wickets for 26 runs and there by decreases his average by 0.4. the number of wickets taken by him before his last match is? | {
"A": "53",
"B": "54",
"C": "55",
"D": "56",
"E": "57"
} | divide(subtract(multiply(floor(12.4), 4), 26), subtract(12.4, floor(12.4))) | floor(n0)|multiply(n1,#0)|subtract(n0,#0)|subtract(#1,n2)|divide(#3,#2)| | "12.4 * x + 26 = ( 4 + x ) 12 solve equation x = 55 answer : c" | general |
math_qa__EPuiN57YVrCAXExt | An engine moves at the speed of 60 kmph without any coaches attached to it.Speed of the train reduces at the rate that varies directly as the square root of the number of coaches attached.When 9 coaches are attached speed decreases to 48 kmph.What will be the speed of train when 25 coaches are attached.
Select the correct option:
A) 35 B) 28 C) 40 D) 44 E) 42 | <gadget id="calculator">25 ** (1/2)</gadget>
<output>5</output>
<gadget id="calculator">60 - 48</gadget>
<output>12</output>
<gadget id="calculator">9 ** (1/2)</gadget>
<output>3</output>
<gadget id="calculator">12 / 3</gadget>
<output>4</output>
<gadget id="calculator">5 * 4</gadget>
<output>20</output>
<gadget id="calculator">60 - 20</gadget>
<output>40</output>
<result>C</result> | C | 40 | An engine moves at the speed of 60 kmph without any coaches attached to it.Speed of the train reduces at the rate that varies directly as the square root of the number of coaches attached.When 9 coaches are attached speed decreases to 48 kmph.What will be the speed of train when 25 coaches are attached. | {
"A": "35",
"B": "28",
"C": "40",
"D": "44",
"E": "42"
} | subtract(60, multiply(sqrt(25), divide(subtract(60, 48), sqrt(9)))) | sqrt(n1)|sqrt(n3)|subtract(n0,n2)|divide(#2,#0)|multiply(#3,#1)|subtract(n0,#4) | 1 . no . of coaches = 9 sqr root = 3 speed decreases by 12 12 = k * 3 k = 4 no . of coaches = 25 swr root = 5 decrease = 5 * 4 = 20 new speed = 60 - 20 = 40 c | physics |
math_qa__H31JWWRdDQ3TCKCt | In a mixture of 60 litres the ratio of milk to water is 5:1. Additional 20 litres of water is added to the mixture. Find the ratio of milk to water in the resulting mixture. Answers.
A) 2 : 3 B) 5 : 3 C) 1 : 4 D) 3 : 2 E) 3 : 1 | <gadget id="calculator">5 + 1</gadget>
<output>6</output>
<gadget id="calculator">60 / 6</gadget>
<output>10</output>
<gadget id="calculator">60 - 10</gadget>
<output>50</output>
<gadget id="calculator">10 + 20</gadget>
<output>30</output>
<gadget id="calculator">50 / 30</gadget>
<output>5/3 = around 1.666667</output>
<result>B</result> | B | 1.666667 | In a mixture of 60 litres the ratio of milk to water is 5:1. Additional 20 litres of water is added to the mixture. Find the ratio of milk to water in the resulting mixture. | {
"A": "2 : 3",
"B": "5 : 3",
"C": "1 : 4",
"D": "3 : 2",
"E": "3 : 1"
} | divide(subtract(60, divide(60, add(5, 1))), add(divide(60, add(5, 1)), 20)) | add(n1,n2)|divide(n0,#0)|add(n3,#1)|subtract(n0,#1)|divide(#3,#2)| | "given that milk / water = 5 x / x and 5 x + x = 60 - - > x = 10 . thus milk = 5 x = 50 liters and water = x = 10 liters . new ratio = 50 / ( 20 + 10 ) = 50 / 30 = 5 / 3 . answer is b" | general |
math_qa__IztLNWwicCjSgJ9J | A train traveling at 72 kmph crosses a platform in 34 seconds and a man standing on the platform in 18 seconds. What is the length of the platform in meters?
Choose the correct choice from the following choices
A) 240 meters
B) 320 meters
C) 420 meters
D) 600 meters
E) can not be determined | <gadget id="calculator">72 * 1_000</gadget>
<output>72_000</output>
<gadget id="calculator">72_000 / 3_600</gadget>
<output>20</output>
<gadget id="calculator">20 * 34</gadget>
<output>680</output>
<gadget id="calculator">20 * 18</gadget>
<output>360</output>
<gadget id="calculator">680 - 360</gadget>
<output>320</output>
<result>B</result> | B | 320 | A train traveling at 72 kmph crosses a platform in 34 seconds and a man standing on the platform in 18 seconds. What is the length of the platform in meters? | {
"A": "240 meters",
"B": "320 meters",
"C": "420 meters",
"D": "600 meters",
"E": "can not be determined"
} | subtract(multiply(divide(multiply(72, const_1000), const_3600), 34), multiply(divide(multiply(72, const_1000), const_3600), 18)) | multiply(n0,const_1000)|divide(#0,const_3600)|multiply(n1,#1)|multiply(n2,#1)|subtract(#2,#3)| | "speed of train = 72 * ( 5 / 18 ) = 20 m / s lets consider the man as a stationery point on the platform . crossing the point gives us the length of the train . lt = 20 * 18 = 360 m . crossing the platform gives us the length of trainlength of platform . l ( t + p ) = 20 * 34 = 680 m . so , length of platform = 680 - 360 = 320 m imo , answer b" | physics |
math_qa__x6d0WLbCt3bZya4M | In an NGO the daily average wages of 20 illiterate employees is decreased from Rs.25 to Rs.10, thus the average salary of all the literate and illiterate employees is decreased Rs.10 per day. The No. of educated employees working in the NGO is : Select the correct option: A) 12 B) 11 C) 10 D) 27 E) 22 | <gadget id="calculator">20 - 10</gadget>
<output>10</output>
<result>C</result> | C | 10 | In an NGO the daily average wages of 20 illiterate employees is decreased from Rs.25 to Rs.10, thus the average salary of all the literate and illiterate employees is decreased Rs.10 per day. The No. of educated employees working in the NGO is : | {
"A": "12",
"B": "11",
"C": "10",
"D": "27",
"E": "22"
} | subtract(20, 10) | subtract(n0,n2) | explanation : total employees = \ inline \ frac { ( 25 - 10 ) \ times 20 } { 10 } = 30 hence number of educated employees = 30 - 20 = 10 answer : c ) 10 | general |
math_qa__5Ew6EbW2GdlEqTX0 | You have been given a physical balance and 7 weights of 52, 50, 48, 44, 45, 46 and 78 kgs. Keeping weights on one pan and object on the other, what is the maximum you can weigh less than 183 kgs.
Choose the correct choice from the following:
A) 180 B) 181 C) 182 D) 178 E) 168 | <gadget id="calculator">50 + 48</gadget>
<output>98</output>
<gadget id="calculator">98 + 44</gadget>
<output>142</output>
<gadget id="calculator">142 + 46</gadget>
<output>188</output>
<result>A</result> | A | 180 | You have been given a physical balance and 7 weights of 52, 50, 48, 44, 45, 46 and 78 kgs. Keeping weights on one pan and object on the other, what is the maximum you can weigh less than 183 kgs. | {
"A": "180",
"B": "181",
"C": "182",
"D": "178",
"E": "168"
} | add(add(add(50, 48), 44), 46) | add(n2,n3)|add(n4,#0)|add(n6,#1)| | "add the max weights 52 + 50 + 78 = 180 answer : a" | general |
math_qa__7BLOoRXz1qyAXUar | Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 34 kmph. Of how many minutes does the train stop per hour? Choose the correct option.
A) e 982 B) 27 C) 12 D) 14.6 E) 28 | <gadget id="calculator">34 / 45</gadget>
<output>34/45 = around 0.755556</output>
<gadget id="calculator">60 * (34/45)</gadget>
<output>136/3 = around 45.333333</output>
<gadget id="calculator">60 - (136/3)</gadget>
<output>44/3 = around 14.666667</output>
<result>D</result> | D | 14.6 | Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 34 kmph. Of how many minutes does the train stop per hour? | {
"A": "e 982",
"B": "27",
"C": "12",
"D": "14.6",
"E": "28"
} | subtract(const_60, multiply(const_60, divide(34, 45))) | divide(n1,n0)|multiply(#0,const_60)|subtract(const_60,#1)| | "explanation : t = 11 / 45 * 60 = 14.6 answer : option d" | physics |
math_qa__ByxYPsNAeDwIPSsH | 5 men or 8 women do equal amount of work in a day. a job requires 3 men and 5 women to finish the job in 10 days how many woman are required to finish the job in 14 days. Select the correct option: A) 10 B) 7 C) 6 D) 12 E) 13 | <gadget id="calculator">8 / 5</gadget>
<output>8/5 = around 1.6</output>
<gadget id="calculator">(8/5) * 3</gadget>
<output>24/5 = around 4.8</output>
<gadget id="calculator">(24/5) + 5</gadget>
<output>49/5 = around 9.8</output>
<gadget id="calculator">(49/5) * 10</gadget>
<output>98</output>
<gadget id="calculator">98 / 14</gadget>
<output>7</output>
<result>B</result> | B | 7 | 5 men or 8 women do equal amount of work in a day. a job requires 3 men and 5 women to finish the job in 10 days how many woman are required to finish the job in 14 days. | {
"A": "10",
"B": "7",
"C": "6",
"D": "12",
"E": "13"
} | divide(multiply(add(multiply(divide(8, 5), 3), 5), 10), 14) | divide(n1,n0)|multiply(n2,#0)|add(n0,#1)|multiply(n4,#2)|divide(#3,n5) | 1 man can do the work of 8 / 5 = 1.6 women equivalent of 3 * 1.6 + 5 = 9.8 women take 10 days so women needed to do the work in 14 days = [ 10 / 14 ] * 9.8 = 7 answer : b | physics |
math_qa__IlhCFuMMuZGoQ6v0 | Ajay can walk 10km in 1 hour. In how many hours he can walk 50km? Choose the correct choice from the following answers:
A) 5 hrs B) 10 hrs C) 15 hrs D) 20 hrs E) 30 hrs | <gadget id="calculator">50 / 10</gadget>
<output>5</output>
<result>A</result> | A | 5 | Ajay can walk 10km in 1 hour. In how many hours he can walk 50km? | {
"A": "5 hrs",
"B": "10 hrs",
"C": "15 hrs",
"D": "20 hrs",
"E": "30 hrs"
} | divide(50, 10) | divide(n2,n0) | 1 hour he walk 10 km he walk 50 km in = 50 / 10 * 1 = 5 hours answer is a | physics |
math_qa__aqGehqiId1TOuF88 | Factory X's bulbs work for over 5000 hours in 75% of cases, whereas factory Y's bulbs work for over 5000 hours in 65% of cases. It is known that factory X supplies 70% of the total bulbs available. What is the chance that a purchased bulb will work for longer than 5000 hours? Choose the correct choice.
A) 76.4 % B) 78 % C) 77.4 % D) 72 % E) 73.9 % | <gadget id="calculator">75 + 65</gadget>
<output>140</output>
<gadget id="calculator">140 / 2</gadget>
<output>70</output>
<result>D</result> | D | 72 | Factory X's bulbs work for over 5000 hours in 75% of cases, whereas factory Y's bulbs work for over 5000 hours in 65% of cases. It is known that factory X supplies 70% of the total bulbs available. What is the chance that a purchased bulb will work for longer than 5000 hours? | {
"A": "76.4 %",
"B": "78 %",
"C": "77.4 %",
"D": "72 %",
"E": "73.9 %"
} | divide(add(75, 65), const_2) | add(n1,n3)|divide(#0,const_2)| | "for x , 70 % of 75 % will work . for y , 30 % of 65 % will work . * 30 % is the rest of the bulb supply in the market . so , the probability that a purchased bulb will work is : 0.70 ( 0.75 ) = . 525 0.30 ( 0.65 ) = 0.195 the combined probability then is 52.5 + 19.5 = 72 % ans d" | physics |
math_qa__YvDSEkqlmqkBQtmT | The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 1500 resolutions? Choose the correct choice from the following choices: A) 2112 m B) 2704 m C) 2278 m D) 2288 m E) 2378 m | <gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">7 * 3</gadget>
<output>21</output>
<gadget id="calculator">21 + 1</gadget>
<output>22</output>
<gadget id="calculator">22 / 7</gadget>
<output>22/7 = around 3.142857</output>
<gadget id="calculator">(22/7) * 22.4</gadget>
<output>70.4</output>
<gadget id="calculator">70.4 * 2</gadget>
<output>140.8</output>
<gadget id="calculator">140.8 * 1_500</gadget>
<output>211_200</output>
<gadget id="calculator">211_200 / 100</gadget>
<output>2_112</output>
<result>A</result> | A | 2,112 | The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 1500 resolutions? | {
"A": "2112 m",
"B": "2704 m",
"C": "2278 m",
"D": "2288 m",
"E": "2378 m"
} | divide(multiply(multiply(multiply(divide(add(multiply(add(const_3, const_4), const_3), const_1), add(const_3, const_4)), 22.4), const_2), 1500), const_100) | add(const_3,const_4)|multiply(#0,const_3)|add(#1,const_1)|divide(#2,#0)|multiply(n0,#3)|multiply(#4,const_2)|multiply(n1,#5)|divide(#6,const_100)| | "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 1500 resolutions . = 1500 * 2 * 22 / 7 * 22.4 = 211200 cm = 2112 m answer : a" | physics |
math_qa__mSFRqs7M9Fs2UK6M | A 300 meter long train running at the speed of 120 kmph crosses another train running in the opposite direction at the speed of 80 kmph in 9 seconds.What is the lenght of other train. Choose the correct choice from the following choices
A) 210 m B) 220 m C) 230 m D) 240 m E) 200 m | <gadget id="calculator">120 + 80</gadget>
<output>200</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">200 * (5/18)</gadget>
<output>500/9 = around 55.555556</output>
<gadget id="calculator">9 * (500/9)</gadget>
<output>500</output>
<gadget id="calculator">500 - 300</gadget>
<output>200</output>
<result>E</result> | E | 200 | A 300 meter long train running at the speed of 120 kmph crosses another train running in the opposite direction at the speed of 80 kmph in 9 seconds.What is the lenght of other train. | {
"A": "210 m",
"B": "220 m",
"C": "230 m",
"D": "240 m",
"E": "200 m"
} | subtract(multiply(9, multiply(add(120, 80), const_0_2778)), 300) | add(n1,n2)|multiply(#0,const_0_2778)|multiply(n3,#1)|subtract(#2,n0) | relative speeds = ( 120 + 80 ) km / hr = 200 km / hr = ( 200 * 5 / 18 ) m / s = ( 500 / 9 ) m / s let length of train be xm x + 300 / 9 = 500 / 9 x = 200 ans is 200 m answer : e | physics |
math_qa__5xiI9by2TwECixWD | By selling 12 pens for a rupee a woman loses 20%. How many for a rupee should he sell in order to gain 20%?
Pick: A) 12 B) 14 C) 45 D) 8 E) 65 | <gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">100 / 80</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">(5/4) / 12</gadget>
<output>5/48 = around 0.104167</output>
<gadget id="calculator">(5/48) * 20</gadget>
<output>25/12 = around 2.083333</output>
<gadget id="calculator">(25/12) / 100</gadget>
<output>1/48 = around 0.020833</output>
<gadget id="calculator">(5/48) + (1/48)</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">1 / (1/8)</gadget>
<output>8</output>
<result>D</result> | D | 8 | By selling 12 pens for a rupee a woman loses 20%. How many for a rupee should he sell in order to gain 20%? | {
"A": "12",
"B": "14",
"C": "45",
"D": "8",
"E": "65"
} | inverse(add(divide(divide(const_100, subtract(const_100, 20)), 12), divide(multiply(divide(divide(const_100, subtract(const_100, 20)), 12), 20), const_100))) | subtract(const_100,n1)|divide(const_100,#0)|divide(#1,n0)|multiply(n2,#2)|divide(#3,const_100)|add(#2,#4)|inverse(#5)| | "d 80 % - - - 12 120 % - - - ? 80 / 120 * 12 = 8" | gain |
math_qa__wLRFZWMhK91N2V0d | Find unit digit of N when N = 63^1!+2!+...+63! + 18^1!+2!+...+18! + 37^1!+2!+...37! Choose the most appropriate option
A) 2
B) 4
C) 6
D) 8
E) 0 | <gadget id="calculator">63 + 18</gadget>
<output>81</output>
<gadget id="calculator">81 + 37</gadget>
<output>118</output>
<gadget id="calculator">118 - 100</gadget>
<output>18</output>
<gadget id="calculator">18 - 10</gadget>
<output>8</output>
<result>D</result> | D | 8 | Find unit digit of N when N = 63^1!+2!+...+63! + 18^1!+2!+...+18! + 37^1!+2!+...37! | {
"A": "2",
"B": "4",
"C": "6",
"D": "8",
"E": "0"
} | subtract(subtract(add(add(63, 18), 37), const_100), const_10) | add(n0,n4)|add(n8,#0)|subtract(#1,const_100)|subtract(#2,const_10) | 3,8 and 7 have a power cycle of 4 , i . e . the units digit in each case will repeat after every 4 th power . for eg : 3 ^ 1 = 3 , 3 ^ 2 = 9 , 3 ^ 3 = 27 , 3 ^ 4 = 81 , 3 ^ 5 = 243 all the powers given ( 1 ! + 2 ! + . . . . ) , are multiples of 4 . it is so because the last 2 digits of the total sum will be 00 , for each one of them , which make them divisible by 4 . thus , the given problem boils down to 3 ^ 4 + 8 ^ 4 + 7 ^ 4 = 1 + 6 + 1 = 8 thus , the units digit is 8 . answer : d | general |
math_qa__ONnpWNW2RKZ8PpvY | 6 students are equally divided into 3 groups , then , the 3 groups were assigned to 3 different topics . how many different arrangements w are possible ? Select the correct option.
A) 30 B) 60 C) 90 D) 180 E) 540 | <gadget id="calculator">factorial(6)</gadget>
<output>720</output>
<gadget id="calculator">6 - 2</gadget>
<output>4</output>
<gadget id="calculator">factorial(4)</gadget>
<output>24</output>
<gadget id="calculator">720 / 24</gadget>
<output>30</output>
<gadget id="calculator">30 / 2</gadget>
<output>15</output>
<gadget id="calculator">factorial(3)</gadget>
<output>6</output>
<gadget id="calculator">15 * 6</gadget>
<output>90</output>
<result>C</result> | C | 90 | 6 students are equally divided into 3 groups , then , the 3 groups were assigned to 3 different topics . how many different arrangements w are possible ? | {
"A": "30",
"B": "60",
"C": "90",
"D": "180",
"E": "540"
} | multiply(divide(divide(factorial(6), factorial(subtract(6, const_2))), const_2), factorial(3)) | factorial(n0)|factorial(n1)|subtract(n0,const_2)|factorial(#2)|divide(#0,#3)|divide(#4,const_2)|multiply(#5,#1) | 90 is the number of ways you can assign 3 teams formed out of 12 people to 3 different tasks . but now you can order the 3 tasks in 3 ! ways . t 1 t 2 t 3 or t 2 t 1 t 3 . . . . etc etc . i was confused between 90 and 540 but since question used the wordarrangementsdecided to go with complete arrangements w including the order of tasks . could you explain the highlighted step . . . i ' m getting 90 = 15 * 3 ! suppose the students are numbered 12 , 34 , 56 and tasks are x , y and z one of the 15 possible ways of forming teams is 12 , 34 , 56 . these teams can be assigned to 3 tasks in 3 ! = 6 ways x - - y - - z 12 - - 34 - - 56 12 - - 56 - - 34 34 - - 12 - - 56 34 - - 56 - - 12 56 - - 12 - - 34 56 - - 34 - - 12 so the answer should be 15 * 6 = 90 but now you can fruther decide which task you want to perform first x y or z . . = c | probability |
math_qa__is9rucTYO8JVZgek | Find the value of (√1.5)/(√0.81) + (√1.44)/(√0.49) is
Choose the correct choice from the following answers.
A) 195 / 63 B) 145 / 63 C) 155 / 63 D) 125 / 63 E) 3.075 | <gadget id="calculator">1.5 ** (1/2)</gadget>
<output>1.224745</output>
<gadget id="calculator">0.81 ** (1/2)</gadget>
<output>0.9</output>
<gadget id="calculator">1.224745 / 0.9</gadget>
<output>1.360828</output>
<gadget id="calculator">1.44 ** (1/2)</gadget>
<output>1.2</output>
<gadget id="calculator">0.49 ** (1/2)</gadget>
<output>0.7</output>
<gadget id="calculator">1.2 / 0.7</gadget>
<output>1.714286</output>
<gadget id="calculator">1.360828 + 1.714286</gadget>
<output>3.075114</output>
<result>E</result> | E | 3.075 | Find the value of (√1.5)/(√0.81) + (√1.44)/(√0.49) is | {
"A": "195 / 63",
"B": "145 / 63",
"C": "155 / 63",
"D": "125 / 63",
"E": "3.075"
} | add(divide(sqrt(1.5), sqrt(0.81)), divide(sqrt(1.44), sqrt(0.49))) | sqrt(n0)|sqrt(n1)|sqrt(n2)|sqrt(n3)|divide(#0,#1)|divide(#2,#3)|add(#4,#5)| | "( √ 1.5 ) / ( √ 0.81 ) + ( √ 1.44 ) / ( √ 0.49 ) = > 3.075 answer is e ." | general |
math_qa__nVCWY6KPMiEdDtpy | A completes a piece of work in 3/4 of the time in B does, B takes 4/5 of the time in C does. They got a profit of Rs. 40000 how much B gets? Choose the correct choice from the following answers:
A) 12765
B) 121227
C) 26887
D) 19977
E) 26992 | <gadget id="calculator">1_000 + 1_000</gadget>
<output>2_000</output>
<gadget id="calculator">40_000 / 4</gadget>
<output>10_000</output>
<gadget id="calculator">2_000 + 10_000</gadget>
<output>12_000</output>
<gadget id="calculator">60 * 10</gadget>
<output>600</output>
<gadget id="calculator">600 + 100</gadget>
<output>700</output>
<gadget id="calculator">60 + 5</gadget>
<output>65</output>
<gadget id="calculator">700 + 65</gadget>
<output>765</output>
<gadget id="calculator">12_000 + 765</gadget>
<output>12_765</output>
<result>A</result> | A | 12,765 | A completes a piece of work in 3/4 of the time in B does, B takes 4/5 of the time in C does. They got a profit of Rs. 40000 how much B gets? | {
"A": "12765",
"B": "121227",
"C": "26887",
"D": "19977",
"E": "26992"
} | add(add(add(const_1000, const_1000), divide(40000, 4)), add(add(multiply(const_60, const_10), const_100), add(const_60, 5))) | add(const_1000,const_1000)|add(n3,const_60)|divide(n4,n1)|multiply(const_10,const_60)|add(#0,#2)|add(#3,const_100)|add(#5,#1)|add(#4,#6) | assume c takes 20 days . now b takes 4 / 5 ( 20 ) = 16 days . a takes 3 / 4 ( 16 ) = 12 now their efficiencies ratio = 1 / 20 : 1 / 16 : 1 / 12 = 12 : 15 : 20 b ' s share in the profit of rs . 40000 = 15 / 47 ( 40000 ) = rs . 12765 answer : a | general |
math_qa__KTCrKXuP5BWEOJrr | Right triangle PQR is to be constructed in the xy-plane so that the right angle is at P and PR is parallel to the x-axis. The x and Y coordinates of P,Q and R are to be integers that satisfy the inequalitites -4≤ X≤ 5 and 6≤ y≤ 16. How many different triangles with these properties could be constructed?
Choose the correct choice from the following answers.
A) 110 B) 1100 C) 9900 D) 10000 E) 12100 | <gadget id="calculator">10 - 1</gadget>
<output>9</output>
<gadget id="calculator">6 + 4</gadget>
<output>10</output>
<gadget id="calculator">16 - 5</gadget>
<output>11</output>
<gadget id="calculator">10 * 11</gadget>
<output>110</output>
<gadget id="calculator">9 * 110</gadget>
<output>990</output>
<gadget id="calculator">990 * 10</gadget>
<output>9_900</output>
<result>C</result> | C | 9,900 | Right triangle PQR is to be constructed in the xy-plane so that the right angle is at P and PR is parallel to the x-axis. The x and Y coordinates of P,Q and R are to be integers that satisfy the inequalitites -4≤ X≤ 5 and 6≤ y≤ 16. How many different triangles with these properties could be constructed? | {
"A": "110",
"B": "1100",
"C": "9900",
"D": "10000",
"E": "12100"
} | multiply(multiply(subtract(const_10, const_1), multiply(add(6, 4), subtract(16, 5))), const_10) | add(n0,n2)|subtract(n3,n1)|subtract(const_10,const_1)|multiply(#0,#1)|multiply(#3,#2)|multiply(#4,const_10) | total values for x = 10 ; y = 11 x 1 , y 1 = 10 * 11 . . . . . . . . . . . . . . . . . . . . . . . coordinates of 1 st pnt x 2 , y 2 = 9 * 1 ( y 2 = y 1 ) . . . . . . . . . . . . . . . coordinates of 2 nd pnt y coordinates will be same as that of 1 st pnt bcoz it is parallel to x axis x 3 , y 3 = 1 * 10 ( x 2 = x 3 ) . . . . . . . . . . coordinates of 3 rd pt . x coordinates will be same as that of 2 nd point bcoz to make a right angle it has to be parallel to y axis tot ways = 10 * 11 * 9 * 1 * 1 * 10 = 9900 ans : c | geometry |
math_qa__IOxXsDscSchNfV3B | When a student Joe, weighing 40 kg, joins a group of students whose average weight is 30 kg, the average weight goes up by 1 kg. Subsequently, if two students, excluding Joe, leave the group the average weight comes back to 30 kg. What is the difference between the average weight of the two students who left and the weight of Joe? Choose one.
A) 5 kg
B) 11 kg
C) 30 kg
D) 36.5 kg
E) 71 kg | <gadget id="calculator">30 + 1</gadget>
<output>31</output>
<gadget id="calculator">40 - 31</gadget>
<output>9</output>
<gadget id="calculator">30 * 9</gadget>
<output>270</output>
<gadget id="calculator">270 + 40</gadget>
<output>310</output>
<gadget id="calculator">9 - 1</gadget>
<output>8</output>
<gadget id="calculator">8 * 30</gadget>
<output>240</output>
<gadget id="calculator">310 - 240</gadget>
<output>70</output>
<gadget id="calculator">70 / 2</gadget>
<output>35</output>
<gadget id="calculator">40 - 35</gadget>
<output>5</output>
<result>A</result> | A | 5 | When a student Joe, weighing 40 kg, joins a group of students whose average weight is 30 kg, the average weight goes up by 1 kg. Subsequently, if two students, excluding Joe, leave the group the average weight comes back to 30 kg. What is the difference between the average weight of the two students who left and the weight of Joe? | {
"A": "5 kg",
"B": "11 kg",
"C": "30 kg",
"D": "36.5 kg",
"E": "71 kg"
} | subtract(40, divide(subtract(add(multiply(30, subtract(40, add(30, 1))), 40), multiply(subtract(subtract(40, add(30, 1)), 1), 30)), const_2)) | add(n1,n2)|subtract(n0,#0)|multiply(n1,#1)|subtract(#1,n2)|add(n0,#2)|multiply(n1,#3)|subtract(#4,#5)|divide(#6,const_2)|subtract(n0,#7)| | "after two persons leave the group the average remains the same . that means the weight of the two persons = 40 + 30 = 70 so , the average the two persons = 35 that gives the answer 40 - 35 = 5 answer a" | general |
math_qa__nqY0xgBU2v7HMRun | A certain clock marks every hour by striking a number of times equal to the hour,and the time required for a stroke is exactly equal to the time interval between strokes. At 6:00 the time lapse between the beginning of the first stroke and the end of the last stroke is 33 seconds. at 12:00 ,how many seconds elapse between the beginning of the first stroke and the end of the last stroke? Choose the correct choice from the following answers
A) a . 72 B) b . 50 C) c . 48 D) d . 69 E) e . 44 | <gadget id="calculator">1 + 4</gadget>
<output>5</output>
<gadget id="calculator">6 + 5</gadget>
<output>11</output>
<gadget id="calculator">33 / 11</gadget>
<output>3</output>
<gadget id="calculator">12 + 11</gadget>
<output>23</output>
<gadget id="calculator">3 * 23</gadget>
<output>69</output>
<result>D</result> | D | 69 | A certain clock marks every hour by striking a number of times equal to the hour,and the time required for a stroke is exactly equal to the time interval between strokes. At 6:00 the time lapse between the beginning of the first stroke and the end of the last stroke is 33 seconds. at 12:00 ,how many seconds elapse between the beginning of the first stroke and the end of the last stroke? | {
"A": "a . 72",
"B": "b . 50",
"C": "c . 48",
"D": "d . 69",
"E": "e . 44"
} | multiply(divide(33, add(6, add(const_1, const_4))), add(12, add(6, add(const_1, const_4)))) | add(const_1,const_4)|add(n0,#0)|add(n3,#1)|divide(n2,#1)|multiply(#2,#3)| | "at 6 : 00 it ' ll chime 6 times . if we assume that the time taken to chime is x , then time between chimes is also x . so you have 6 chimes , which is 6 x and 5 time intervals between chimes . this means that 11 x = 33 seconds . thus x = 3 seconds . by a similar logic , at 12 : 00 , there are 12 chimes and 11 intervals so the total time is ( 12 + 11 ) x = 23 x = 69 seconds . answer d" | general |
math_qa__LnjSeDNUTH9915Ww | A goods train runs at a speed of 72 kmph and crosses a 240 m long platform in 26 seconds.What is the length of the goods train? Choose the correct option
A) 230 m B) 240 m C) 260 m D) 270 m E) 280 m | <gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">72 * (5/18)</gadget>
<output>20</output>
<gadget id="calculator">20 * 26</gadget>
<output>520</output>
<gadget id="calculator">520 - 240</gadget>
<output>280</output>
<result>E</result> | E | 280 | A goods train runs at a speed of 72 kmph and crosses a 240 m long platform in 26 seconds.What is the length of the goods train? | {
"A": "230 m",
"B": "240 m",
"C": "260 m",
"D": "270 m",
"E": "280 m"
} | subtract(multiply(multiply(72, const_0_2778), 26), 240) | multiply(n0,const_0_2778)|multiply(n2,#0)|subtract(#1,n1)| | "s = 240 + x / t 72 * 5 / 18 = 240 + x / 26 x = 280 answer : e" | physics |
math_qa__o1lENIfHGFcraNOW | A certain manufacturer of cake, muffin, and bread mixes has 100 buyers, of whom 50 purchases cake mix, 40 purchase muffin mix, and 15 purchase both cake mix and muffin mix. If a buyer is to be selected at random from the 100 buyers, what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix? Pick one.
A) 1 / 10 B) 3 / 10 C) 1 / 4 D) 7 / 10 E) 9 / 10 | <gadget id="calculator">50 + 40</gadget>
<output>90</output>
<gadget id="calculator">90 - 15</gadget>
<output>75</output>
<gadget id="calculator">100 - 75</gadget>
<output>25</output>
<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<result>C</result> | C | 0.25 | A certain manufacturer of cake, muffin, and bread mixes has 100 buyers, of whom 50 purchases cake mix, 40 purchase muffin mix, and 15 purchase both cake mix and muffin mix. If a buyer is to be selected at random from the 100 buyers, what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix? | {
"A": "1 / 10",
"B": "3 / 10",
"C": "1 / 4",
"D": "7 / 10",
"E": "9 / 10"
} | divide(subtract(100, subtract(add(50, 40), 15)), 100) | add(n1,n2)|subtract(#0,n3)|subtract(n0,#1)|divide(#2,n0)| | "c + m + b - cm - mb - cb - 2 cmb = 100 c - cake buyers , m - muffin and b - bread buyers . cm , mb , cb and cmb are intersecting regions . the question asks for people who have bought only bread mixes = b - cb - mb - 2 cmb has to be found out . 50 + 40 + b - cb - mb - 15 - 2 cmb = 100 b - cb - mb - 2 cmb = 25 hence the probability = 25 / 100 = 1 / 4 . c" | other |
math_qa__I6ZoHdzZDkdELa9z | When the price of an article was reduced by 40% its sale increased by 80%. What was the net effect on the sale? Pick.
A) 8 % increase B) 4 % decrease C) 6 % increase D) 66 % increase E) 66 % decrease | <gadget id="calculator">80 + 100</gadget>
<output>180</output>
<gadget id="calculator">100 - 40</gadget>
<output>60</output>
<gadget id="calculator">180 * 60</gadget>
<output>10_800</output>
<gadget id="calculator">10_800 / 100</gadget>
<output>108</output>
<gadget id="calculator">108 - 100</gadget>
<output>8</output>
<result>A</result> | A | 8 | When the price of an article was reduced by 40% its sale increased by 80%. What was the net effect on the sale? | {
"A": "8 % increase",
"B": "4 % decrease",
"C": "6 % increase",
"D": "66 % increase",
"E": "66 % decrease"
} | subtract(divide(multiply(add(80, const_100), subtract(const_100, 40)), const_100), const_100) | add(n1,const_100)|subtract(const_100,n0)|multiply(#0,#1)|divide(#2,const_100)|subtract(#3,const_100)| | "if n items are sold for $ p each , revenue is $ np . if we reduce the price by 40 % , the new price is 0.6 p . if we increase the number sold by 80 % , the new number sold is 1.8 n . so the new revenue is ( 0.6 p ) ( 1.8 n ) = 1.08 np , which is 1.08 times the old revenue , so is 8 % greater . answer : a" | gain |
math_qa__Yz4Csri6QR1qOIGP | The ratio of petrol and kerosene in the container is 3:2 when 10 liters of the mixture is taken out and is replaced by the kerosene, the ratio become 2:3. Then total quantity of the mixture in the container is:
Choices
A) 33 B) 30 C) 38 D) 37 E) 27 | <gadget id="calculator">2 / 3</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">10 / (1/3)</gadget>
<output>30</output>
<result>B</result> | B | 30 | The ratio of petrol and kerosene in the container is 3:2 when 10 liters of the mixture is taken out and is replaced by the kerosene, the ratio become 2:3. Then total quantity of the mixture in the container is: | {
"A": "33",
"B": "30",
"C": "38",
"D": "37",
"E": "27"
} | divide(10, subtract(const_1, divide(2, 3))) | divide(n1,n0)|subtract(const_1,#0)|divide(n2,#1) | explanation : pool : kerosene 3 : 2 ( initially ) 2 : 3 ( after replacement ) \ frac { remaining \ : ( or \ : left ) \ : quantity } { initial \ : quantity } = \ left ( 1 - \ frac { replaced \ : quantity } { total \ : quantity } \ right ) ( for petrol ) \ frac { 2 } { 3 } = \ left ( 1 - \ frac { 10 } { k } \ right ) \ rightarrow \ frac { 1 } { 3 } = \ frac { 10 } { k } \ rightarrow k = 30 l therefore the total quantity of the mixture in the container is 30 liters . answer : b ) 30 | general |
math_qa__FPaTPXOcNxQI9RHQ | ABCD is a square. E,F,G,H is the midpoint of the sides of square. J and K is the midpoint of the sides HG and FG . L is a point on sides EF such that LF= 1/3 EF. Find the ratio of area of triangle JKL to the area of square ABCD.
Choose the correct answer:
A) 5 : 46
B) 5 : 44
C) 4 : 48
D) 5 : 48
E) 5 : 4 | <gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(1/2) * (1/3)</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(1/2) * (1/2)</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/6) + (1/4)</gadget>
<output>5/12 = around 0.416667</output>
<gadget id="calculator">((1/2) * (5/12)) / 2</gadget>
<output>5/48 = around 0.104167</output>
<result>D</result> | D | 0.104167 | ABCD is a square. E,F,G,H is the midpoint of the sides of square. J and K is the midpoint of the sides HG and FG . L is a point on sides EF such that LF= 1/3 EF. Find the ratio of area of triangle JKL to the area of square ABCD. | {
"A": "5 : 46",
"B": "5 : 44",
"C": "4 : 48",
"D": "5 : 48",
"E": "5 : 4"
} | triangle_area(divide(const_1, const_2), add(multiply(divide(const_1, const_2), divide(1, 3)), multiply(divide(const_1, const_2), divide(const_1, const_2)))) | divide(const_1,const_2)|divide(n0,n1)|multiply(#0,#1)|multiply(#0,#0)|add(#2,#3)|triangle_area(#4,#0) | ratio = 5 : 48 answer : d | geometry |
math_qa__4BT1W1a4ksbq83o7 | A part-time employee whose hourly wage was decreased by 20 percent decided to increase the number of hours worked per week so that the employee's total income did not change. By what percent Q should the number of hours worked be increased?
Choices.
A) 12.5 % B) 20 % C) 25 % D) 50 % E) 100 % | <gadget id="calculator">10 * 4</gadget>
<output>40</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">(4/5) * 10</gadget>
<output>8</output>
<gadget id="calculator">40 / 8</gadget>
<output>5</output>
<gadget id="calculator">5 - 4</gadget>
<output>1</output>
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 100</gadget>
<output>25</output>
<result>C</result> | C | 25 | A part-time employee whose hourly wage was decreased by 20 percent decided to increase the number of hours worked per week so that the employee's total income did not change. By what percent Q should the number of hours worked be increased? | {
"A": "12.5 %",
"B": "20 %",
"C": "25 %",
"D": "50 %",
"E": "100 %"
} | multiply(divide(subtract(divide(multiply(const_10, const_4), multiply(divide(subtract(const_100, 20), const_100), const_10)), const_4), const_4), const_100) | multiply(const_10,const_4)|subtract(const_100,n0)|divide(#1,const_100)|multiply(#2,const_10)|divide(#0,#3)|subtract(#4,const_4)|divide(#5,const_4)|multiply(#6,const_100)| | "correct answer : c solution : c . we can set up equations for income before and after the wage reduction . initially , the employee earns w wage and works h hours per week . after the reduction , the employee earns . 8 w wage and works x hours . by setting these equations equal to each other , we can determine the increase in hours worked : wh = . 8 wx ( divide both sides by . 8 w ) 1.25 h = x we know that the new number of hours worked will be q = 25 % greater than the original number . the answer is c ." | general |
math_qa__daop590xeKyImIxr | If the sum of a number and its square is 20, what is the number? Choose the correct choice from the following answers.
A) 15 B) 26 C) 28 D) 4 E) none of these | <gadget id="calculator">20 ** (1/2)</gadget>
<output>2*sqrt(5) = around 4.472136</output>
<gadget id="calculator">floor(2*sqrt(5))</gadget>
<output>4</output>
<result>D</result> | D | 4 | If the sum of a number and its square is 20, what is the number? | {
"A": "15",
"B": "26",
"C": "28",
"D": "4",
"E": "none of these"
} | floor(sqrt(20)) | sqrt(n0)|floor(#0)| | "let the number be x . then , x + x 2 = 20 ( x + 5 ) ( x - 4 ) = 0 x = 4 answer : d" | geometry |
math_qa__ZbzvG7XGxwWxwmGH | Roy is now 8 years older than Julia and half of that amount older than Kelly. If in 4 years, Roy will be twice as old as Julia, then in 4 years what would be Roy’s age multiplied by Kelly’s age?
Options.
A) 172 B) 180 C) 192 D) 200 E) 216 | <gadget id="calculator">8 - 4</gadget>
<output>4</output>
<gadget id="calculator">8 + 4</gadget>
<output>12</output>
<gadget id="calculator">12 + 4</gadget>
<output>16</output>
<gadget id="calculator">8 / 2</gadget>
<output>4</output>
<gadget id="calculator">12 - 4</gadget>
<output>8</output>
<gadget id="calculator">16 * 12</gadget>
<output>192</output>
<result>C</result> | C | 192 | Roy is now 8 years older than Julia and half of that amount older than Kelly. If in 4 years, Roy will be twice as old as Julia, then in 4 years what would be Roy’s age multiplied by Kelly’s age? | {
"A": "172",
"B": "180",
"C": "192",
"D": "200",
"E": "216"
} | multiply(add(add(8, subtract(8, 4)), 4), add(subtract(add(8, subtract(8, 4)), divide(8, const_2)), 4)) | divide(n0,const_2)|subtract(n0,n1)|add(n0,#1)|add(n1,#2)|subtract(#2,#0)|add(n1,#4)|multiply(#3,#5)| | "r = j + 8 = k + 4 r + 4 = 2 ( j + 4 ) ( j + 8 ) + 4 = 2 j + 8 j = 4 r = 12 k = 8 in 4 years ( r + 4 ) ( k + 4 ) = 16 * 12 = 192 the answer is c ." | general |
math_qa__S7tZaGsgLzeAIWRZ | An investor deposited $5,000 to open a new savings account that earned 4 percent annual interest, compounded quarterly. If there were no other transactions in the account, what was the amount of money in the account 6 months after the account was opened?
Choose the correct choice from the following choices: A) $ 5050.50 B) $ 5100.50 C) $ 5200.50 D) $ 5300.50 E) $ 5400.50 | <gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">5 * 100</gadget>
<output>500</output>
<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">500 * 10</gadget>
<output>5_000</output>
<gadget id="calculator">4 / 4</gadget>
<output>1</output>
<gadget id="calculator">1 / 100</gadget>
<output>1/100 = around 0.01</output>
<gadget id="calculator">(1/100) + 1</gadget>
<output>101/100 = around 1.01</output>
<gadget id="calculator">(101/100) ** 2</gadget>
<output>10_201/10_000 = around 1.0201</output>
<gadget id="calculator">5_000 * (10_201/10_000)</gadget>
<output>10_201/2 = around 5_100.5</output>
<result>B</result> | B | 5,100.5 | An investor deposited $5,000 to open a new savings account that earned 4 percent annual interest, compounded quarterly. If there were no other transactions in the account, what was the amount of money in the account 6 months after the account was opened? | {
"A": "$ 5050.50",
"B": "$ 5100.50",
"C": "$ 5200.50",
"D": "$ 5300.50",
"E": "$ 5400.50"
} | multiply(multiply(multiply(add(const_2, const_3), const_100), multiply(add(const_2, const_3), const_2)), power(add(divide(divide(4, const_4), const_100), const_1), const_2)) | add(const_2,const_3)|divide(n1,const_4)|divide(#1,const_100)|multiply(#0,const_100)|multiply(#0,const_2)|add(#2,const_1)|multiply(#3,#4)|power(#5,const_2)|multiply(#6,#7) | the amount in the account after 6 months is 1.01 * 1.01 ( $ 5,000 ) = $ 5100.50 the answer is b . | gain |
math_qa__YpIsIyzGH5pYNpjE | In a group of people, if 30 people were made to stand in each column, 16 columns could be formed. If 48 people were made to stand in a column, how many columns could be formed?
Options
A) 10 B) 12 C) 14 D) 16 E) 18 | <gadget id="calculator">48 / 16</gadget>
<output>3</output>
<gadget id="calculator">30 / 3</gadget>
<output>10</output>
<result>A</result> | A | 10 | In a group of people, if 30 people were made to stand in each column, 16 columns could be formed. If 48 people were made to stand in a column, how many columns could be formed? | {
"A": "10",
"B": "12",
"C": "14",
"D": "16",
"E": "18"
} | divide(30, divide(48, 16)) | divide(n2,n1)|divide(n0,#0) | 16 * 30 = 48 * n n = 10 the answer is a . | other |
math_qa__CrTuX425rb6p1sCk | 18 buckets of water fill a tank when the capacity of each bucket is 60 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 5 litres? Choices:
A) 216
B) 200
C) 212
D) 220
E) 210 | <gadget id="calculator">60 * 18</gadget>
<output>1_080</output>
<gadget id="calculator">1_080 / 5</gadget>
<output>216</output>
<result>A</result> | A | 216 | 18 buckets of water fill a tank when the capacity of each bucket is 60 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 5 litres? | {
"A": "216",
"B": "200",
"C": "212",
"D": "220",
"E": "210"
} | divide(multiply(60, 18), 5) | multiply(n0,n1)|divide(#0,n2)| | "capacity of the tank = ( 18 ã — 60 ) litre number of buckets required of capacity of each bucket is 17 litre = 18 ã — 60 / 5 = 18 ã — 12 = 216 answer is a" | physics |
math_qa__xk1DQezC98OCEz35 | James took a 3-hour bike ride. In the second hour he traveled 36 miles, which was 20 percent farther than he traveled the first hour. If he traveled 25 percent farther in the third hour than he did in the second hour, how many miles did jose travel during the entire ride? Answers: A) 54.0 B) 54.9 C) 111.0 D) 157.0 E) 163.0 | <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">(4/5) * 36</gadget>
<output>144/5 = around 28.8</output>
<gadget id="calculator">(144/5) + 36</gadget>
<output>324/5 = around 64.8</output>
<gadget id="calculator">100 + 25</gadget>
<output>125</output>
<gadget id="calculator">125 / 100</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">(5/4) * 36</gadget>
<output>45</output>
<gadget id="calculator">(324/5) + 45</gadget>
<output>549/5 = around 109.8</output>
<result>C</result> | C | 111 | James took a 3-hour bike ride. In the second hour he traveled 36 miles, which was 20 percent farther than he traveled the first hour. If he traveled 25 percent farther in the third hour than he did in the second hour, how many miles did jose travel during the entire ride? | {
"A": "54.0",
"B": "54.9",
"C": "111.0",
"D": "157.0",
"E": "163.0"
} | add(add(multiply(divide(subtract(const_100, 20), const_100), 36), 36), multiply(divide(add(const_100, 25), const_100), 36)) | add(n3,const_100)|subtract(const_100,n2)|divide(#1,const_100)|divide(#0,const_100)|multiply(n1,#2)|multiply(n1,#3)|add(n1,#4)|add(#6,#5)| | "let the distance travelled in the first hour be x . thus , 1.2 x = 36 , x = 30 . now , the distance travelled in the 3 rd hour = 36 + 1 / 4 â ˆ — 36 = 45 . 36 + 30 + 45 = 111 answer : c" | physics |
math_qa__pGm4xpWAB8JRGFgH | A large tanker can be filled by two pipes A and B in 30 and 15 hours respectively. How many hours will it take to fill the tanker from empty state if A and B fill it together? Choose the correct choice:
A) 8 hr
B) 10 hr
C) 12 hr
D) 9 hr
E) 5 hr | <gadget id="calculator">1 / 30</gadget>
<output>1/30 = around 0.033333</output>
<gadget id="calculator">1 / 15</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">(1/30) + (1/15)</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 / (1/10)</gadget>
<output>10</output>
<result>B</result> | B | 10 | A large tanker can be filled by two pipes A and B in 30 and 15 hours respectively. How many hours will it take to fill the tanker from empty state if A and B fill it together? | {
"A": "8 hr",
"B": "10 hr",
"C": "12 hr",
"D": "9 hr",
"E": "5 hr"
} | inverse(add(inverse(30), inverse(15))) | inverse(n0)|inverse(n1)|add(#0,#1)|inverse(#2) | part filled by a in 1 hr = 1 / 30 part filled by b in 1 hr = 1 / 15 part filled by a + b = 1 / 30 + 1 / 15 = 1 / 10 both the pipes can fill the tank in = 10 hours answer is b | physics |
math_qa__6r8UY8eUAjJCX2ll | A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 440 sq. feet, how many feet of fencing will be required? Pick
A) 34 B) 40 C) 64 D) 88 E) 92 | <gadget id="calculator">440 / 20</gadget>
<output>22</output>
<gadget id="calculator">22 * 2</gadget>
<output>44</output>
<gadget id="calculator">44 + 20</gadget>
<output>64</output>
<result>C</result> | C | 64 | A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 440 sq. feet, how many feet of fencing will be required? | {
"A": "34",
"B": "40",
"C": "64",
"D": "88",
"E": "92"
} | add(multiply(divide(440, 20), const_2), 20) | divide(n1,n0)|multiply(#0,const_2)|add(n0,#1)| | "given that length and area , so we can find the breadth . length x breadth = area 20 x breadth = 440 breadth = 22 feet area to be fenced = 2 b + l = 2 ( 22 ) + 20 = 64 feet answer : c" | geometry |
math_qa__TgCpGKnNyzaFPoNM | The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 3600 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units? Choose the correct choice: A) 240 B) 250 C) 260 D) 270 E) 280 | <gadget id="calculator">3_600 ** (1/2)</gadget>
<output>60</output>
<gadget id="calculator">10 / 2</gadget>
<output>5</output>
<gadget id="calculator">60 / 5</gadget>
<output>12</output>
<gadget id="calculator">2 * 12</gadget>
<output>24</output>
<gadget id="calculator">10 * 24</gadget>
<output>240</output>
<result>A</result> | A | 240 | The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 3600 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units? | {
"A": "240",
"B": "250",
"C": "260",
"D": "270",
"E": "280"
} | multiply(10, multiply(const_2, divide(sqrt(3600), divide(10, const_2)))) | divide(n1,const_2)|sqrt(n0)|divide(#1,#0)|multiply(#2,const_2)|multiply(n1,#3)| | "given that the area of the square = 3600 sq . units = > side of square = √ 3600 = 60 units the radius of the circle = side of the square = 60 units length of the rectangle = 2 / 5 * 60 = 24 units given that breadth = 10 units area of the rectangle = lb = 24 * 10 = 240 sq . units answer : option a" | geometry |
math_qa__wg133DhUEj25CP3q | If L is the least positive integer that is divisible by every integer from 1 to 9 inclusive, then L/2 is =
Choose the correct answer
A) 5040
B) 2520
C) 1890
D) 1260
E) 630 | <gadget id="calculator">2 + 1</gadget>
<output>3</output>
<gadget id="calculator">2 ** 3</gadget>
<output>8</output>
<gadget id="calculator">3 ** 2</gadget>
<output>9</output>
<gadget id="calculator">8 * 9</gadget>
<output>72</output>
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">5 + 2</gadget>
<output>7</output>
<gadget id="calculator">72 * 7</gadget>
<output>504</output>
<gadget id="calculator">504 * 5</gadget>
<output>2_520</output>
<gadget id="calculator">2_520 / 2</gadget>
<output>1_260</output>
<result>D</result> | D | 1,260 | If L is the least positive integer that is divisible by every integer from 1 to 9 inclusive, then L/2 is = | {
"A": "5040",
"B": "2520",
"C": "1890",
"D": "1260",
"E": "630"
} | divide(multiply(multiply(multiply(power(2, add(2, 1)), power(add(2, 1), 2)), add(add(add(2, 1), 2), 2)), add(add(2, 1), 2)), 2) | add(n0,n2)|add(n2,#0)|power(n2,#0)|power(#0,n2)|add(n2,#1)|multiply(#2,#3)|multiply(#4,#5)|multiply(#1,#6)|divide(#7,n2) | the integer should be divisible by : 2 , 3 , 4 , 5 , 6 , 7 , 8 and 9 , that is 2 , 3 , 2 ^ 2 , 5 , 2 * 3 , 7 , 2 ^ 3 and 3 ^ 2 . the least common multiple of these integers is the product of 7 , 5 , 3 ^ 2 and 2 ^ 3 . then , l / 2 is ( 7 * 5 * 3 ^ 2 * 2 ^ 3 ) / 2 = 7 * 5 * 9 * 4 = 1260 . answer : d . | general |
math_qa__JeLsSTKwAeqqbJbr | In a certain Parallelogram the degree measure of one angle exceeds that of the other by 50 what is the degree measure of the smaller angle? Pick:
A) 65
B) 80
C) 85
D) 90
E) 95 | <gadget id="calculator">3_600 / 10</gadget>
<output>360</output>
<gadget id="calculator">50 * 2</gadget>
<output>100</output>
<gadget id="calculator">360 - 100</gadget>
<output>260</output>
<gadget id="calculator">260 / 4</gadget>
<output>65</output>
<result>A</result> | A | 65 | In a certain Parallelogram the degree measure of one angle exceeds that of the other by 50 what is the degree measure of the smaller angle? | {
"A": "65",
"B": "80",
"C": "85",
"D": "90",
"E": "95"
} | divide(subtract(divide(const_3600, const_10), multiply(50, const_2)), const_4) | divide(const_3600,const_10)|multiply(n0,const_2)|subtract(#0,#1)|divide(#2,const_4)| | "in a parallelogram opposite angles are equal and the angles at each side are supplementary to each other ( supplementary angles are two angles that add up to 180 ° ) . given : x + ( x + 50 ) = 180 - - > x = 65 . answer : a ." | geometry |
math_qa__qSyFc7lDzBQDLekm | Jim is able to sell a hand-carved statue for $550 which was a 35% profit over his cost. How much did the statue originally cost him?
Choose the correct choice from the following answers:
A) $ 407.41 B) $ 412.40 C) $ 455.40 D) $ 474.90 E) $ 488.20 | <gadget id="calculator">35 / 100</gadget>
<output>7/20 = around 0.35</output>
<gadget id="calculator">(7/20) + 1</gadget>
<output>27/20 = around 1.35</output>
<gadget id="calculator">550 / (27/20)</gadget>
<output>11_000/27 = around 407.407407</output>
<result>A</result> | A | 407.41 | Jim is able to sell a hand-carved statue for $550 which was a 35% profit over his cost. How much did the statue originally cost him? | {
"A": "$ 407.41",
"B": "$ 412.40",
"C": "$ 455.40",
"D": "$ 474.90",
"E": "$ 488.20"
} | divide(550, add(divide(35, const_100), const_1)) | divide(n1,const_100)|add(#0,const_1)|divide(n0,#1)| | "550 = 1.35 * x x = 550 / 1.35 = 407.407407 . . . which rounds to $ 407.41 , which is ( a ) ." | gain |
math_qa__oGrH56YmAHu9QdxC | Pipe B that can fill a tank in an hour and pipe A that can fill the tank in half an hour are opened simultaneously when the tank is empty. Pipe A is shut 15 minutes before the tank overflows. When will the tank overflow? Choose the correct choice from the following choices:
A) 32 mins B) 35 mins C) 40 mins D) 30 mins E) 36 mins | <gadget id="calculator">1 * 60</gadget>
<output>60</output>
<gadget id="calculator">1 / 60</gadget>
<output>1/60 = around 0.016667</output>
<gadget id="calculator">15 * (1/60)</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 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) * 60</gadget>
<output>30</output>
<gadget id="calculator">1 / 30</gadget>
<output>1/30 = around 0.033333</output>
<gadget id="calculator">(1/30) + (1/60)</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(3/4) / (1/20)</gadget>
<output>15</output>
<gadget id="calculator">15 + 15</gadget>
<output>30</output>
<result>D</result> | D | 30 | Pipe B that can fill a tank in an hour and pipe A that can fill the tank in half an hour are opened simultaneously when the tank is empty. Pipe A is shut 15 minutes before the tank overflows. When will the tank overflow? | {
"A": "32 mins",
"B": "35 mins",
"C": "40 mins",
"D": "30 mins",
"E": "36 mins"
} | add(divide(subtract(const_1, multiply(15, divide(const_1, multiply(const_1, const_60)))), add(divide(const_1, multiply(divide(const_1, const_2), const_60)), divide(const_1, multiply(const_1, const_60)))), 15) | divide(const_1,const_2)|multiply(const_1,const_60)|divide(const_1,#1)|multiply(#0,const_60)|divide(const_1,#3)|multiply(n0,#2)|add(#4,#2)|subtract(const_1,#5)|divide(#7,#6)|add(n0,#8) | the last 15 minutes only pipe b was open . since it needs 1 hour to fill the tank , then in 15 minutes it fills 1 / 4 th of the tank , thus 3 / 4 of the tank is filled with both pipes open . the combined rate of two pipes is 1 + 2 = 3 tanks / hour , therefore to fill 3 / 4 th of the tank they need ( time ) = ( work ) / ( rate ) = ( 3 / 4 ) / 3 = 1 / 4 hours = 15 minutes . total time = 15 + 15 = 30 minutes . answer : d | physics |
math_qa__o719WO6Z39qFexJd | Working together, Tim and Tom can type 12 pages in one hour. If they would be able to type 15 pages in one hour if Tom increases his typing speed by 30%, what is the ratio of Tom's normal typing speed to that of Tim?
Choose the correct choice from the following options:
A) 1 / 5 B) 5 / 1 C) 4 / 1 D) 1 / 4 E) 1 / 3 | <gadget id="calculator">15 - 12</gadget>
<output>3</output>
<gadget id="calculator">100 * 1</gadget>
<output>100</output>
<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">3 / (3/10)</gadget>
<output>10</output>
<gadget id="calculator">12 - 10</gadget>
<output>2</output>
<gadget id="calculator">10 / 2</gadget>
<output>5</output>
<result>B</result> | B | 5 | Working together, Tim and Tom can type 12 pages in one hour. If they would be able to type 15 pages in one hour if Tom increases his typing speed by 30%, what is the ratio of Tom's normal typing speed to that of Tim? | {
"A": "1 / 5",
"B": "5 / 1",
"C": "4 / 1",
"D": "1 / 4",
"E": "1 / 3"
} | divide(divide(subtract(15, 12), divide(30, multiply(const_100, const_1))), subtract(12, divide(subtract(15, 12), divide(30, multiply(const_100, const_1))))) | multiply(const_1,const_100)|subtract(n1,n0)|divide(n2,#0)|divide(#1,#2)|subtract(n0,#3)|divide(#3,#4) | lets say tim types x pages an hour and tom types y pages an hour . we know that x + y = 12 tom increase speed by 30 % means he will type 1.3 y pages an hour . so we get x + 1.3 y = 15 we need to know the ratio of tom ' s speed to tim ' s speed . this is going to be proportional to the number of pages each can type in an hour , hence ( y / x ) . subtracting both : 0.3 y = 3 so y = 10 . . . so x = 2 ( y / x ) = 10 / 2 = 5 / 1 answer is ( b ) | physics |
math_qa__OGu0e5KRIfYxWEKq | The interest on a certain deposit at 5% per annum is Rs. 101.20 in one year. How much will the additional interest in one year be on the same deposit at 6% per annum? Pick
A) rs . 20.8
B) rs . 19.74
C) rs . 20.24
D) rs . 19.5
E) rs . 19.00 | <gadget id="calculator">100 * 101.2</gadget>
<output>10_120</output>
<gadget id="calculator">10_120 / 5</gadget>
<output>2_024</output>
<gadget id="calculator">2_024 * 6</gadget>
<output>12_144</output>
<gadget id="calculator">12_144 / 100</gadget>
<output>3_036/25 = around 121.44</output>
<gadget id="calculator">(3_036/25) - 101.2</gadget>
<output>20.24</output>
<result>C</result> | C | 20.24 | The interest on a certain deposit at 5% per annum is Rs. 101.20 in one year. How much will the additional interest in one year be on the same deposit at 6% per annum? | {
"A": "rs . 20.8",
"B": "rs . 19.74",
"C": "rs . 20.24",
"D": "rs . 19.5",
"E": "rs . 19.00"
} | subtract(divide(multiply(divide(multiply(const_100, 101.2), 5), 6), const_100), 101.2) | multiply(n1,const_100)|divide(#0,n0)|multiply(n2,#1)|divide(#2,const_100)|subtract(#3,n1) | explanation : principal , p = 100 × si / rt = 100 × 101.20 / 5 × 1 = 20 × 101.20 = rs . 2024 simple interest for rs . 2024 at 6 % per annum for 1 year , si = 2024 × 6 × 1100 = 121.44 additional interest = rs . 121.44 - rs . 101.20 = rs . 20.24 answer : option c | gain |
math_qa__ngkXzueFIiXhFWWg | In an election, candidate A got 65% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favor of candidate. Choose the most appropriate option: A) 330000 B) 309400 C) 347000 D) 356000 E) 357000 | <gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">1 - (3/20)</gadget>
<output>17/20 = around 0.85</output>
<gadget id="calculator">560_000 * (17/20)</gadget>
<output>476_000</output>
<gadget id="calculator">65 / 100</gadget>
<output>13/20 = around 0.65</output>
<gadget id="calculator">476_000 * (13/20)</gadget>
<output>309_400</output>
<result>B</result> | B | 309,400 | In an election, candidate A got 65% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favor of candidate. | {
"A": "330000",
"B": "309400",
"C": "347000",
"D": "356000",
"E": "357000"
} | multiply(multiply(560000, subtract(const_1, divide(15, const_100))), divide(65, const_100)) | divide(n0,const_100)|divide(n1,const_100)|subtract(const_1,#1)|multiply(n2,#2)|multiply(#0,#3)| | "total number of invalid votes = 15 % of 560000 = 15 / 100 × 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 – 84000 = 476000 percentage of votes polled in favour of candidate a = 65 % therefore , the number of valid votes polled in favour of candidate a = 65 % of 476000 = 65 / 100 × 476000 = 30940000 / 100 = 309400 b )" | gain |
math_qa__DWSRQ8H8p5oMP8nR | The profit obtained by selling an article for Rs. 86 is the same as the loss obtained by selling it for Rs. 42. What is the cost price of the article? Select the correct option: A) rs . 40 B) rs . 50 C) rs . 49 D) rs . 59 E) rs . 64 | <gadget id="calculator">86 + 42</gadget>
<output>128</output>
<gadget id="calculator">128 / 2</gadget>
<output>64</output>
<result>E</result> | E | 64 | The profit obtained by selling an article for Rs. 86 is the same as the loss obtained by selling it for Rs. 42. What is the cost price of the article? | {
"A": "rs . 40",
"B": "rs . 50",
"C": "rs . 49",
"D": "rs . 59",
"E": "rs . 64"
} | divide(add(86, 42), const_2) | add(n0,n1)|divide(#0,const_2)| | "s . p 1 - c . p = c . p – s . p 2 86 - c . p = c . p - 42 2 c . p = 86 + 42 ; c . p = 128 / 2 = 64 answer : e" | gain |
math_qa__KSmQI6qxAByQNJR2 | A squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 4 feet . How many feet does the squirrel travels if the post is 16 feet tall and 3 feet in circumference? Select: A) 12 B) 13 C) 14 D) 15 E) 16 | <gadget id="calculator">16 / 4</gadget>
<output>4</output>
<gadget id="calculator">4 * 3</gadget>
<output>12</output>
<result>A</result> | A | 12 | A squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 4 feet . How many feet does the squirrel travels if the post is 16 feet tall and 3 feet in circumference? | {
"A": "12",
"B": "13",
"C": "14",
"D": "15",
"E": "16"
} | multiply(divide(16, 4), 3) | divide(n1,n0)|multiply(n2,#0)| | "total circuit = 16 / 4 = 4 total feet squirrel travels = 4 * 3 = 12 feet answer : a" | geometry |
math_qa__exrzFRmx9svOHQhX | A batsman in his 12th innings makes a score of 70 and thereby increases his average by 3 runs. What is his average after the 12th innings if he had never been ‘not out’? Choose the correct choice from the following answers: A) 42 B) 37 C) 44 D) 45 E) 46 | <gadget id="calculator">12 * 3</gadget>
<output>36</output>
<gadget id="calculator">70 - 36</gadget>
<output>34</output>
<gadget id="calculator">34 + 3</gadget>
<output>37</output>
<result>B</result> | B | 37 | A batsman in his 12th innings makes a score of 70 and thereby increases his average by 3 runs. What is his average after the 12th innings if he had never been ‘not out’? | {
"A": "42",
"B": "37",
"C": "44",
"D": "45",
"E": "46"
} | add(subtract(70, multiply(12, 3)), 3) | multiply(n0,n2)|subtract(n1,#0)|add(n2,#1)| | "let ‘ x ’ be the average score after 12 th innings ⇒ 12 x = 11 × ( x – 3 ) + 70 ∴ x = 37 answer b" | general |
math_qa__p5zEBSIJEiHn0LvP | 50 persons like apple. 7 like orange and mango dislike apple. 10 like mango and apple and dislike orange. 4 like all. How many people like apple? Select the correct option.
A) 47 B) 46 C) 54 D) 57 E) 62 | <gadget id="calculator">50 - 4</gadget>
<output>46</output>
<gadget id="calculator">46 + 7</gadget>
<output>53</output>
<gadget id="calculator">10 - 7</gadget>
<output>3</output>
<gadget id="calculator">53 + 3</gadget>
<output>56</output>
<result>D</result> | D | 57 | 50 persons like apple. 7 like orange and mango dislike apple. 10 like mango and apple and dislike orange. 4 like all. How many people like apple? | {
"A": "47",
"B": "46",
"C": "54",
"D": "57",
"E": "62"
} | add(add(subtract(50, 4), 7), subtract(10, 7)) | subtract(n0,n3)|subtract(n2,n1)|add(n1,#0)|add(#2,#1)| | "orange + mango - apple = 7 mango + apple - orange = 10 apple = 50 orange + mango + apple = 4 50 + 10 + 4 - 7 = 57 like apple answer : d" | general |
math_qa__EyNaNHGcDn0DVdpc | 5^100 is divided by 18. Then what is the remainder? Choose the correct choice from the following options.
A) 10
B) 11
C) 13
D) 15
E) 16 | <gadget id="calculator">18 - 5</gadget>
<output>13</output>
<result>C</result> | C | 13 | 5^100 is divided by 18. Then what is the remainder? | {
"A": "10",
"B": "11",
"C": "13",
"D": "15",
"E": "16"
} | subtract(18, 5) | subtract(n2,n0)| | "here n = 18 = 2 × 32 ϕ ( 18 ) = 18 ( 1 − 12 ) ( 1 − 13 ) = 6 so 56 when divided by 18 , remainder is 1 . so we can write the given expression 5100 = ( 56 ) 16 × 54 = ( 1 ) 16 × 54 = 52 × 52 = 7 × 7 = 49 now 49 when divided by 18 , remainder is 13 . c" | general |
math_qa__cmhdr3VymvfUDWxC | A corporation that had $120 billion in profits for the year paid out $200 million in employee benefits. Approximately what percent of the profits were the employee benefits? (Note: 1 billion = 10^9) Select the correct option
A) 50 % B) 20 % C) 5 % D) 4 % E) 0.17 % | <gadget id="calculator">3 + 3</gadget>
<output>6</output>
<gadget id="calculator">10 ** 6</gadget>
<output>1_000_000</output>
<gadget id="calculator">200 * 1_000_000</gadget>
<output>200_000_000</output>
<gadget id="calculator">10 ** 9</gadget>
<output>1_000_000_000</output>
<gadget id="calculator">120 * 1_000_000_000</gadget>
<output>120_000_000_000</output>
<gadget id="calculator">200_000_000 / 120_000_000_000</gadget>
<output>1/600 = around 0.001667</output>
<gadget id="calculator">(1/600) * 100</gadget>
<output>1/6 = around 0.166667</output>
<result>E</result> | E | 0.17 | A corporation that had $120 billion in profits for the year paid out $200 million in employee benefits. Approximately what percent of the profits were the employee benefits? (Note: 1 billion = 10^9) | {
"A": "50 %",
"B": "20 %",
"C": "5 %",
"D": "4 %",
"E": "0.17 %"
} | multiply(divide(multiply(200, power(10, add(const_3, const_3))), multiply(120, power(10, 9))), const_100) | add(const_3,const_3)|power(n3,n4)|multiply(n0,#1)|power(n3,#0)|multiply(n1,#3)|divide(#4,#2)|multiply(#5,const_100)| | "required answer = [ employee benefit / profit ] * 100 = [ ( 200 million ) / ( 120 billion ) ] * 100 = [ ( 200 * 10 ^ 6 ) / ( 120 * 10 ^ 9 ) ] * 100 = ( 1.7 / 1000 ) * 100 = 0.17 % so answer is ( e )" | general |
math_qa__DCMpr75wX7SwxkUy | A, B and C have Rs.900 between them, A and C together have Rs.400 and B and C Rs.750. How much does C have?
Options.
A) 100 B) 150 C) 200 D) 250 E) 350 | <gadget id="calculator">400 + 750</gadget>
<output>1_150</output>
<gadget id="calculator">1_150 - 900</gadget>
<output>250</output>
<result>D</result> | D | 250 | A, B and C have Rs.900 between them, A and C together have Rs.400 and B and C Rs.750. How much does C have? | {
"A": "100",
"B": "150",
"C": "200",
"D": "250",
"E": "350"
} | subtract(add(400, 750), 900) | add(n1,n2)|subtract(#0,n0)| | "a + b + c = 900 a + c = 400 b + c = 750 - - - - - - - - - - - - - - a + b + 2 c = 1150 a + b + c = 900 - - - - - - - - - - - - - - - - c = 250 answer : d" | general |
math_qa__Cg3lCRHfI2TuRsMI | There are 84 supermarkets in the FGH chain. All of them are either in the US or Canada. If there are 10 more FGH supermarkets in the US than in Canada, how many FGH supermarkets are there in the US? Choose the correct choice from the following
A) 20 B) 31 C) 42 D) 47 E) 64 | <gadget id="calculator">84 + 10</gadget>
<output>94</output>
<gadget id="calculator">94 / 2</gadget>
<output>47</output>
<result>D</result> | D | 47 | There are 84 supermarkets in the FGH chain. All of them are either in the US or Canada. If there are 10 more FGH supermarkets in the US than in Canada, how many FGH supermarkets are there in the US? | {
"A": "20",
"B": "31",
"C": "42",
"D": "47",
"E": "64"
} | divide(add(84, 10), const_2) | add(n0,n1)|divide(#0,const_2)| | "x + ( x - 10 ) = 84 - - > x = 47 . answer : d ." | general |
math_qa__BRQMhiJTOQzJCqcB | A positive integer, which when added to 1000, gives a sum which is greater than when it is multiplied by 1000. This positive integer is Choose the correct answer: A) 1 B) 3 C) 5 D) 7 E) 9 | <gadget id="calculator">1_000 + 1</gadget>
<output>1_001</output>
<gadget id="calculator">1_000 * 1</gadget>
<output>1_000</output>
<gadget id="calculator">1_001 - 1_000</gadget>
<output>1</output>
<result>A</result> | A | 1 | A positive integer, which when added to 1000, gives a sum which is greater than when it is multiplied by 1000. This positive integer is | {
"A": "1",
"B": "3",
"C": "5",
"D": "7",
"E": "9"
} | subtract(add(1000, const_1), multiply(1000, const_1)) | add(n0,const_1)|multiply(n0,const_1)|subtract(#0,#1) | solution ( 1000 + n ) > ( 1000 n ) clearly , n = 1 . answer a | general |
math_qa__Dclk3eBPPJLHgFQG | The average of 11 numbers is 22. Average of the first 6 of them is 19 and that of the last 6 is 27. Find the 6th number? Choose the correct choice from the following
A) 12 B) 25 C) 34 D) 29 E) 27 | <gadget id="calculator">6 * 27</gadget>
<output>162</output>
<gadget id="calculator">11 * 22</gadget>
<output>242</output>
<gadget id="calculator">19 * 6</gadget>
<output>114</output>
<gadget id="calculator">242 - 114</gadget>
<output>128</output>
<gadget id="calculator">162 - 128</gadget>
<output>34</output>
<result>C</result> | C | 34 | The average of 11 numbers is 22. Average of the first 6 of them is 19 and that of the last 6 is 27. Find the 6th number? | {
"A": "12",
"B": "25",
"C": "34",
"D": "29",
"E": "27"
} | subtract(multiply(6, 27), subtract(multiply(11, 22), multiply(19, 6))) | multiply(n5,n6)|multiply(n0,n1)|multiply(n2,n3)|subtract(#1,#2)|subtract(#0,#3)| | sum of all the 11 numbers = 11 * 22 = 242 sum of the first 6 of them = 6 * 19 = 114 sum of the last 6 of them = 6 * 27 = 162 so , the 8 th number = 242 + 114 - 162 = 34 . answer : c | general |
math_qa__Wwl4GOjgziuvInBb | 10 men,working 6 hours a day can complete a work in 18 days.How many hours a day must 15 men work to complete the same work in 12 days ? Pick:
A) 6 B) 7 C) 8 D) 9 E) 10 | <gadget id="calculator">10 * 6</gadget>
<output>60</output>
<gadget id="calculator">60 * 18</gadget>
<output>1_080</output>
<gadget id="calculator">15 * 12</gadget>
<output>180</output>
<gadget id="calculator">1_080 / 180</gadget>
<output>6</output>
<result>A</result> | A | 6 | 10 men,working 6 hours a day can complete a work in 18 days.How many hours a day must 15 men work to complete the same work in 12 days ? | {
"A": "6",
"B": "7",
"C": "8",
"D": "9",
"E": "10"
} | divide(multiply(multiply(10, 6), 18), multiply(15, 12)) | multiply(n0,n1)|multiply(n3,n4)|multiply(n2,#0)|divide(#2,#1)| | "solution let the required number of hours per day be x . more men , less hours per day ( indirect proportion ) less days , more hours per day ( indirect proportion ) ∴ 15 × 12 × x = 10 × 18 × 6 ⇔ x = 10 x 18 x 6 / 15 x 12 = x = 6 . answer a" | physics |
math_qa__fttYiskwMMVjhku6 | 15 men can complete a piece of work in 30 days. In how many days can 10 men complete that piece of work? Pick one:
A) 45 B) 50 C) 34 D) 27 E) 11 | <gadget id="calculator">30 * 15</gadget>
<output>450</output>
<gadget id="calculator">450 / 10</gadget>
<output>45</output>
<result>A</result> | A | 45 | 15 men can complete a piece of work in 30 days. In how many days can 10 men complete that piece of work? | {
"A": "45",
"B": "50",
"C": "34",
"D": "27",
"E": "11"
} | divide(multiply(30, 15), 10) | multiply(n0,n1)|divide(#0,n2)| | "15 * 30 = 10 * x = > x = 45 days answer : a" | physics |
math_qa__uh0zojj2Xnlg4v7m | 6 bells commence tolling together and toll at intervals of 2 , 4 , 6 , 8 10 and 12 seconds respectively . in 30 minutes , how many times do they toll together ? Select.
A) 4
B) 10
C) 15
D) 16
E) none | <gadget id="calculator">30 * 60</gadget>
<output>1_800</output>
<gadget id="calculator">lcm(12, 10)</gadget>
<output>60</output>
<gadget id="calculator">lcm(60, 8)</gadget>
<output>120</output>
<gadget id="calculator">1_800 / 120</gadget>
<output>15</output>
<gadget id="calculator">15 + 1</gadget>
<output>16</output>
<result>D</result> | D | 16 | 6 bells commence tolling together and toll at intervals of 2 , 4 , 6 , 8 10 and 12 seconds respectively . in 30 minutes , how many times do they toll together ? | {
"A": "4",
"B": "10",
"C": "15",
"D": "16",
"E": "none"
} | add(divide(multiply(30, const_60), lcm(lcm(12, 10), 8)), const_1) | lcm(n5,n6)|multiply(n7,const_60)|lcm(n4,#0)|divide(#1,#2)|add(#3,const_1) | l . c . m . of 2 , 4 , 6 , 8 , 10 , 12 is 120 . so , the bells will toll together after every 120 seconds ( 2 minutes ) . in 30 minutes , they will toll together 30 / 2 + 1 = 16 times answer d | physics |
math_qa__VZ3dBwrdX3kCNDma | A sporting goods store sold 64 Frisbees in one week, some for $3 and the rest for $4 each. If receipts from Frisbee sales for the week totaled $200, what is the fewest number of $4 Frisbees that could have been sold? Answers.
A) 24 B) 8 C) 12 D) 4 E) 2 | <gadget id="calculator">64 * 3</gadget>
<output>192</output>
<gadget id="calculator">200 - 192</gadget>
<output>8</output>
<result>B</result> | B | 8 | A sporting goods store sold 64 Frisbees in one week, some for $3 and the rest for $4 each. If receipts from Frisbee sales for the week totaled $200, what is the fewest number of $4 Frisbees that could have been sold? | {
"A": "24",
"B": "8",
"C": "12",
"D": "4",
"E": "2"
} | subtract(200, multiply(64, 3)) | multiply(n0,n1)|subtract(n3,#0)| | "in this question however , because we are told that exactly 64 frisbees have been sold and revenue was exactly $ 204 , there is only one possible solution for the number of $ 3 and $ 4 frisbees sold . to solve , we have 2 equations and 2 unknowns let x = number of $ 3 frisbees sold let y = number of $ 4 frisbees sold x + y = 64 3 x + 4 y = 200 x = 64 - y 3 ( 64 - y ) + 4 y = 200 192 - 3 y + 4 y = 200 y = 8 answer : b" | general |
math_qa__OBOYTsPzQUoMf4fy | When average age of 24 members are 0, how many members greater than 0? Choose the correct option: A) 17 B) 23 C) 21 D) 24 E) 25 | <gadget id="calculator">24 - 1</gadget>
<output>23</output>
<result>B</result> | B | 23 | When average age of 24 members are 0, how many members greater than 0? | {
"A": "17",
"B": "23",
"C": "21",
"D": "24",
"E": "25"
} | subtract(24, const_1) | subtract(n0,const_1)| | "average of 24 numbers = 0 . sum of 24 numbers ( 0 x 24 ) = 0 . it is quite possible that 23 of these numbers may be positive and if their sum is a then 24 th number is ( - a ) answer is 23 ( b )" | general |
math_qa__v9uDUNKjZN2MHemz | A shopkeeper sold an article at $100 with 15% profit. Then find its cost price? Choose the correct choice from the following options.
A) $ 120 B) $ 100 C) $ 91 D) $ 87 E) $ 69 | <gadget id="calculator">100 + 15</gadget>
<output>115</output>
<gadget id="calculator">100 / 115</gadget>
<output>20/23 = around 0.869565</output>
<gadget id="calculator">100 * (20/23)</gadget>
<output>2_000/23 = around 86.956522</output>
<result>D</result> | D | 87 | A shopkeeper sold an article at $100 with 15% profit. Then find its cost price? | {
"A": "$ 120",
"B": "$ 100",
"C": "$ 91",
"D": "$ 87",
"E": "$ 69"
} | multiply(100, divide(100, add(100, 15))) | add(n1,n0)|divide(n0,#0)|multiply(n0,#1)| | "cost price = selling price * 100 / ( 100 + profit ) c . p . = 100 * 100 / 115 = $ 87 ( approximately ) answer is d" | gain |
math_qa__nFuWBsh2r7HDWbbN | Marcella has 26 pairs of shoes. If she loses 9 individual shoes, what is the greatest number of matching pairs she could have left? Pick one:
A) 21
B) 20
C) 19
D) 16
E) 15 | <gadget id="calculator">9 / 2</gadget>
<output>9/2 = around 4.5</output>
<gadget id="calculator">floor(9/2)</gadget>
<output>4</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">26 - 5</gadget>
<output>21</output>
<result>A</result> | A | 21 | Marcella has 26 pairs of shoes. If she loses 9 individual shoes, what is the greatest number of matching pairs she could have left? | {
"A": "21",
"B": "20",
"C": "19",
"D": "16",
"E": "15"
} | subtract(26, add(floor(divide(9, const_2)), const_1)) | divide(n1,const_2)|floor(#0)|add(#1,const_1)|subtract(n0,#2)| | "marcella has 26 pairs of shoes and loses 9 shoes . to minimize the loss of identical pairs of shoes we want marcella to lose as many identical pairs as possible . this would yield 4 identical pairs and 1 additional shoe ( destroying 5 pairs of shoes ) . the 26 pairs of shoes minus the 5 ' destroyed ' pairs yields 21 pairs that still fulfill the requirements . answer : a" | general |
math_qa__ZLQhnKWLSVlmwwHg | How many different ways can 2 students be seated in a row of 8 desks, so that there is always at least one empty desk between the students? Choose the correct answer
A) 50
B) 42
C) 24
D) 20
E) 12 | <gadget id="calculator">8 - 1</gadget>
<output>7</output>
<gadget id="calculator">factorial(7) / factorial(7 - 2)</gadget>
<output>42</output>
<result>B</result> | B | 42 | How many different ways can 2 students be seated in a row of 8 desks, so that there is always at least one empty desk between the students? | {
"A": "50",
"B": "42",
"C": "24",
"D": "20",
"E": "12"
} | permutation(subtract(8, const_1), 2) | subtract(n1,const_1)|permutation(#0,n0)| | "21 ways to seat the students : with two empty seats between 1 empty w / one student on the left most 1 empty . . . . right most two students can be interchanged 21 x 2 = 42 b" | probability |
math_qa__NDiH26Dk3kiwgHaa | 60 is increased by 50%. Find the final number. Pick.
A) 100 B) 110 C) 90 D) 30 E) 160 | <gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">60 * (1/2)</gadget>
<output>30</output>
<gadget id="calculator">60 + 30</gadget>
<output>90</output>
<result>C</result> | C | 90 | 60 is increased by 50%. Find the final number. | {
"A": "100",
"B": "110",
"C": "90",
"D": "30",
"E": "160"
} | add(60, multiply(60, divide(50, const_100))) | divide(n1,const_100)|multiply(n0,#0)|add(n0,#1)| | "final number = initial number + 50 % ( original number ) = 60 + 50 % ( 60 ) = 60 + 30 = 90 . answer c" | gain |
math_qa__HHJUIRc9ZhkDYO7w | A retailer bought a machine at a wholesale price of $90 and later on sold it after a 10% discount of the retail price. If the retailer made a profit equivalent to 20% of the whole price, what is the retail price q of the machine? Choose the most appropriate option.
A) 81 B) 100 C) 120 D) 135 E) 160 | <gadget id="calculator">90 * 20</gadget>
<output>1_800</output>
<gadget id="calculator">1_800 / 100</gadget>
<output>18</output>
<gadget id="calculator">90 + 18</gadget>
<output>108</output>
<gadget id="calculator">108 * 100</gadget>
<output>10_800</output>
<gadget id="calculator">3 * 3</gadget>
<output>9</output>
<gadget id="calculator">9 * 10</gadget>
<output>90</output>
<gadget id="calculator">10_800 / 90</gadget>
<output>120</output>
<result>C</result> | C | 120 | A retailer bought a machine at a wholesale price of $90 and later on sold it after a 10% discount of the retail price. If the retailer made a profit equivalent to 20% of the whole price, what is the retail price q of the machine? | {
"A": "81",
"B": "100",
"C": "120",
"D": "135",
"E": "160"
} | divide(multiply(add(90, divide(multiply(90, 20), const_100)), const_100), multiply(multiply(const_3, const_3), 10)) | multiply(n0,n2)|multiply(const_3,const_3)|divide(#0,const_100)|multiply(n1,#1)|add(n0,#2)|multiply(#4,const_100)|divide(#5,#3)| | "since the wholesale price was $ 90 and the profit was 20 % of the wholesale price ( [ . 2 ] [ 90 ] = $ 18 ) , the retail price would have to be above $ 108 , but not that much greater than that . let ' s start by testing answer c : $ 120 . . . . if . . . . . retail price q = $ 120 10 % discount off = $ 120 - ( . 1 ) ( 120 ) = 120 - 12 = 108 20 % profit on wholesale price = 90 + ( . 2 ) ( 90 ) = 90 + 18 = 108 these two numbers match , so this must be the answer ! final answer : [ reveal ] spoiler : c" | gain |
math_qa__Jr2L39bAGzqAPrRe | A large box contains 16 small boxes and each small box contains 25 chocolate bars. How many chocolate bars are in the large box? Pick
A) 250 B) 350 C) 450 D) 400 E) 650 | <gadget id="calculator">16 * 25</gadget>
<output>400</output>
<result>D</result> | D | 400 | A large box contains 16 small boxes and each small box contains 25 chocolate bars. How many chocolate bars are in the large box? | {
"A": "250",
"B": "350",
"C": "450",
"D": "400",
"E": "650"
} | multiply(16, 25) | multiply(n0,n1)| | "the number of chocolate bars is equal to 16 * 25 = 400 correct answer d" | general |
math_qa__hfiLgvhxCnaoURN8 | the sum of 4 consecutive even numbers is 52 , find the third number ?
Choose the correct choice from the following.
A) 14 B) 10 C) 12 D) 16 E) 20 | <gadget id="calculator">52 / 4</gadget>
<output>13</output>
<gadget id="calculator">13 + 1</gadget>
<output>14</output>
<result>A</result> | A | 14 | the sum of 4 consecutive even numbers is 52 , find the third number ? | {
"A": "14",
"B": "10",
"C": "12",
"D": "16",
"E": "20"
} | add(divide(52, 4), const_1) | divide(n1,n0)|add(#0,const_1) | let the first number be n let the second number be n + 2 let the third number be n + 4 let the third number be n + 6 n + n + 2 + n + 4 + n + 6 = 52 combine like terms : 4 n + 12 = 52 4 n + 12 = 52 4 n = 52 - 12 4 n = 40 n = 10 n + 2 = 12 n + 4 = 14 n + 6 = 16 the third number is 14 answer : a | physics |
math_qa__atOrZ985EU3XLacA | A rectangular parking space is marked out by painting three of its sides. If the length of the unpainted side is 99 feet, and the sum of the lengths of the painted sides is 37 feet, find out the area of the parking space in square feet? Choose the correct choice from the following
A) 126 sq . ft B) 64 sq . ft C) 100 sq . ft D) 120 sq . ft E) 140 sq . ft | <gadget id="calculator">3 * 3</gadget>
<output>9</output>
<gadget id="calculator">37 - 9</gadget>
<output>28</output>
<gadget id="calculator">28 / 2</gadget>
<output>14</output>
<gadget id="calculator">14 * 9</gadget>
<output>126</output>
<result>A</result> | A | 126 | A rectangular parking space is marked out by painting three of its sides. If the length of the unpainted side is 99 feet, and the sum of the lengths of the painted sides is 37 feet, find out the area of the parking space in square feet? | {
"A": "126 sq . ft",
"B": "64 sq . ft",
"C": "100 sq . ft",
"D": "120 sq . ft",
"E": "140 sq . ft"
} | multiply(divide(subtract(37, multiply(const_3, const_3)), const_2), multiply(const_3, const_3)) | multiply(const_3,const_3)|subtract(n1,#0)|divide(#1,const_2)|multiply(#2,#0) | explanation : solution 1 length = 9 feet breadth = 37 − 9 / 2 = 14 feet area = 9 × 14 = 126 square feet answer : option a | geometry |
math_qa__T5OMCdgvmqszAELX | The ratio between the presents of the A and B is 6:7. If B is 4 years older than A, what will be the ratio of the ages of A and B after 4 years? Choices: A) 1 : 2 B) 9 : 11 C) 7 : 8 D) 6 : 7 E) 3 : 4 | <gadget id="calculator">7 * 4</gadget>
<output>28</output>
<gadget id="calculator">28 - 4</gadget>
<output>24</output>
<gadget id="calculator">24 + 4</gadget>
<output>28</output>
<gadget id="calculator">28 + 4</gadget>
<output>32</output>
<gadget id="calculator">28 / 32</gadget>
<output>7/8 = around 0.875</output>
<result>C</result> | C | 0.875 | The ratio between the presents of the A and B is 6:7. If B is 4 years older than A, what will be the ratio of the ages of A and B after 4 years? | {
"A": "1 : 2",
"B": "9 : 11",
"C": "7 : 8",
"D": "6 : 7",
"E": "3 : 4"
} | divide(add(subtract(multiply(7, 4), 4), 4), add(multiply(7, 4), 4)) | multiply(n1,n2)|add(n2,#0)|subtract(#0,n2)|add(n2,#2)|divide(#3,#1) | let a and b ages will be 6 x and 7 x 7 x - 6 x = 4 x = 4 required ratio = 6 x + 4 : 7 x + 4 = 28 : 32 = 7 : 8 answer is c | other |
math_qa__WwDHhrZx8mU9eZtL | Joe drives 420 miles at 60 miles per hour, and then he drives the next 120 miles at 40 miles per hour. What is his average speed for the entire trip in miles per hour? Answers:
A) 42 B) 54 C) 50 D) 54 E) 56 | <gadget id="calculator">420 + 120</gadget>
<output>540</output>
<gadget id="calculator">420 / 60</gadget>
<output>7</output>
<gadget id="calculator">120 / 40</gadget>
<output>3</output>
<gadget id="calculator">7 + 3</gadget>
<output>10</output>
<gadget id="calculator">540 / 10</gadget>
<output>54</output>
<result>B</result> | B | 54 | Joe drives 420 miles at 60 miles per hour, and then he drives the next 120 miles at 40 miles per hour. What is his average speed for the entire trip in miles per hour? | {
"A": "42",
"B": "54",
"C": "50",
"D": "54",
"E": "56"
} | divide(add(420, 120), add(divide(420, 60), divide(120, 40))) | add(n0,n2)|divide(n0,n1)|divide(n2,n3)|add(#1,#2)|divide(#0,#3)| | "t 1 = 420 / 60 = 7 hours t 2 = 120 / 40 = 3 hours t = t 1 + t 2 = 10 hours avg speed = total distance / t = 540 / 10 = 54 mph = b" | physics |
math_qa__eOA3AHCiVmGLJzhD | In a caravan, in addition to 60 hens, there are 35 goats and 6 camels with some keepers. If the total number of feet be 193 more than the number of heads in the caravan, the number of keepers is Answers:
A) 5 B) 10 C) 15 D) 20 E) 25 | <gadget id="calculator">60 + 35</gadget>
<output>95</output>
<gadget id="calculator">95 + 6</gadget>
<output>101</output>
<gadget id="calculator">101 + 193</gadget>
<output>294</output>
<gadget id="calculator">2 * 60</gadget>
<output>120</output>
<gadget id="calculator">4 * 35</gadget>
<output>140</output>
<gadget id="calculator">120 + 140</gadget>
<output>260</output>
<gadget id="calculator">4 * 6</gadget>
<output>24</output>
<gadget id="calculator">260 + 24</gadget>
<output>284</output>
<gadget id="calculator">294 - 284</gadget>
<output>10</output>
<result>B</result> | B | 10 | In a caravan, in addition to 60 hens, there are 35 goats and 6 camels with some keepers. If the total number of feet be 193 more than the number of heads in the caravan, the number of keepers is | {
"A": "5",
"B": "10",
"C": "15",
"D": "20",
"E": "25"
} | subtract(add(add(add(60, 35), 6), 193), add(add(multiply(const_2, 60), multiply(const_4, 35)), multiply(const_4, 6))) | add(n0,n1)|multiply(n0,const_2)|multiply(n1,const_4)|multiply(n2,const_4)|add(n2,#0)|add(#1,#2)|add(n3,#4)|add(#5,#3)|subtract(#6,#7)| | explanation : let number of keepers be x . then , total number of feet = 2 x 60 + 4 x 35 + 4 x 6 + 2 x = 2 x + 284 . total number of heads = 60 + 35 + 6 + x = 101 + x . therefore ( 2 x + 284 ) = ( 101 + x ) + 193 or x = 10 . answer : b | general |
math_qa__NorcNMMm6d5PBa76 | 100 liter solution of cool-drink is made from 10% jasmine water. If 5 liters of jasmine and 10 liters of water were added to the solution, what percent of the solution is jasmine? Choose one
A) 1 / 13 B) 2 / 23 C) 3 / 31 D) 4 / 15 E) 2 / 3 | <gadget id="calculator">100 + 10</gadget>
<output>110</output>
<gadget id="calculator">5 + 110</gadget>
<output>115</output>
<gadget id="calculator">10 / 115</gadget>
<output>2/23 = around 0.086957</output>
<result>B</result> | B | 0.086957 | 100 liter solution of cool-drink is made from 10% jasmine water. If 5 liters of jasmine and 10 liters of water were added to the solution, what percent of the solution is jasmine? | {
"A": "1 / 13",
"B": "2 / 23",
"C": "3 / 31",
"D": "4 / 15",
"E": "2 / 3"
} | divide(10, add(5, add(100, 10))) | add(n0,n1)|add(n2,#0)|divide(n1,#1) | denominator 100 + 5 + 10 115 numerator 100 * 0.1 = 10 - - - > jasmine water 10 + 5 = 15 - - - > new content of jasmine water in new solution ratio 3 / 23 answer is b | gain |
math_qa__yu2IOO3bmA2sOX2r | In a division, divident is 725, divisior is 36 and quotient is 20. Find the remainder. Answers.
A) 4 B) 3 C) 2 D) 5 E) 6 | <gadget id="calculator">725 % 36</gadget>
<output>5</output>
<result>D</result> | D | 5 | In a division, divident is 725, divisior is 36 and quotient is 20. Find the remainder. | {
"A": "4",
"B": "3",
"C": "2",
"D": "5",
"E": "6"
} | reminder(725, 36) | reminder(n0,n1)| | "explanation : 725 = 36 x 20 + r 725 = 720 + r r = 725 - 720 = 5 answer : option d" | general |
math_qa__XBbWNQacobwKkUqV | A number is selected at random from the first 30 natural numbers. What is the probability that the number is a multiple of either 4 or 15? Choices:
A) 17 / 30
B) 2 / 5
C) 3 / 10
D) 4 / 15
E) 11 / 30 | <gadget id="calculator">30 / 4</gadget>
<output>15/2 = around 7.5</output>
<gadget id="calculator">floor(15/2)</gadget>
<output>7</output>
<gadget id="calculator">30 / 15</gadget>
<output>2</output>
<gadget id="calculator">7 + 2</gadget>
<output>9</output>
<gadget id="calculator">9 / 30</gadget>
<output>3/10 = around 0.3</output>
<result>C</result> | C | 0.3 | A number is selected at random from the first 30 natural numbers. What is the probability that the number is a multiple of either 4 or 15? | {
"A": "17 / 30",
"B": "2 / 5",
"C": "3 / 10",
"D": "4 / 15",
"E": "11 / 30"
} | divide(add(floor(divide(30, 4)), divide(30, 15)), 30) | divide(n0,n2)|divide(n0,n1)|floor(#1)|add(#0,#2)|divide(#3,n0) | number of multiples of 4 from 1 through 30 = 30 / 4 = 7 number of multiples of 15 from 1 through 30 = 30 / 15 = 2 number of multiples of 4 and 15 both from 1 through 30 = number of multiples of 15 * 4 ( = 60 ) = 0 total favourable cases = 7 + 2 - 0 = 9 probability = 9 / 30 = 3 / 10 answer : option c | probability |
math_qa__Jsamfnn15brVyGjl | A car gets 28 miles to the gallon. If it is modified to use a solar panel, it will use only 80 percent as much fuel as it does now. If the fuel tank holds 15 gallons, how many more miles will the car be able to travel, per full tank of fuel, after it has been modified? Choose the most appropriate option:
A) 85 B) 90 C) 95 D) 100 E) 105 | <gadget id="calculator">28 / 80</gadget>
<output>7/20 = around 0.35</output>
<gadget id="calculator">(7/20) * 100</gadget>
<output>35</output>
<gadget id="calculator">35 * 15</gadget>
<output>525</output>
<gadget id="calculator">28 * 15</gadget>
<output>420</output>
<gadget id="calculator">525 - 420</gadget>
<output>105</output>
<result>E</result> | E | 105 | A car gets 28 miles to the gallon. If it is modified to use a solar panel, it will use only 80 percent as much fuel as it does now. If the fuel tank holds 15 gallons, how many more miles will the car be able to travel, per full tank of fuel, after it has been modified? | {
"A": "85",
"B": "90",
"C": "95",
"D": "100",
"E": "105"
} | subtract(multiply(multiply(divide(28, 80), const_100), 15), multiply(28, 15)) | divide(n0,n1)|multiply(n0,n2)|multiply(#0,const_100)|multiply(n2,#2)|subtract(#3,#1)| | "originally , the distance the car could go on a full tank was 15 * 28 = 420 miles . after it has been modified , the car can go 28 / 0.8 = 35 miles per gallon . on a full tank , the car can go 15 * 35 = 525 miles , thus 105 miles more . the answer is e ." | physics |
math_qa__XMrAVdEGC6DXHakX | A cistern 10 m long and 8 m wide contains water up to a depth of 1 m 50 cm. The total area of the wet surface is:
Choose the most appropriate option
A) 120 m 2 B) 136 m 2 C) 128 m 2 D) 130 m 2 E) 134 m 2 | <gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) + 1</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">(3/2) * 8</gadget>
<output>12</output>
<gadget id="calculator">(3/2) * 10</gadget>
<output>15</output>
<gadget id="calculator">12 + 15</gadget>
<output>27</output>
<gadget id="calculator">2 * 27</gadget>
<output>54</output>
<gadget id="calculator">8 * 10</gadget>
<output>80</output>
<gadget id="calculator">54 + 80</gadget>
<output>134</output>
<result>E</result> | E | 134 | A cistern 10 m long and 8 m wide contains water up to a depth of 1 m 50 cm. The total area of the wet surface is: | {
"A": "120 m 2",
"B": "136 m 2",
"C": "128 m 2",
"D": "130 m 2",
"E": "134 m 2"
} | add(multiply(const_2, add(multiply(add(divide(50, const_100), 1), 8), multiply(add(divide(50, const_100), 1), 10))), multiply(8, 10)) | divide(n3,const_100)|multiply(n0,n1)|add(n2,#0)|multiply(n1,#2)|multiply(n0,#2)|add(#3,#4)|multiply(#5,const_2)|add(#6,#1)| | "area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 8 x 1.50 + 10 x 1.50 ) + 8 x 10 ] m 2 = 134 m 2 . answer : e" | physics |
math_qa__VDhipXxY8ubbN0lk | Jim and Cara begin running at the same time and they start at the same place on a straight path. Jim runs at 6 miles per hour, and Cara runs at 5 miles per hour. After 30 minutes, Jim stops to stretch. If it takes Jim 18 minutes to stretch and Cara continues to run during this time, how many minutes will it take Jim to catch up to Cara? Answers
A) 40 B) 50 C) 60 D) 70 E) 80 | <gadget id="calculator">18 / 60</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">5 * (3/10)</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">30 / 60</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">5 * (1/2)</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">(3/2) + (5/2)</gadget>
<output>4</output>
<gadget id="calculator">6 * (1/2)</gadget>
<output>3</output>
<gadget id="calculator">4 - 3</gadget>
<output>1</output>
<gadget id="calculator">1 * 60</gadget>
<output>60</output>
<result>C</result> | C | 60 | Jim and Cara begin running at the same time and they start at the same place on a straight path. Jim runs at 6 miles per hour, and Cara runs at 5 miles per hour. After 30 minutes, Jim stops to stretch. If it takes Jim 18 minutes to stretch and Cara continues to run during this time, how many minutes will it take Jim to catch up to Cara? | {
"A": "40",
"B": "50",
"C": "60",
"D": "70",
"E": "80"
} | multiply(subtract(add(multiply(5, divide(18, const_60)), multiply(5, divide(30, const_60))), multiply(6, divide(30, const_60))), const_60) | divide(n3,const_60)|divide(n2,const_60)|multiply(n1,#0)|multiply(n1,#1)|multiply(n0,#1)|add(#2,#3)|subtract(#5,#4)|multiply(#6,const_60) | in 30 minutes , jim runs 3 miles . in 48 minutes , cara runs 4 miles . jim can catch cara at a rate of 1 mile per hour . since cara is ahead by 1 mile , it will take jim 1 hour = 60 minutes to catch cara . the answer is c . | physics |
math_qa__FasYvbahv33KNcK6 | In a public show 50 % of the seats were filled. If there were 600 seats in the hall, how many seats were vacant?
Choose the correct choice from the following answers
A) 100
B) 110
C) 120
D) 300
E) 150 | <gadget id="calculator">100 - 50</gadget>
<output>50</output>
<gadget id="calculator">600 * 50</gadget>
<output>30_000</output>
<gadget id="calculator">30_000 / 100</gadget>
<output>300</output>
<result>D</result> | D | 300 | In a public show 50 % of the seats were filled. If there were 600 seats in the hall, how many seats were vacant? | {
"A": "100",
"B": "110",
"C": "120",
"D": "300",
"E": "150"
} | divide(multiply(600, subtract(const_100, 50)), const_100) | subtract(const_100,n0)|multiply(n1,#0)|divide(#1,const_100)| | "50 % of 600 = 50 / 100 × 600 = 300 therefore , the number of vacant seats = 600 - 300 = 300 . answer : d" | gain |
math_qa__l3xA84rIMsDiQO4C | How many even number in the range between 10 to 100 inclusive are not divisible by 3 Options: A) 15 B) 30 C) 31 D) 33 E) 46 | <gadget id="calculator">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">90 - 2</gadget>
<output>88</output>
<gadget id="calculator">88 / 2</gadget>
<output>44</output>
<gadget id="calculator">100 - 2</gadget>
<output>98</output>
<gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">98 - 12</gadget>
<output>86</output>
<gadget id="calculator">86 - 3</gadget>
<output>83</output>
<gadget id="calculator">83 - 3</gadget>
<output>80</output>
<gadget id="calculator">80 / 3</gadget>
<output>80/3 = around 26.666667</output>
<gadget id="calculator">(80/3) / 2</gadget>
<output>40/3 = around 13.333333</output>
<gadget id="calculator">44 - (40/3)</gadget>
<output>92/3 = around 30.666667</output>
<result>C</result> | C | 31 | How many even number in the range between 10 to 100 inclusive are not divisible by 3 | {
"A": "15",
"B": "30",
"C": "31",
"D": "33",
"E": "46"
} | subtract(divide(subtract(subtract(100, 10), const_2), const_2), divide(divide(subtract(subtract(subtract(subtract(100, const_2), multiply(3, const_4)), 3), 3), 3), const_2)) | multiply(n2,const_4)|subtract(n1,n0)|subtract(n1,const_2)|subtract(#1,const_2)|subtract(#2,#0)|divide(#3,const_2)|subtract(#4,n2)|subtract(#6,n2)|divide(#7,n2)|divide(#8,const_2)|subtract(#5,#9)| | "we have to find the number of terms that are divisible by 2 but not by 6 ( as the question asks for the even numbers only which are not divisible by 3 ) for 2 , 10 , 12,14 . . . 100 using ap formula , we can say 100 = 10 + ( n - 1 ) * 2 or n = 46 . for 6 , 12,18 , . . . 96 using ap formula , we can say 96 = 12 + ( n - 1 ) * 6 or n = 15 . hence , only divisible by 2 but not 3 = 46 - 15 = 31 . hence , answer c" | general |
math_qa__1axmhDBJIqu2dWmS | A and B are partners in a business. A contributes 1/4 of the capital for 15 months and B received 2/3 of the profit. For how long B’s money was used?
Select the correct option: A) 4 months B) 6 months C) 8 months D) 10 months E) none | <gadget id="calculator">10 + 1</gadget>
<output>11</output>
<gadget id="calculator">11 - 1</gadget>
<output>10</output>
<result>D</result> | D | 10 | A and B are partners in a business. A contributes 1/4 of the capital for 15 months and B received 2/3 of the profit. For how long B’s money was used? | {
"A": "4 months",
"B": "6 months",
"C": "8 months",
"D": "10 months",
"E": "none"
} | subtract(add(const_10, 1), 1) | add(n0,const_10)|subtract(#0,n0)| | "sol . let the total profit be rs . z . then , b ’ share = rs . 2 z / 3 , a ’ s share = rs . [ z - 2 z / 3 ] = rs . z / 3 ∴ a : b = z / 3 : 2 z / 3 = 1 : 2 . let the total capital be rs . x and suppose b ’ s money was used for x months . then , [ 1 / 4 x * 15 ] / [ 3 / 4 x * y ] = 1 / 2 ⇔ y = [ 15 * 2 / 3 ] = 10 . thus , b ’ s money was used for 10 months . answer d" | gain |
math_qa__rHbfcboBvPFkffC3 | A man buys Rs. 52 shares paying 9% dividend. The man wants to have an interest of 12% on his money. The market value of each share is: Choose the correct choice from the following answers
A) s . 12 B) s . 15 C) s . 18 D) s . 21 E) s . 39 | <gadget id="calculator">100 / 12</gadget>
<output>25/3 = around 8.333333</output>
<gadget id="calculator">9 / 100</gadget>
<output>9/100 = around 0.09</output>
<gadget id="calculator">(9/100) * 52</gadget>
<output>117/25 = around 4.68</output>
<gadget id="calculator">(25/3) * (117/25)</gadget>
<output>39</output>
<result>E</result> | E | 39 | A man buys Rs. 52 shares paying 9% dividend. The man wants to have an interest of 12% on his money. The market value of each share is: | {
"A": "s . 12",
"B": "s . 15",
"C": "s . 18",
"D": "s . 21",
"E": "s . 39"
} | multiply(divide(const_100, 12), multiply(divide(9, const_100), 52)) | divide(const_100,n2)|divide(n1,const_100)|multiply(n0,#1)|multiply(#0,#2)| | "dividend on rs . 52 = rs . 9 / 100 x 52 = rs . 4.68 . rs . 12 is an income on rs . 100 . rs . 4.68 is an income on rs . 100 / 12 x 4.68 = rs . 39 . answer : option e" | gain |
math_qa__Q9Pu2i8LVxXf3Vk9 | At Deluxe paint store, Fuchsia paint is made by mixing 5 parts of red paint with 3 parts of blue paint. Mauve paint is made by mixing 4 parts of red paint with 5 parts blue paint. How many liters of blue paint must be added to 32 liters of Fuchsia to change it to Mauve paint? Pick:
A) 9 B) 13 C) 15 D) 16 E) 18 | <gadget id="calculator">5 + 3</gadget>
<output>8</output>
<gadget id="calculator">5 / 8</gadget>
<output>5/8 = around 0.625</output>
<gadget id="calculator">32 * (5/8)</gadget>
<output>20</output>
<gadget id="calculator">4 / 8</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">20 / (1/2)</gadget>
<output>40</output>
<gadget id="calculator">40 * (5/8)</gadget>
<output>25</output>
<gadget id="calculator">32 - 20</gadget>
<output>12</output>
<gadget id="calculator">25 - 12</gadget>
<output>13</output>
<result>B</result> | B | 13 | At Deluxe paint store, Fuchsia paint is made by mixing 5 parts of red paint with 3 parts of blue paint. Mauve paint is made by mixing 4 parts of red paint with 5 parts blue paint. How many liters of blue paint must be added to 32 liters of Fuchsia to change it to Mauve paint? | {
"A": "9",
"B": "13",
"C": "15",
"D": "16",
"E": "18"
} | subtract(multiply(divide(multiply(32, divide(5, add(5, 3))), divide(4, add(5, 3))), divide(5, add(5, 3))), subtract(32, multiply(32, divide(5, add(5, 3))))) | add(n0,n1)|divide(n0,#0)|divide(n2,#0)|divide(n3,#0)|multiply(n4,#1)|divide(#4,#2)|subtract(n4,#4)|multiply(#5,#3)|subtract(#7,#6)| | "in 32 liters , red = 5 / 8 * 32 = 20 and blue = 12 so , 20 / ( 12 + x ) = 4 / 5 or , x = 13 ( answer b )" | general |
math_qa__HaYQQn97lMDAs1rj | If 5/w + 5/x = 5/y and wx = y, then the average (arithmetic mean) of w and x is Choose the correct choice from the following.
A) 1 / 2 B) 1 C) 2 D) 4 E) 8 | <gadget id="calculator">5 + 5</gadget>
<output>10</output>
<gadget id="calculator">5 / 10</gadget>
<output>1/2 = around 0.5</output>
<result>A</result> | A | 0.5 | If 5/w + 5/x = 5/y and wx = y, then the average (arithmetic mean) of w and x is | {
"A": "1 / 2",
"B": "1",
"C": "2",
"D": "4",
"E": "8"
} | divide(5, add(5, 5)) | add(n0,n0)|divide(n0,#0)| | "given : 5 / w + 5 / x = 5 / ywx = y find : ( w + x ) / 2 = ? 5 ( 1 / w + 1 / x ) = 5 ( 1 / y ) - divide both sides by 5 ( 1 / w + 1 / x ) = 1 / y ( x + w ) / wx = 1 / wx - sub ' d in y = wx x + w - 1 = 0 x + w = 1 therefore ( w + x ) / 2 = 1 / 2 ans : a" | general |
math_qa__9SXWpYsJ0lvwkayt | On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $0.60 per glass on the first day, what was the price E per glass on the second day? Select
A) $ 015 B) $ 0.20 C) $ 0.30 D) $ 0.40 E) $ 0.45 | <gadget id="calculator">1 + 1</gadget>
<output>2</output>
<gadget id="calculator">2 * 0.6</gadget>
<output>1.2</output>
<gadget id="calculator">1 + 2</gadget>
<output>3</output>
<gadget id="calculator">1.2 / 3</gadget>
<output>0.4</output>
<result>D</result> | D | 0.4 | On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $0.60 per glass on the first day, what was the price E per glass on the second day? | {
"A": "$ 015",
"B": "$ 0.20",
"C": "$ 0.30",
"D": "$ 0.40",
"E": "$ 0.45"
} | divide(multiply(add(const_1, const_1), 0.60), add(const_1, const_2)) | add(const_1,const_1)|add(const_1,const_2)|multiply(n0,#0)|divide(#2,#1)| | "on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.6 = 3 * x - - > x = $ 0.4 . answer : d ." | general |
math_qa__5v0or3mXOUlaqk10 | Jerry went to a shop and bought things worth Rs. 45, out of which 30 % went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
Pick one:
A) 19 B) 19.7 C) 21.3 D) 29.5 E) 39.7 | <gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">100 / 6</gadget>
<output>50/3 = around 16.666667</output>
<gadget id="calculator">(3/10) * (50/3)</gadget>
<output>5</output>
<gadget id="calculator">5 + (3/10)</gadget>
<output>53/10 = around 5.3</output>
<gadget id="calculator">45 - (53/10)</gadget>
<output>397/10 = around 39.7</output>
<result>E</result> | E | 39.7 | Jerry went to a shop and bought things worth Rs. 45, out of which 30 % went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? | {
"A": "19",
"B": "19.7",
"C": "21.3",
"D": "29.5",
"E": "39.7"
} | subtract(45, add(multiply(divide(30, const_100), divide(const_100, 6)), divide(30, const_100))) | divide(n1,const_100)|divide(const_100,n2)|multiply(#0,#1)|add(#0,#2)|subtract(n0,#3)| | "total cost of the items he purchased = rs . 45 given that out of this rs . 45 , 30 % is given as tax = > total tax incurred = 30 % = rs . 30 / 100 let the cost of the tax free items = x given that tax rate = 6 % ∴ ( 45 − 30 / 100 − x ) 6 / 100 = 30 / 100 ⇒ 6 ( 45 − 0.3 − x ) = 30 ⇒ ( 45 − 0.3 − x ) = 5 ⇒ x = 45 − 0.3 − 5 = 39.7 e )" | gain |
math_qa__T5PwFaOgO3QmLCgE | In an examination, 25% of total students failed in Hindi, 48% failed in English and 27% in both. The percentage of these who passed in both the subjects is : Pick one:
A) 23
B) 54
C) 28
D) 40
E) 81 | <gadget id="calculator">25 + 48</gadget>
<output>73</output>
<gadget id="calculator">73 - 27</gadget>
<output>46</output>
<gadget id="calculator">100 - 46</gadget>
<output>54</output>
<result>B</result> | B | 54 | In an examination, 25% of total students failed in Hindi, 48% failed in English and 27% in both. The percentage of these who passed in both the subjects is : | {
"A": "23",
"B": "54",
"C": "28",
"D": "40",
"E": "81"
} | subtract(const_100, subtract(add(25, 48), 27)) | add(n0,n1)|subtract(#0,n2)|subtract(const_100,#1)| | "explanation : formula n ( a â ˆ ª b ) = n ( a ) + n ( b ) â ˆ ’ n ( a â ˆ © b ) fail in hindi or english = 25 + 48 â € “ 27 = 46 therefore students who passed = 100 â € “ 46 = 54 . answer : b" | general |
math_qa__spyVSWnfCHUbcszd | If john makes a contribution to a charity fund at school, the average contribution size will increase by 50% reaching $75 per person. If there were 2 other contributions made before john's, what is the size of his donation?
Answers
A) $ 125 B) $ 150 C) $ 200 D) $ 250 E) $ 450 | <gadget id="calculator">2 + 1</gadget>
<output>3</output>
<gadget id="calculator">3 * 75</gadget>
<output>225</output>
<gadget id="calculator">3 * 50</gadget>
<output>150</output>
<gadget id="calculator">225 - 150</gadget>
<output>75</output>
<gadget id="calculator">75 + 50</gadget>
<output>125</output>
<result>A</result> | A | 125 | If john makes a contribution to a charity fund at school, the average contribution size will increase by 50% reaching $75 per person. If there were 2 other contributions made before john's, what is the size of his donation? | {
"A": "$ 125",
"B": "$ 150",
"C": "$ 200",
"D": "$ 250",
"E": "$ 450"
} | add(subtract(multiply(add(2, const_1), 75), multiply(add(2, const_1), 50)), 50) | add(n2,const_1)|multiply(n1,#0)|multiply(n0,#0)|subtract(#1,#2)|add(n0,#3)| | "cavg = average contribution before john cavg * 1.5 = 75 , therefore the average cont is $ 50 before john . if he needs to increase the average contribution by $ 25 , he must put in $ 25 for each of the 2 people . so $ 50 . but , he also has to put in the average for himself ( the threeth person ) , so add $ 75 . so $ 125 is your answer . answer a" | general |
math_qa__KK30IsmbGsOE15DX | If 20% of a number = 100, then 120% of that number will be? Choose the most appropriate option:
A) 20 B) 120 C) 360 D) 600 E) 820 | <gadget id="calculator">120 * 100</gadget>
<output>12_000</output>
<gadget id="calculator">12_000 / 20</gadget>
<output>600</output>
<result>D</result> | D | 600 | If 20% of a number = 100, then 120% of that number will be? | {
"A": "20",
"B": "120",
"C": "360",
"D": "600",
"E": "820"
} | divide(multiply(120, 100), 20) | multiply(n1,n2)|divide(#0,n0) | let the number x . then , 20 % of x = 100 x = ( 100 * 100 ) / 20 = 500 120 % of x = ( 120 / 100 * 500 ) = 600 . answer : d | gain |
math_qa__1Wj8CfDN907PVZjz | In what ratio should a variety of Rice costing Rs. 20 per kg be mixed with another variety of Rice costing Rs. 31.50 per kg to obtain a mixture costing Rs. 23.75 per kg?
Select the correct option:
A) 16 : 30
B) 30 : 14
C) 16 : 31
D) 31 : 15
E) 15 : 31 | <gadget id="calculator">31.5 - 23.75</gadget>
<output>7.75</output>
<gadget id="calculator">31.5 - 20</gadget>
<output>11.5</output>
<gadget id="calculator">7.75 / 11.5</gadget>
<output>0.673913</output>
<gadget id="calculator">1 - 0.673913</gadget>
<output>0.326087</output>
<gadget id="calculator">0.673913 / 0.326087</gadget>
<output>2.066666</output>
<result>D</result> | D | 2.066667 | In what ratio should a variety of Rice costing Rs. 20 per kg be mixed with another variety of Rice costing Rs. 31.50 per kg to obtain a mixture costing Rs. 23.75 per kg? | {
"A": "16 : 30",
"B": "30 : 14",
"C": "16 : 31",
"D": "31 : 15",
"E": "15 : 31"
} | divide(divide(subtract(31.50, 23.75), subtract(31.50, 20)), subtract(const_1, divide(subtract(31.50, 23.75), subtract(31.50, 20)))) | subtract(n1,n2)|subtract(n1,n0)|divide(#0,#1)|subtract(const_1,#2)|divide(#2,#3)| | "let us say the ratio of the quantities of cheaper and dearer varieties = x : y by the rule of allegation , x / y = ( 31.50 - 23.75 ) / ( 23.75 - 20 ) = 31 / 15 answer : d" | other |
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