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__k0skkHpIJWBdCiGc | Find the remainder when 2^31 is divided by 5. Choose the correct choice from the following answers
A) 3 B) 7 C) 1 D) 9 E) none of them | <gadget id="calculator">2 ** 31</gadget>
<output>2_147_483_648</output>
<gadget id="calculator">2_147_483_648 % 5</gadget>
<output>3</output>
<result>A</result> | A | 3 | Find the remainder when 2^31 is divided by 5. | {
"A": "3",
"B": "7",
"C": "1",
"D": "9",
"E": "none of them"
} | reminder(power(2, 31), 5) | power(n0,n1)|reminder(#0,n2) | 2 ^ 10 = 1024 . unit digit of 2 ^ 10 x 2 ^ 10 x 2 ^ 10 is 4 [ as 4 x 4 x 4 gives unit digit 4 ] . unit digit of 231 is 8 . now , 8 when divided by 5 , gives 3 as remainder . hence , 231 when divided by 5 , gives 3 as remainder . answer is a . | general |
math_qa__UYWclu7sPip8Fbuq | Laxmi and Prasanna set on a journey. Laxmi moves northwards at a speed of 25kmph and Prasanna moves southward at a speed of 35 kmph. How far will be Prasanna from Laxmi after 60 minutes ? Pick one
A) 11 B) 50 C) 60 D) 27 E) 18 | <gadget id="calculator">25 + 35</gadget>
<output>60</output>
<result>C</result> | C | 60 | Laxmi and Prasanna set on a journey. Laxmi moves northwards at a speed of 25kmph and Prasanna moves southward at a speed of 35 kmph. How far will be Prasanna from Laxmi after 60 minutes ? | {
"A": "11",
"B": "50",
"C": "60",
"D": "27",
"E": "18"
} | add(25, 35) | add(n0,n1)| | "explanation : we know 60 min = 1 hr total northward laxmi ' s distance = 25 kmph x 1 hr = 25 km total southward prasanna ' s distance = 35 kmph x 1 hr = 35 km total distance between prasanna and laxmi is = 25 + 35 = 60 km . answer : c" | physics |
math_qa__JGS70fqksFhNaRYv | John was thrice as old as Tom 6 years ago. John will be 15/13 times as old as Tom in 6 years. How old is Tom today? Choose the correct choice from the following.
A) 5 B) 7 C) 9 D) 11 E) 13 | <gadget id="calculator">15 / 13</gadget>
<output>15/13 = around 1.153846</output>
<gadget id="calculator">6 * (15/13)</gadget>
<output>90/13 = around 6.923077</output>
<result>B</result> | B | 7 | John was thrice as old as Tom 6 years ago. John will be 15/13 times as old as Tom in 6 years. How old is Tom today? | {
"A": "5",
"B": "7",
"C": "9",
"D": "11",
"E": "13"
} | multiply(6, divide(15, 13)) | divide(n1,n2)|multiply(n0,#0) | j - 6 = 3 ( t - 6 ) , so j = 3 t - 12 j + 6 = 15 / 13 * ( t + 6 ) 13 j + 78 = 15 t + 90 13 ( 3 t - 12 ) + 78 = 15 t + 90 24 t = 168 t = 7 the answer is b . | general |
math_qa__BhsIfiQqNMLTAZjc | A can complete a project in 10 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed? Select the correct option: A) 18 days B) 15 days C) 26.67 days D) 16 days E) 12 days | <gadget id="calculator">1 / 30</gadget>
<output>1/30 = around 0.033333</output>
<gadget id="calculator">(1/30) * 10</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 - (1/3)</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">1 / 10</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/10) + (1/30)</gadget>
<output>2/15 = around 0.133333</output>
<gadget id="calculator">(2/3) / (2/15)</gadget>
<output>5</output>
<gadget id="calculator">5 + 10</gadget>
<output>15</output>
<result>B</result> | B | 15 | A can complete a project in 10 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed? | {
"A": "18 days",
"B": "15 days",
"C": "26.67 days",
"D": "16 days",
"E": "12 days"
} | add(divide(subtract(const_1, multiply(divide(const_1, 30), 10)), add(divide(const_1, 10), divide(const_1, 30))), 10) | divide(const_1,n1)|divide(const_1,n0)|add(#1,#0)|multiply(n2,#0)|subtract(const_1,#3)|divide(#4,#2)|add(n2,#5)| | "let x = the number of days taken to complete the project . the amount of work done by a is ( x - 10 ) * ( 1 / 20 ) . the amount of work done by b is ( x ) * ( 1 / 30 ) . ( 1 / 10 ) * ( x - 10 ) + ( 1 / 30 ) * ( x ) = 1 ( x / 10 ) + ( x / 30 ) - 1 ) = 1 4 x / 30 = 2 x = 15 therefore , the answer is b : 15 ." | physics |
math_qa__mk1cKL1SHrYv1p46 | a, b, and c are integers and a<b<c. S is the set of all integers from a to b, inclusive. Q is the set of all integers from b to c, inclusive. The median of set S is (3/4)*b. The median of set Q is (8/8)*c. If R is the set of all integers from a to c, inclusive, what fraction of c is the median of set R?
Choose the correct choice from the following options.
A) 3 / 8 B) 1 / 2 C) 11 / 16 D) 5 / 7 E) 3 / 4 | <gadget id="calculator">8 / 8</gadget>
<output>1</output>
<gadget id="calculator">1 * 2</gadget>
<output>2</output>
<gadget id="calculator">2 - 1</gadget>
<output>1</output>
<gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(3/4) * 2</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">(3/2) - 1</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 / (1/2)</gadget>
<output>2</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 + (1/2)</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">(3/2) / 2</gadget>
<output>3/4 = around 0.75</output>
<result>E</result> | E | 0.75 | a, b, and c are integers and a<b<c. S is the set of all integers from a to b, inclusive. Q is the set of all integers from b to c, inclusive. The median of set S is (3/4)*b. The median of set Q is (8/8)*c. If R is the set of all integers from a to c, inclusive, what fraction of c is the median of set R? | {
"A": "3 / 8",
"B": "1 / 2",
"C": "11 / 16",
"D": "5 / 7",
"E": "3 / 4"
} | divide(add(const_1, divide(subtract(multiply(divide(8, 8), const_2), const_1), divide(const_1, subtract(multiply(divide(3, 4), const_2), const_1)))), const_2) | divide(n2,n3)|divide(n0,n1)|multiply(#0,const_2)|multiply(#1,const_2)|subtract(#2,const_1)|subtract(#3,const_1)|divide(const_1,#5)|divide(#4,#6)|add(#7,const_1)|divide(#8,const_2)| | "the answer isc : 11 / 16 . the key to this problem is remembering that the median for a consecutive set of numbers is equivalent to its mean . for example , the mean and median of a set consisting of x , x + 1 , x + 2 , . . . , y will always be ( x + y ) / 2 . for set s , consisting of numbers ( a , a + 1 , . . . , b ) , the median is given to be 3 / 4 * b : ( a + b ) / 2 = ( 3 / 4 ) * b a = b / 2 for set q , consisting of numbers ( b , b + 1 , . . . , c ) , the median is given to be 8 / 8 * c : ( b + c ) / 2 = ( 8 / 8 ) * c b = ( 1 ) * c for set r , consisting of numbers ( a , a + 1 , . . . c ) , the median needs to be found : a = b / 2 = ( 1 * c ) / 2 = ( 1 / 2 ) * c median = ( a + c ) / 2 = ( 1 / 2 * c + c ) / 2 = ( 3 / 2 ) * c / 2 = ( 3 / 4 ) * c ( answer e )" | general |
math_qa__iJxoUcxXNgF19a1d | A car traveling at a certain constant speed takes 10 seconds longer to travel 1 km than it would take to travel 1 km at 80 km/hour. At what speed, in km/hr, is the car traveling?
Select.
A) 70
B) 72
C) 74
D) 65
E) 78 | <gadget id="calculator">1 / 80</gadget>
<output>1/80 = around 0.0125</output>
<gadget id="calculator">3_600 * (1/80)</gadget>
<output>45</output>
<gadget id="calculator">45 + 10</gadget>
<output>55</output>
<gadget id="calculator">55 / 3_600</gadget>
<output>11/720 = around 0.015278</output>
<gadget id="calculator">1 / (11/720)</gadget>
<output>720/11 = around 65.454545</output>
<result>D</result> | D | 65 | A car traveling at a certain constant speed takes 10 seconds longer to travel 1 km than it would take to travel 1 km at 80 km/hour. At what speed, in km/hr, is the car traveling? | {
"A": "70",
"B": "72",
"C": "74",
"D": "65",
"E": "78"
} | divide(1, divide(add(multiply(const_3600, divide(1, 80)), 10), const_3600)) | divide(n1,n3)|multiply(#0,const_3600)|add(n0,#1)|divide(#2,const_3600)|divide(n1,#3) | time to cover 1 kilometer at 80 kilometers per hour is 1 / 80 hours = 3,600 / 80 seconds = 45 seconds ; time to cover 1 kilometer at regular speed is 45 + 10 = 55 seconds = 55 / 3,600 hours = 1 / 65 hours ; so , we get that to cover 1 kilometer 1 / 65 hours is needed - - > regular speed 65 kilometers per hour ( rate is a reciprocal of time or rate = distance / time ) . answer : d | physics |
math_qa__2iCfaZUfIqP5mYcH | A bus trip of 210 miles would have taken 1 hour less if the average speed V for the trip had been greater by 5 miles per hour. What was the average speed V, in miles per hour, for the trip? Options:
A) 25 B) 30 C) 35 D) 40 E) 45 | <gadget id="calculator">210 * 5</gadget>
<output>1_050</output>
<gadget id="calculator">1_050 * 4</gadget>
<output>4_200</output>
<gadget id="calculator">5 ** 2</gadget>
<output>25</output>
<gadget id="calculator">4_200 + 25</gadget>
<output>4_225</output>
<gadget id="calculator">4_225 ** (1/2)</gadget>
<output>65</output>
<gadget id="calculator">65 - 5</gadget>
<output>60</output>
<gadget id="calculator">60 / 2</gadget>
<output>30</output>
<result>B</result> | B | 30 | A bus trip of 210 miles would have taken 1 hour less if the average speed V for the trip had been greater by 5 miles per hour. What was the average speed V, in miles per hour, for the trip? | {
"A": "25",
"B": "30",
"C": "35",
"D": "40",
"E": "45"
} | divide(subtract(sqrt(add(multiply(multiply(210, 5), const_4), power(5, const_2))), 5), const_2) | multiply(n0,n2)|power(n2,const_2)|multiply(#0,const_4)|add(#2,#1)|sqrt(#3)|subtract(#4,n2)|divide(#5,const_2)| | "the time is the distance / speed . the time difference is 1 hour . 210 / v - 210 / ( v + 5 ) = 1 210 ( v + 5 ) - 210 v = ( v ) ( v + 5 ) 1050 = ( v ) ( v + 5 ) 30 * 35 = ( v ) ( v + 5 ) v = 30 mph the answer is b ." | physics |
math_qa__ZiSq2xRqSoivw34A | If the 5th date of a month is Tuesday, what date will be 3 days after the 3rd Friday in the month? Choose the correct choice from the following answers.
A) 17 B) 18 C) 20 D) 22 E) 33 | <gadget id="calculator">5 * 3</gadget>
<output>15</output>
<gadget id="calculator">15 + 3</gadget>
<output>18</output>
<result>B</result> | B | 18 | If the 5th date of a month is Tuesday, what date will be 3 days after the 3rd Friday in the month? | {
"A": "17",
"B": "18",
"C": "20",
"D": "22",
"E": "33"
} | add(multiply(5, 3), 3) | multiply(n0,n1)|add(n1,#0) | b 18 5 th date of a month is tuesday friday will be on = 5 + 3 = 8 th of a month 1 st friday is on 1 st of a month 2 nd friday is on 8 th of a month 3 rd friday will be on 15 th of a month 3 days after 15 th = 15 + 3 = 18 | physics |
math_qa__8Du8JvJvrfG2ZNgp | What is the dividend. divisor 19, the quotient is 9 and the remainder is 5? Pick one
A) 130 B) 134 C) 148 D) 176 E) 160 | <gadget id="calculator">19 * 9</gadget>
<output>171</output>
<gadget id="calculator">171 + 5</gadget>
<output>176</output>
<result>D</result> | D | 176 | What is the dividend. divisor 19, the quotient is 9 and the remainder is 5? | {
"A": "130",
"B": "134",
"C": "148",
"D": "176",
"E": "160"
} | add(multiply(19, 9), 5) | multiply(n0,n1)|add(n2,#0)| | "d = d * q + r d = 19 * 9 + 5 d = 171 + 5 d = 176 answer d" | general |
math_qa__684VHungHuHWuURz | 30% of a number is more than 60% of 150 by 120. Find the number? Choose the correct choice from the following answers
A) 770
B) 712
C) 720
D) 740
E) 700 | <gadget id="calculator">150 * 60</gadget>
<output>9_000</output>
<gadget id="calculator">9_000 / 100</gadget>
<output>90</output>
<gadget id="calculator">90 + 120</gadget>
<output>210</output>
<gadget id="calculator">210 * 100</gadget>
<output>21_000</output>
<gadget id="calculator">21_000 / 30</gadget>
<output>700</output>
<result>E</result> | E | 700 | 30% of a number is more than 60% of 150 by 120. Find the number? | {
"A": "770",
"B": "712",
"C": "720",
"D": "740",
"E": "700"
} | divide(multiply(add(divide(multiply(150, 60), const_100), 120), const_100), 30) | multiply(n1,n2)|divide(#0,const_100)|add(n3,#1)|multiply(#2,const_100)|divide(#3,n0)| | "( 30 / 100 ) * x – ( 60 / 100 ) * 650 = 190 2 / 7 x = 210 x = 700 answer : e" | gain |
math_qa__s6NomfflTbrdZmS4 | An investor deposited $5,000 to open a new savings account that earned 12 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?
Options
A) $ 5300.50 B) $ 5304.50 C) $ 5405.50 D) $ 5604.50 E) $ 5805.50 | <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">12 / 4</gadget>
<output>3</output>
<gadget id="calculator">3 / 100</gadget>
<output>3/100 = around 0.03</output>
<gadget id="calculator">(3/100) + 1</gadget>
<output>103/100 = around 1.03</output>
<gadget id="calculator">(103/100) ** 2</gadget>
<output>10_609/10_000 = around 1.0609</output>
<gadget id="calculator">5_000 * (10_609/10_000)</gadget>
<output>10_609/2 = around 5_304.5</output>
<result>B</result> | B | 5,304.5 | An investor deposited $5,000 to open a new savings account that earned 12 percent annual interest, compounded quarterly. If there were no other transactions in the account, what was the amount of money in the account 6 months after the account was opened? | {
"A": "$ 5300.50",
"B": "$ 5304.50",
"C": "$ 5405.50",
"D": "$ 5604.50",
"E": "$ 5805.50"
} | multiply(multiply(multiply(add(const_2, const_3), const_100), multiply(add(const_2, const_3), const_2)), power(add(divide(divide(12, 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 1.03 * 1.03 ( $ 5,000 ) = $ 5304.50 . the answer is b ." | gain |
math_qa__qhKf2W6P02phN3NI | A and B can do a work in 8 days, B and C can do the same work in 12 days. A, B and C together can finish it in 6 days. A and C together will do it in? Choose the most appropriate option.
A) 8 B) 4 C) 6 D) 12 E) 10 | <gadget id="calculator">8 / 2</gadget>
<output>4</output>
<gadget id="calculator">4 + 2</gadget>
<output>6</output>
<gadget id="calculator">8 * 6</gadget>
<output>48</output>
<gadget id="calculator">48 / 6</gadget>
<output>8</output>
<result>A</result> | A | 8 | A and B can do a work in 8 days, B and C can do the same work in 12 days. A, B and C together can finish it in 6 days. A and C together will do it in? | {
"A": "8",
"B": "4",
"C": "6",
"D": "12",
"E": "10"
} | divide(multiply(8, add(divide(8, const_2), const_2)), 6) | divide(n0,const_2)|add(#0,const_2)|multiply(n0,#1)|divide(#2,n2) | ( a + b + c ) ' s 1 day work = 1 / 6 ; ( a + b ) ' s 1 day work = 1 / 8 ( b + c ) ' s 1 day work = 1 / 12 ( a + c ) ' s 1 day work = ( 2 * 1 / 6 ) - ( 1 / 8 + 1 / 12 ) = ( 1 / 3 - 5 / 24 ) = 1 / 8 so , a and c together will do the work in 8 days . answer a | physics |
math_qa__TmNabtsEqojj30yG | oy started cycling along the boundaries of a square field from corner point A. After half an hour he reached the corner point C, diagonally opposite to A. If his speed was 8km/hr, the area of the filed in square km is?
Choose the correct choice from the following
A) 64 B) 4 C) 16 D) 9 E) 5 | <gadget id="calculator">8 / 2</gadget>
<output>4</output>
<gadget id="calculator">4 / 2</gadget>
<output>2</output>
<gadget id="calculator">2 ** 2</gadget>
<output>4</output>
<result>B</result> | B | 4 | oy started cycling along the boundaries of a square field from corner point A. After half an hour he reached the corner point C, diagonally opposite to A. If his speed was 8km/hr, the area of the filed in square km is? | {
"A": "64",
"B": "4",
"C": "16",
"D": "9",
"E": "5"
} | power(divide(divide(8, const_2), const_2), const_2) | divide(n0,const_2)|divide(#0,const_2)|power(#1,const_2) | explanation : distance covered by roy in 1 / 2 hr = 4 kmtherefore , side of the square = 4 / 2 = 2 kmhence , area = 2 × 2 = 4 square km answer : b | geometry |
math_qa__LWzYsIN5lZ0ap6qb | how many 4 - digit numbers are there such that all 3 digits are different and the first digit and last digit is not zero ?
Pick:
A) 2128 B) 3458 C) 4207 D) 5184 E) 8104 | <gadget id="calculator">10 - 1</gadget>
<output>9</output>
<gadget id="calculator">4 / 2</gadget>
<output>2</output>
<gadget id="calculator">9 ** 2</gadget>
<output>81</output>
<gadget id="calculator">9 - 1</gadget>
<output>8</output>
<gadget id="calculator">8 ** 2</gadget>
<output>64</output>
<gadget id="calculator">81 * 64</gadget>
<output>5_184</output>
<result>D</result> | D | 5,184 | how many 4 - digit numbers are there such that all 3 digits are different and the first digit and last digit is not zero ? | {
"A": "2128",
"B": "3458",
"C": "4207",
"D": "5184",
"E": "8104"
} | multiply(power(subtract(const_10, const_1), divide(4, const_2)), power(subtract(subtract(const_10, const_1), const_1), divide(4, const_2))) | divide(n0,const_2)|subtract(const_10,const_1)|power(#1,#0)|subtract(#1,const_1)|power(#3,#0)|multiply(#2,#4) | all three digits are different and first digit is not zero . so first digit can be filled in 8 ways . and , second digit can be filled in 9 ways . and , third digit can be filled in 9 ways . and , fourth digit can be filled in 8 ways . total ways = 8 * 9 * 9 * 8 = 5184 hence option ( d ) . | general |
math_qa__SWW2v83QvQU30fDP | 32 = a + 2b
|a| > 2
If ‘a’ and ‘b’ are both integers, then what is the smallest possible values of ‘a’ that can be used to solve the above equation. Options: A) 2 B) 3 C) 4 D) 5 E) 6 | <gadget id="calculator">2 * 2</gadget>
<output>4</output>
<result>C</result> | C | 4 | 32 = a + 2b
|a| > 2
If ‘a’ and ‘b’ are both integers, then what is the smallest possible values of ‘a’ that can be used to solve the above equation. | {
"A": "2",
"B": "3",
"C": "4",
"D": "5",
"E": "6"
} | multiply(2, 2) | multiply(n1,n1) | let us understand the meaning of | a | > 2 mod is very easy concept if you solve mod question by considering as a distance . when a mod is written as | x - ( a ) | = b , this means the distance from point ' a ' ( both side left and right of ' a ' on number line ) is b . | x - ( a ) | < b means the distance is between the two extreme distance ( left and right side of ' a ' on number line , considering the max distance is ' b ' from ' a ' - as per this scenario . . . . . hence the value of ' a ' must be between these two extremes . | x - ( a ) | > b means the distance is greater than the distance of ' b ' . . i . e the value of a could be anywhere more than ' b ' ( i . e . current case ) . now come to the question . first its given | a | > 2 = = > a > 2 i . e . a can have any value bigger than 2 ( i . e . 3 , 4 , 5 … ) . now , lets move to equation a + 2 b = 32 = = > b = ( 32 – a ) / 2 = = > b = 16 – ( a / 2 ) . according to question , b is an integer , hence to make ‘ b ’ integer a must be divisible by 2 . minimum possible value of ‘ a ’ that is divisible by 2 is 4 ( a is greater than 2 so the next number that is divisible by 2 is 4 ) . so the answer is c ( value 4 ) . | general |
math_qa__IspdEkMIftzZRY2H | A salesman's income consists of a commission and a base salary of $350 per week. Over the past 5 weeks, his weekly income totals have been $406, $413, $420, $436 and $495. What must his average (arithmetic mean) commission be per week over the next two weeks so that his average weekly income is $500 over the 7-week period?
Choose the correct choice from the following.
A) $ 315
B) $ 245
C) $ 365
D) $ 715
E) $ 730 | <gadget id="calculator">500 * 7</gadget>
<output>3_500</output>
<gadget id="calculator">406 + 413</gadget>
<output>819</output>
<gadget id="calculator">436 + 420</gadget>
<output>856</output>
<gadget id="calculator">819 + 856</gadget>
<output>1_675</output>
<gadget id="calculator">1_675 + 495</gadget>
<output>2_170</output>
<gadget id="calculator">3_500 - 2_170</gadget>
<output>1_330</output>
<gadget id="calculator">1_330 / 2</gadget>
<output>665</output>
<gadget id="calculator">665 - 350</gadget>
<output>315</output>
<result>A</result> | A | 315 | A salesman's income consists of a commission and a base salary of $350 per week. Over the past 5 weeks, his weekly income totals have been $406, $413, $420, $436 and $495. What must his average (arithmetic mean) commission be per week over the next two weeks so that his average weekly income is $500 over the 7-week period? | {
"A": "$ 315",
"B": "$ 245",
"C": "$ 365",
"D": "$ 715",
"E": "$ 730"
} | subtract(divide(subtract(multiply(500, 7), add(add(add(406, 413), add(436, 420)), 495)), const_2), 350) | add(n2,n3)|add(n4,n5)|multiply(n7,n8)|add(#0,#1)|add(n6,#3)|subtract(#2,#4)|divide(#5,const_2)|subtract(#6,n0) | total weekly income over 5 weeks = $ 406 + $ 413 + $ 420 + $ 436 + $ 495 = $ 2170 for avg weekly income to be $ 500 over 7 weeks , we need total weekly income over 7 weeks = $ 3500 now , $ 3500 - $ 2170 = $ 1330 from this , we subtract base salary for 2 weeks i . e $ 350 * 2 = $ 700 therefore , commission = $ 1330 - $ 700 = $ 730 for 2 weeks avg weekly commission = $ 315 answer a | general |
math_qa__UNDgw0zeERIqJUMM | The Guests at a football banquet consumed a total of 411 pounds of food. if no individual guest consumed more than 2.5 pounds of food, What is the minimum number of guests that could have attended the banquet?
Answers:
A) 165 B) 161 C) 162 D) 163 E) 164 | <gadget id="calculator">411 / 2.5</gadget>
<output>164.4</output>
<gadget id="calculator">floor(164.4)</gadget>
<output>164</output>
<gadget id="calculator">164 + 1</gadget>
<output>165</output>
<result>A</result> | A | 165 | The Guests at a football banquet consumed a total of 411 pounds of food. if no individual guest consumed more than 2.5 pounds of food, What is the minimum number of guests that could have attended the banquet? | {
"A": "165",
"B": "161",
"C": "162",
"D": "163",
"E": "164"
} | add(floor(divide(411, 2.5)), const_1) | divide(n0,n1)|floor(#0)|add(#1,const_1)| | "to minimize one quantity maximize other . 164 * 2.5 ( max possible amount of food a guest could consume ) = 410 pounds , so there must be more than 164 guests , next integer is 165 . answer : a ." | general |
math_qa__CgYxDyif21O9zQoS | In an institute, 60% of the students are boys and the rest are girls. Further 15% of the boys and 7.5% of the girls are getting a fee waiver. If the number of those getting a fee waiver is 90, find the total number of students getting 50% concessions if it is given that 50% of those not getting a fee waiver are eligible to get half fee concession? Pick one.
A) 360
B) 280
C) 320
D) 330
E) 350 | <gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">(3/5) * (3/20)</gadget>
<output>9/100 = around 0.09</output>
<gadget id="calculator">1 - (3/5)</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">7.5 / 100</gadget>
<output>0.075</output>
<gadget id="calculator">(2/5) * 0.075</gadget>
<output>0.03</output>
<gadget id="calculator">(9/100) + 0.03</gadget>
<output>0.12</output>
<gadget id="calculator">90 / 0.12</gadget>
<output>750</output>
<gadget id="calculator">1 - (3/20)</gadget>
<output>17/20 = around 0.85</output>
<gadget id="calculator">(17/20) * (3/5)</gadget>
<output>51/100 = around 0.51</output>
<gadget id="calculator">(51/100) / 2</gadget>
<output>51/200 = around 0.255</output>
<gadget id="calculator">1 - 0.075</gadget>
<output>0.925</output>
<gadget id="calculator">0.925 * (2/5)</gadget>
<output>0.37</output>
<gadget id="calculator">0.37 / 2</gadget>
<output>0.185</output>
<gadget id="calculator">(51/200) + 0.185</gadget>
<output>0.44</output>
<gadget id="calculator">750 * 0.44</gadget>
<output>330</output>
<result>D</result> | D | 330 | In an institute, 60% of the students are boys and the rest are girls. Further 15% of the boys and 7.5% of the girls are getting a fee waiver. If the number of those getting a fee waiver is 90, find the total number of students getting 50% concessions if it is given that 50% of those not getting a fee waiver are eligible to get half fee concession? | {
"A": "360",
"B": "280",
"C": "320",
"D": "330",
"E": "350"
} | multiply(divide(90, add(multiply(divide(60, const_100), divide(15, const_100)), multiply(subtract(const_1, divide(60, const_100)), divide(7.5, const_100)))), add(divide(multiply(subtract(const_1, divide(15, const_100)), divide(60, const_100)), const_2), divide(multiply(subtract(const_1, divide(7.5, const_100)), subtract(const_1, divide(60, const_100))), const_2))) | divide(n0,const_100)|divide(n1,const_100)|divide(n2,const_100)|multiply(#0,#1)|subtract(const_1,#1)|subtract(const_1,#2)|subtract(const_1,#0)|multiply(#0,#4)|multiply(#5,#6)|multiply(#2,#6)|add(#3,#9)|divide(#7,const_2)|divide(#8,const_2)|add(#11,#12)|divide(n3,#10)|multiply(#13,#14) | solution : let us assume there are 100 students in the institute . then , number of boys = 60 and , number of girls = 40 further , 15 % of boys get fee waiver = 9 boys 7.5 % of girls get fee waiver = 3 girls total = 12 students who gets fee waiver but , here given 90 students are getting fee waiver . so we compare 12 = 90 so , 1 = 90 / 12 = 7.5 now number of students who are not getting fee waiver = 51 boys and 37 girls . 50 % concession = 25.5 boys and 18.5 girls ( i . e . total 44 ) . hence , required students = 44 * 7.5 = 330 . answer : option d | gain |
math_qa__eNU100PLUszFOhVa | If N = 2^0.15 and N^b = 64, b must equal Choices: A) 3 / 80 B) 3 / 5 C) 40 D) 5 / 3 E) 80 / 3 | <gadget id="calculator">log(64)</gadget>
<output>log(64) = around 4.158883</output>
<gadget id="calculator">2 ** 0.15</gadget>
<output>1.109569</output>
<gadget id="calculator">log(1.109569)</gadget>
<output>0.103972</output>
<gadget id="calculator">log(64) / 0.103972</gadget>
<output>9.61797406994191*log(64) = around 40.00003</output>
<result>C</result> | C | 40 | If N = 2^0.15 and N^b = 64, b must equal | {
"A": "3 / 80",
"B": "3 / 5",
"C": "40",
"D": "5 / 3",
"E": "80 / 3"
} | divide(log(64), log(power(2, 0.15))) | log(n2)|power(n0,n1)|log(#1)|divide(#0,#2)| | "15 / 100 = 3 / 20 n = 2 ^ 3 / 20 n ^ b = 2 ^ 6 ( 2 ^ 3 / 20 ) ^ b = 2 ^ 6 b = 40 answer : c" | general |
math_qa__UhEC0NiHCexSk9Bp | Each of the 9 squares shown is to contain one number
chosen from 1, 2, 3, 4, 5, 6, 7, 8, and 9. No number is to
be repeated. Suppose the sum of the 5 squares aligned
vertically on the right is 32 and that the sum of the 5
squares aligned horizontally on the bottom is 20. What
number goes in the shared corner square? Choose the correct choice from the following options:
A) 3 B) 4 C) 5 D) 6 E) 7 | <gadget id="calculator">1 + 2</gadget>
<output>3</output>
<gadget id="calculator">4 + 3</gadget>
<output>7</output>
<result>E</result> | E | 7 | Each of the 9 squares shown is to contain one number
chosen from 1, 2, 3, 4, 5, 6, 7, 8, and 9. No number is to
be repeated. Suppose the sum of the 5 squares aligned
vertically on the right is 32 and that the sum of the 5
squares aligned horizontally on the bottom is 20. What
number goes in the shared corner square? | {
"A": "3",
"B": "4",
"C": "5",
"D": "6",
"E": "7"
} | add(4, add(1, 2)) | add(n1,n2)|add(n4,#0) | if x is the number in the corner square , then the sum of all the numbers in the squares is equal to the sum of the numbers in the five squares aligned vertically plus the sum of the numbers in the five squares aligned horizontally minus x . hence , 1 + 2 + · · · + 9 = 32 + 20 − x . the sum on the left is 45 , so x = 52 − 45 = 7 . correct answer e | geometry |
math_qa__VuvW1ShTEvEazqS5 | In an electric circuit, two resistors with resistances x and y are connected in parallel. If R is the combined resistance of these two resistors, then the reciprocal of R is equal to the sum of the reciprocals of x and y. What is R if x is 5 Ohms and y is 7 Ohms? Select:
A) 3 / 5 B) 1 / 7 C) 12 / 35 D) 31 / 12 E) 35 / 12 | <gadget id="calculator">7 * 5</gadget>
<output>35</output>
<gadget id="calculator">5 + 7</gadget>
<output>12</output>
<gadget id="calculator">35 / 12</gadget>
<output>35/12 = around 2.916667</output>
<result>E</result> | E | 2.916667 | In an electric circuit, two resistors with resistances x and y are connected in parallel. If R is the combined resistance of these two resistors, then the reciprocal of R is equal to the sum of the reciprocals of x and y. What is R if x is 5 Ohms and y is 7 Ohms? | {
"A": "3 / 5",
"B": "1 / 7",
"C": "12 / 35",
"D": "31 / 12",
"E": "35 / 12"
} | divide(multiply(7, 5), add(5, 7)) | add(n0,n1)|multiply(n0,n1)|divide(#1,#0)| | "1 / r = 1 / x + 1 / y 1 / r = 1 / 5 + 1 / 7 = 12 / 35 r = 35 / 12 the answer is e ." | general |
math_qa__DId3hEXyHzUlaM4I | A envelop weight 8.5 gm,if 850 of these envelop are sent with an advertisement mail. How much wieght?
Choose the correct choice from the following choices.
A) 6.6 kg B) 7.225 kg C) 6.7 kg D) 6.9 kg E) 7.8 kg | <gadget id="calculator">8.5 * 850</gadget>
<output>7_225</output>
<gadget id="calculator">7_225 / 1_000</gadget>
<output>289/40 = around 7.225</output>
<result>B</result> | B | 7.225 | A envelop weight 8.5 gm,if 850 of these envelop are sent with an advertisement mail. How much wieght? | {
"A": "6.6 kg",
"B": "7.225 kg",
"C": "6.7 kg",
"D": "6.9 kg",
"E": "7.8 kg"
} | divide(multiply(8.5, 850), const_1000) | multiply(n0,n1)|divide(#0,const_1000) | 850 * 8.5 7225.0 gm 7.225 kg answer : b | general |
math_qa__IZAZ8BI2YrXnnpM2 | A can give B 90 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race? Choose the correct option:
A) 120.88
B) 120.13
C) 111.22
D) 120.0
E) 111.12 | <gadget id="calculator">100 * 10</gadget>
<output>1_000</output>
<gadget id="calculator">1_000 - 200</gadget>
<output>800</output>
<gadget id="calculator">1_000 * 800</gadget>
<output>800_000</output>
<gadget id="calculator">1_000 - 90</gadget>
<output>910</output>
<gadget id="calculator">800_000 / 910</gadget>
<output>80_000/91 = around 879.120879</output>
<gadget id="calculator">1_000 - (80_000/91)</gadget>
<output>11_000/91 = around 120.879121</output>
<result>A</result> | A | 120.88 | A can give B 90 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race? | {
"A": "120.88",
"B": "120.13",
"C": "111.22",
"D": "120.0",
"E": "111.12"
} | subtract(multiply(const_100, const_10), divide(multiply(multiply(const_100, const_10), subtract(multiply(const_100, const_10), 200)), subtract(multiply(const_100, const_10), 90))) | multiply(const_10,const_100)|subtract(#0,n1)|subtract(#0,n0)|multiply(#0,#1)|divide(#3,#2)|subtract(#0,#4)| | "a runs 1000 m while b runs 910 m and c runs 800 m . the number of meters that c runs when b runs 1000 m , = ( 1000 * 800 ) / 910 = 879.12 m . b can give c = 1000 - 879.12 = 120.88 m . answer : a" | physics |
math_qa__p28LbbmIS5nixTdd | A jar contains 6 black and 2 white balls. If you pick two balls at the same time, what's the probability that one ball is black and one is white? Choose one: A) 2 / 7 B) 5 / 7 C) 4 / 7 D) 3 / 15 E) 3 / 14 | <gadget id="calculator">6 + 2</gadget>
<output>8</output>
<gadget id="calculator">6 / 8</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">8 - 1</gadget>
<output>7</output>
<gadget id="calculator">2 / 7</gadget>
<output>2/7 = around 0.285714</output>
<gadget id="calculator">(3/4) * (2/7)</gadget>
<output>3/14 = around 0.214286</output>
<result>E</result> | E | 0.214286 | A jar contains 6 black and 2 white balls. If you pick two balls at the same time, what's the probability that one ball is black and one is white? | {
"A": "2 / 7",
"B": "5 / 7",
"C": "4 / 7",
"D": "3 / 15",
"E": "3 / 14"
} | multiply(divide(6, add(6, 2)), divide(2, subtract(add(6, 2), const_1))) | add(n0,n1)|divide(n0,#0)|subtract(#0,const_1)|divide(n1,#2)|multiply(#1,#3)| | "p ( 1 st black , 2 nd white ) = 6 / 8 * 2 / 7 = 12 / 56 ; p ( 1 st white , 2 nd black ) = 2 / 8 * 6 / 7 = 12 / 56 . p = 12 / 56 + 12 / 56 = 24 / 112 = 12 / 56 = 6 / 28 = 3 / 14 . answer : e ." | probability |
math_qa__49WUHitTl2KIZXRS | If a car had traveled 10 kmh faster than it actually did, the trip would have lasted 30 minutes less. If the car went exactly 30 km, at what speed did it travel?
Select the correct option: A) 20 kmh B) 25 kmh C) 30 kmh D) 35 kmh E) 40 kmh | <gadget id="calculator">30 * 10</gadget>
<output>300</output>
<gadget id="calculator">2 * 300</gadget>
<output>600</output>
<gadget id="calculator">600 * 4</gadget>
<output>2_400</output>
<gadget id="calculator">10 ** 2</gadget>
<output>100</output>
<gadget id="calculator">2_400 + 100</gadget>
<output>2_500</output>
<gadget id="calculator">2_500 ** (1/2)</gadget>
<output>50</output>
<gadget id="calculator">50 - 10</gadget>
<output>40</output>
<gadget id="calculator">40 / 2</gadget>
<output>20</output>
<result>A</result> | A | 20 | If a car had traveled 10 kmh faster than it actually did, the trip would have lasted 30 minutes less. If the car went exactly 30 km, at what speed did it travel? | {
"A": "20 kmh",
"B": "25 kmh",
"C": "30 kmh",
"D": "35 kmh",
"E": "40 kmh"
} | divide(subtract(sqrt(add(multiply(multiply(const_2, multiply(30, 10)), const_4), power(10, const_2))), 10), const_2) | multiply(n0,n2)|power(n0,const_2)|multiply(#0,const_2)|multiply(#2,const_4)|add(#3,#1)|sqrt(#4)|subtract(#5,n0)|divide(#6,const_2)| | "time = distance / speed difference in time = 1 / 2 hrs 30 / x - 30 / ( x + 10 ) = 1 / 2 substitute the value of x from the options . - - > x = 20 - - > 30 / 20 - 30 / 30 = 3 / 2 - 1 = 1 / 2 answer : a" | physics |
math_qa__VLgRJE2NMhh3uyRH | A man is 28 years older than his son. In two years, his age will be twice the age of his son. What is the present age of his son?
Choose the most appropriate option.
A) 23 years B) 22 years C) 21 years D) 20 years E) 26 years | <gadget id="calculator">2 * 2</gadget>
<output>4</output>
<gadget id="calculator">4 - 2</gadget>
<output>2</output>
<gadget id="calculator">28 - 2</gadget>
<output>26</output>
<gadget id="calculator">2 - 1</gadget>
<output>1</output>
<gadget id="calculator">26 / 1</gadget>
<output>26</output>
<result>E</result> | E | 26 | A man is 28 years older than his son. In two years, his age will be twice the age of his son. What is the present age of his son? | {
"A": "23 years",
"B": "22 years",
"C": "21 years",
"D": "20 years",
"E": "26 years"
} | divide(subtract(28, subtract(multiply(const_2, const_2), const_2)), subtract(const_2, const_1)) | multiply(const_2,const_2)|subtract(const_2,const_1)|subtract(#0,const_2)|subtract(n0,#2)|divide(#3,#1)| | "let present age of the son = x years then , present age the man = ( x + 28 ) years given that , in 2 years , man ' s age will be twice the age of his son â ‡ ’ ( x + 28 ) + 2 = 2 ( x + 2 ) â ‡ ’ x = 26 answer : e" | general |
math_qa__X6iTbMfIyWSgV1rS | How many numbers from 10 to 100 are exactly divisible by 9? Pick one: A) 7 B) 8 C) 10 D) 12 E) 14 | <gadget id="calculator">100 / 9</gadget>
<output>100/9 = around 11.111111</output>
<gadget id="calculator">floor(100/9)</gadget>
<output>11</output>
<gadget id="calculator">11 * 9</gadget>
<output>99</output>
<gadget id="calculator">10 / 9</gadget>
<output>10/9 = around 1.111111</output>
<gadget id="calculator">floor(10/9)</gadget>
<output>1</output>
<gadget id="calculator">1 + 1</gadget>
<output>2</output>
<gadget id="calculator">2 * 9</gadget>
<output>18</output>
<gadget id="calculator">99 - 18</gadget>
<output>81</output>
<gadget id="calculator">81 / 9</gadget>
<output>9</output>
<gadget id="calculator">9 + 1</gadget>
<output>10</output>
<result>C</result> | C | 10 | How many numbers from 10 to 100 are exactly divisible by 9? | {
"A": "7",
"B": "8",
"C": "10",
"D": "12",
"E": "14"
} | add(divide(subtract(multiply(floor(divide(100, 9)), 9), multiply(add(floor(divide(10, 9)), const_1), 9)), 9), const_1) | divide(n1,n2)|divide(n0,n2)|floor(#0)|floor(#1)|add(#3,const_1)|multiply(n2,#2)|multiply(n2,#4)|subtract(#5,#6)|divide(#7,n2)|add(#8,const_1)| | "option ' c ' 10 / 9 = 1 and 100 / 9 = 11 = = > 11 - 1 = 10 . therefore 10 digits ." | general |
math_qa__ZqOdyAPcNyXXVgLj | what is the units digit of the expression 7^75+6? Select the correct option
A) 1 B) 3 C) 5 D) 7 E) 9 | <gadget id="calculator">4 + 3</gadget>
<output>7</output>
<gadget id="calculator">7 + 2</gadget>
<output>9</output>
<result>E</result> | E | 9 | what is the units digit of the expression 7^75+6? | {
"A": "1",
"B": "3",
"C": "5",
"D": "7",
"E": "9"
} | add(add(const_4, const_3), const_2) | add(const_3,const_4)|add(#0,const_2)| | "7 in power repeats pattern of 4 : 7 - 9 - 3 - 1 . as 75 = 4 * 18 + 3 then the last digit of 7 ^ 75 is the same as the last digit of 7 ^ 3 , which is 3 . units digit of 7 ^ 75 + 6 will be : 3 + 6 = 9 . answer is e" | general |
math_qa__4uP2x133Z4l2ECxt | Two tains of equal lengths take 10 seconds and 12 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction? Pick.
A) 12 B) 14 C) 10.9 D) 20 E) 18 | <gadget id="calculator">120 + 120</gadget>
<output>240</output>
<gadget id="calculator">120 / 12</gadget>
<output>10</output>
<gadget id="calculator">120 / 10</gadget>
<output>12</output>
<gadget id="calculator">10 + 12</gadget>
<output>22</output>
<gadget id="calculator">240 / 22</gadget>
<output>120/11 = around 10.909091</output>
<result>C</result> | C | 10.9 | Two tains of equal lengths take 10 seconds and 12 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction? | {
"A": "12",
"B": "14",
"C": "10.9",
"D": "20",
"E": "18"
} | divide(add(120, 120), add(divide(120, 12), divide(120, 10))) | add(n2,n2)|divide(n2,n1)|divide(n2,n0)|add(#1,#2)|divide(#0,#3)| | "sol . speed of the first train = [ 120 / 10 ] m / sec = 12 m / sec . speed of the second train = [ 120 / 12 ] m / sec = 10 m / sec . relative speed = ( 12 + 10 ) = m / sec = 22 m / sec . ∴ required time = ( 120 + 120 ) / 22 secc = 10.9 sec . answer c" | physics |
math_qa__2t4xdjFWJjIjuU1U | 108. Triangle A’s base is 8% greater than the base of triangle B, and A’s height is 8% less than the height of triangle B. The area of triangle A is what percent less or more than the area of triangle B?
Choose the correct choice from the following options.
A) 9 % less B) 1 % less C) equal to each other D) 1.6 % more E) 9 % more | <gadget id="calculator">100 * 100</gadget>
<output>10_000</output>
<gadget id="calculator">100 + 8</gadget>
<output>108</output>
<gadget id="calculator">100 - 8</gadget>
<output>92</output>
<gadget id="calculator">108 * 92</gadget>
<output>9_936</output>
<gadget id="calculator">10_000 - 9_936</gadget>
<output>64</output>
<gadget id="calculator">100 / 64</gadget>
<output>25/16 = around 1.5625</output>
<result>D</result> | D | 1.6 | 108. Triangle A’s base is 8% greater than the base of triangle B, and A’s height is 8% less than the height of triangle B. The area of triangle A is what percent less or more than the area of triangle B? | {
"A": "9 % less",
"B": "1 % less",
"C": "equal to each other",
"D": "1.6 % more",
"E": "9 % more"
} | divide(const_100, subtract(multiply(const_100, const_100), multiply(add(const_100, 8), subtract(const_100, 8)))) | add(n1,const_100)|multiply(const_100,const_100)|subtract(const_100,n1)|multiply(#0,#2)|subtract(#1,#3)|divide(const_100,#4)| | "wish the question specified that we are talking about corresponding height . base of a = 9 / 8 * base of b height of a = 7 / 8 * height of b area of a = ( 1 / 2 ) * base of a * height of a = 9 / 8 * 7 / 8 * area of b = 63 / 64 * area of b area of a is 1.6 % more than the area of b . answer ( d )" | geometry |
math_qa__C1JJ6dWH6xZI9O5J | An agent, gets a commission of 4% on the sales of cloth. If on a certain day, he gets Rs. 12.50 as commission, the cloth sold through him on that day is worth Choose the most appropriate option:
A) 312
B) 500
C) 887
D) 299
E) 132 | <gadget id="calculator">4 / 100</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">12.5 / (1/25)</gadget>
<output>312.5</output>
<result>A</result> | A | 312 | An agent, gets a commission of 4% on the sales of cloth. If on a certain day, he gets Rs. 12.50 as commission, the cloth sold through him on that day is worth | {
"A": "312",
"B": "500",
"C": "887",
"D": "299",
"E": "132"
} | divide(12.50, divide(4, const_100)) | divide(n0,const_100)|divide(n1,#0)| | "explanation : let the total sale be rs . x . then , 4 % . of x = 12.50 = ( 4 / 100 * x ) = 12.5 < = > x = 312.5 . answer : a" | gain |
math_qa__sYACytYqM01xgC6J | The breadth of a rectangular field is 60% of its length. If the perimeter of the field is 800 m.What is the area of the field? Choose one
A) 18750 sq . m B) 37500 sq . m C) 40000 sq . m D) 48000 sq . m E) none of these | <gadget id="calculator">800 / 2</gadget>
<output>400</output>
<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(3/5) + 1</gadget>
<output>8/5 = around 1.6</output>
<gadget id="calculator">400 / (8/5)</gadget>
<output>250</output>
<gadget id="calculator">400 - 250</gadget>
<output>150</output>
<gadget id="calculator">250 * 150</gadget>
<output>37_500</output>
<result>B</result> | B | 37,500 | The breadth of a rectangular field is 60% of its length. If the perimeter of the field is 800 m.What is the area of the field? | {
"A": "18750 sq . m",
"B": "37500 sq . m",
"C": "40000 sq . m",
"D": "48000 sq . m",
"E": "none of these"
} | multiply(divide(divide(800, const_2), add(divide(60, const_100), const_1)), subtract(divide(800, const_2), divide(divide(800, const_2), add(divide(60, const_100), const_1)))) | divide(n1,const_2)|divide(n0,const_100)|add(#1,const_1)|divide(#0,#2)|subtract(#0,#3)|multiply(#3,#4) | solution so length = 250 m ; breadth = 150 m area = ( 250 x 150 ) m ² = 37500 m ² answer b | geometry |
math_qa__YRNJNGCE6Ti5UAX2 | A shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 20% while buying and by 20% while selling. What is his percentage profit? Answers.
A) 10.22 %
B) 20.22 %
C) 21.22 %
D) 50 %
E) ca n ' t be calculated | <gadget id="calculator">100 + 20</gadget>
<output>120</output>
<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">120 - 80</gadget>
<output>40</output>
<gadget id="calculator">40 * 100</gadget>
<output>4_000</output>
<gadget id="calculator">4_000 / 80</gadget>
<output>50</output>
<result>D</result> | D | 50 | A shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 20% while buying and by 20% while selling. What is his percentage profit? | {
"A": "10.22 %",
"B": "20.22 %",
"C": "21.22 %",
"D": "50 %",
"E": "ca n ' t be calculated"
} | divide(multiply(subtract(add(const_100, 20), subtract(const_100, 20)), const_100), subtract(const_100, 20)) | add(n0,const_100)|subtract(const_100,n1)|subtract(#0,#1)|multiply(#2,const_100)|divide(#3,#1)| | "the owner buys 100 kg but actually gets 120 kg ; the owner sells 100 kg but actually gives 80 kg ; profit : ( 120 - 80 ) / 80 * 100 = ~ 50 % answer : d ." | gain |
math_qa__QKHgg0zIIsuLIHtw | Compare the rates of two trains, one travelling at 45 km/hr and other is at 10m/s? Choose the correct choice from the following choices.
A) 5 : 4 B) 3 : 2 C) 1 : 5 D) 2 : 7 E) 3 : 5 | <gadget id="calculator">10 / 1_000</gadget>
<output>1/100 = around 0.01</output>
<gadget id="calculator">(1/100) * 3_600</gadget>
<output>36</output>
<gadget id="calculator">45 / 36</gadget>
<output>5/4 = around 1.25</output>
<result>A</result> | A | 1.25 | Compare the rates of two trains, one travelling at 45 km/hr and other is at 10m/s? | {
"A": "5 : 4",
"B": "3 : 2",
"C": "1 : 5",
"D": "2 : 7",
"E": "3 : 5"
} | divide(45, multiply(divide(10, const_1000), const_3600)) | divide(n1,const_1000)|multiply(#0,const_3600)|divide(n0,#1)| | "speed of the 1 st train = 45 km / hr speed of the 2 nd train = 10 m / s = 10 * 18 / 5 = 36 km / hr ratio of the speeds of the train = 45 : 36 = 5 : 4 answer is a" | gain |
math_qa__EWtZWVUw4YadaLIH | A scuba diver descends at a rate of 32 feet per minute. a diver dive from a ship to search for a lost ship at the depth of 6400feet below the sea level..how long will he take to reach the ship? Choose the correct choice from the following:
A) 200 minutes B) 240 minutes C) 220 minutes D) 210 minutes E) 77 minutes | <gadget id="calculator">6_400 / 32</gadget>
<output>200</output>
<result>A</result> | A | 200 | A scuba diver descends at a rate of 32 feet per minute. a diver dive from a ship to search for a lost ship at the depth of 6400feet below the sea level..how long will he take to reach the ship? | {
"A": "200 minutes",
"B": "240 minutes",
"C": "220 minutes",
"D": "210 minutes",
"E": "77 minutes"
} | divide(6400, 32) | divide(n1,n0)| | "time taken to reach = 6400 / 32 = 200 minutes answer : a" | gain |
math_qa__1DrVdzVK2gTMThFL | A clock shows the time as 9 a.m. If the minute hand gains 5 minutes every hour, how many minutes will the clock gain by 6 p.m.?
Pick.
A) 30 min B) 35 min C) 45 min D) 50 min E) 55 min | <gadget id="calculator">3 + 6</gadget>
<output>9</output>
<gadget id="calculator">9 * 5</gadget>
<output>45</output>
<result>C</result> | C | 45 | A clock shows the time as 9 a.m. If the minute hand gains 5 minutes every hour, how many minutes will the clock gain by 6 p.m.? | {
"A": "30 min",
"B": "35 min",
"C": "45 min",
"D": "50 min",
"E": "55 min"
} | multiply(add(const_3, 6), 5) | add(const_3,n2)|multiply(n1,#0)| | "there are 9 hours in between 9 a . m . to 6 p . m . 9 * 5 = 45 minutes . answer : c" | physics |
math_qa__wWTahzZH6b2aWLiV | A box contains either blue or red flags. The total number of flags in the box is an even number. A group of children are asked to pick up two flags each. If all the flags are used up in the process such that 60% of the children have blue flags, and 65% have red flags, what percentage of children have flags of both the colors? Choose the correct choice from the following answers.
A) 5 %
B) 10 %
C) 15 %
D) 20 %
E) 25 % | <gadget id="calculator">60 + 65</gadget>
<output>125</output>
<gadget id="calculator">125 - 100</gadget>
<output>25</output>
<result>E</result> | E | 25 | A box contains either blue or red flags. The total number of flags in the box is an even number. A group of children are asked to pick up two flags each. If all the flags are used up in the process such that 60% of the children have blue flags, and 65% have red flags, what percentage of children have flags of both the colors? | {
"A": "5 %",
"B": "10 %",
"C": "15 %",
"D": "20 %",
"E": "25 %"
} | subtract(add(60, 65), const_100) | add(n0,n1)|subtract(#0,const_100)| | "solution : let the total number of flags be 100 ( even number ) let the total number of ' blue ' flags alone be ' a ' let the total number of ' red ' flags alone be ' b ' let the total number of ' both ' flags be ' c ' we have given , total number of blue flags = 60 % = 60 = a + c total number of red flags = 65 % = 65 = b + c total number of flags = a + b + c = 100 ( since all the flags have been utilized ) so , substituting for c in the third equation , we have , 60 - c + c + 65 - c = 100 c = 25 option e ." | general |
math_qa__8qTWJDiNvyC17zy9 | The profit earned by selling an article for Rs. 832 is equal to the loss incurred when the same article is sold for Rs. 448. What should be the sale price for making 80% profit? Answers
A) 1152
B) 230
C) 960
D) 780
E) 400 | <gadget id="calculator">832 - 448</gadget>
<output>384</output>
<gadget id="calculator">384 / 2</gadget>
<output>192</output>
<gadget id="calculator">832 - 192</gadget>
<output>640</output>
<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">1 + (4/5)</gadget>
<output>9/5 = around 1.8</output>
<gadget id="calculator">640 * (9/5)</gadget>
<output>1_152</output>
<result>A</result> | A | 1,152 | The profit earned by selling an article for Rs. 832 is equal to the loss incurred when the same article is sold for Rs. 448. What should be the sale price for making 80% profit? | {
"A": "1152",
"B": "230",
"C": "960",
"D": "780",
"E": "400"
} | multiply(subtract(832, divide(subtract(832, 448), const_2)), add(const_1, divide(80, const_100))) | divide(n2,const_100)|subtract(n0,n1)|add(#0,const_1)|divide(#1,const_2)|subtract(n0,#3)|multiply(#2,#4)| | "c . p . = rs . x . then , 832 - x = x - 448 2 x = 1280 = > x = 640 required s . p . = 180 % of rs . 640 = 180 / 100 * 640 = rs . 1152 . a" | gain |
math_qa__SYuDm0hFDKcn7wrF | Find the distance covered by a man walking for 30min at a speed of 5km/hr? Answers:
A) 1 km
B) 3 km
C) 4 km
D) 2.5 km
E) 6 km | <gadget id="calculator">5 * 1_000</gadget>
<output>5_000</output>
<gadget id="calculator">5_000 / 60</gadget>
<output>250/3 = around 83.333333</output>
<gadget id="calculator">30 * (250/3)</gadget>
<output>2_500</output>
<gadget id="calculator">2_500 / 1_000</gadget>
<output>5/2 = around 2.5</output>
<result>D</result> | D | 2.5 | Find the distance covered by a man walking for 30min at a speed of 5km/hr? | {
"A": "1 km",
"B": "3 km",
"C": "4 km",
"D": "2.5 km",
"E": "6 km"
} | divide(multiply(30, divide(multiply(5, const_1000), const_60)), const_1000) | multiply(n1,const_1000)|divide(#0,const_60)|multiply(n0,#1)|divide(#2,const_1000)| | "distance = 5 * 30 / 60 = 2.5 km answer is d" | physics |
math_qa__wigdnZCxvHP7qSZR | Dacid obtained 96, 95, 82, 87 and 92 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
Choices: A) 67 B) 26 C) 87 D) 26 E) 90 | <gadget id="calculator">96 + 95</gadget>
<output>191</output>
<gadget id="calculator">191 + 82</gadget>
<output>273</output>
<gadget id="calculator">273 + 87</gadget>
<output>360</output>
<gadget id="calculator">360 + 92</gadget>
<output>452</output>
<gadget id="calculator">10 / 2</gadget>
<output>5</output>
<gadget id="calculator">452 / 5</gadget>
<output>452/5 = around 90.4</output>
<result>E</result> | E | 90 | Dacid obtained 96, 95, 82, 87 and 92 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks? | {
"A": "67",
"B": "26",
"C": "87",
"D": "26",
"E": "90"
} | divide(add(add(add(add(96, 95), 82), 87), 92), divide(const_10, const_2)) | add(n0,n1)|divide(const_10,const_2)|add(n2,#0)|add(n3,#2)|add(n4,#3)|divide(#4,#1)| | "average = ( 96 + 95 + 82 + 87 + 92 ) / 5 = 452 / 5 = 90 . answer : e" | general |
math_qa__CYz73w6WSIY2tRmZ | A person can row at 10 kmph in still water. If the velocity of the current is 2 kmph and it takes him 15 hour to row to a place and come back, how far is the place?
Select: A) 24 km B) 30 km C) 48 km D) 72 km E) 15 km | <gadget id="calculator">10 - 2</gadget>
<output>8</output>
<gadget id="calculator">10 + 2</gadget>
<output>12</output>
<gadget id="calculator">8 * 12</gadget>
<output>96</output>
<gadget id="calculator">96 * 15</gadget>
<output>1_440</output>
<gadget id="calculator">8 + 12</gadget>
<output>20</output>
<gadget id="calculator">1_440 / 20</gadget>
<output>72</output>
<result>D</result> | D | 72 | A person can row at 10 kmph in still water. If the velocity of the current is 2 kmph and it takes him 15 hour to row to a place and come back, how far is the place? | {
"A": "24 km",
"B": "30 km",
"C": "48 km",
"D": "72 km",
"E": "15 km"
} | divide(multiply(multiply(subtract(10, 2), add(10, 2)), 15), add(subtract(10, 2), add(10, 2))) | add(n0,n1)|subtract(n0,n1)|add(#0,#1)|multiply(#0,#1)|multiply(n2,#3)|divide(#4,#2)| | "speed of down stream = 10 + 2 = 12 kmph speed of upstream = 10 - 2 = 8 kmph let the required distance be xkm x / 12 + x / 8 = 15 2 x + 3 x = 360 x = 72 km answer is d" | physics |
math_qa__CBTROoHAgmV1ULDn | Of the 80 people in a room, 2/5 are women. If 1/2 of the people are married, what is the maximum number of women in the room who could be unmarried? Choose the correct answer
A) 20
B) 22
C) 26
D) 30
E) 32 | <gadget id="calculator">2 / 5</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">80 * (2/5)</gadget>
<output>32</output>
<result>E</result> | E | 32 | Of the 80 people in a room, 2/5 are women. If 1/2 of the people are married, what is the maximum number of women in the room who could be unmarried? | {
"A": "20",
"B": "22",
"C": "26",
"D": "30",
"E": "32"
} | multiply(80, divide(2, 5)) | divide(n1,n2)|multiply(n0,#0)| | "women = 2 / 5 * 80 = 32 married = 1 / 2 * 80 = 40 unmarried = 40 max ( un - married women ) = 32 e" | general |
math_qa__3v3kvLX7IC4lSN0r | In a group of ducks and cows, the total number of legs are 32 more than twice the no. of heads. Find the total no.of buffaloes. Choose the correct option: A) 11 B) 12 C) 14 D) 16 E) 18 | <gadget id="calculator">32 / 2</gadget>
<output>16</output>
<result>D</result> | D | 16 | In a group of ducks and cows, the total number of legs are 32 more than twice the no. of heads. Find the total no.of buffaloes. | {
"A": "11",
"B": "12",
"C": "14",
"D": "16",
"E": "18"
} | divide(32, const_2) | divide(n0,const_2)| | "let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 32 = > 2 x = 32 = > x = 16 d" | general |
math_qa__essaeC4w6sfNkvlL | Two pipes A and B can fill a tank in 24 hours and 36 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?
Select:
A) 20 hours B) 15 hours C) 14 2 / 5 hours D) 12 hours E) 8 hours | <gadget id="calculator">1 / 24</gadget>
<output>1/24 = around 0.041667</output>
<gadget id="calculator">1 / 36</gadget>
<output>1/36 = around 0.027778</output>
<gadget id="calculator">(1/24) + (1/36)</gadget>
<output>5/72 = around 0.069444</output>
<gadget id="calculator">1 / (5/72)</gadget>
<output>72/5 = around 14.4</output>
<result>C</result> | C | 14 | Two pipes A and B can fill a tank in 24 hours and 36 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank? | {
"A": "20 hours",
"B": "15 hours",
"C": "14 2 / 5 hours",
"D": "12 hours",
"E": "8 hours"
} | divide(const_1, add(divide(const_1, 24), divide(const_1, 36))) | divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|divide(const_1,#2)| | "part filled by a in 1 hour = 1 / 24 part filled by b in 1 hour = 1 / 36 part filled by ( a + b ) in 1 hour = 1 / 24 + 1 / 36 = 5 / 72 both the pipes together fill the tank in 72 / 5 = 14 2 / 5 hours answer is c" | physics |
math_qa__oIaep8YlMCckrYF0 | In 1 kg mixture of iron and manganese 20% of manganese. How much iron should be added so that
the proportion of manganese becomes 10% Choose one
A) 1.5 kg B) 2 kg C) . 5 kg D) 1 kg E) none of these | <gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/5) / (1/10)</gadget>
<output>2</output>
<gadget id="calculator">2 - 1</gadget>
<output>1</output>
<result>D</result> | D | 1 | In 1 kg mixture of iron and manganese 20% of manganese. How much iron should be added so that
the proportion of manganese becomes 10% | {
"A": "1.5 kg",
"B": "2 kg",
"C": ". 5 kg",
"D": "1 kg",
"E": "none of these"
} | subtract(divide(divide(20, const_100), divide(10, const_100)), 1) | divide(n1,const_100)|divide(n2,const_100)|divide(#0,#1)|subtract(#2,n0) | explanation : by the rule of alligation , we have percentage concentration of manganese in the mixture : 20 percentage concentration of manganese in pure iron : 0 percentage concentration of manganese in the final mixture 10 10 - 0 = 10 20 - 10 = 10 = > quantity of the mixture : quantity of iron = 10 : 10 = 1 : 1 given that quantity of the mixture = 1 kg hence quantity of iron to be added = 1 kg answer : option d | general |
math_qa__dkOdpZ11ffEv2K2T | A recipe requires 2 1/2 (mixed number) cups of flour 2 3/4 (mixed number) cups of sugar and 1 1/3 (mixed number) cups of milk to make one cake. Victor has 15 cups if flour, 16 cups of sugar and 8 cups of milk. What is the greatest number of cakes john can make using this recipe? Choose the correct choice from the following:
A) 5
B) 6
C) 7
D) 8
E) 9 | <gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">2 + (1/2)</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">15 / (5/2)</gadget>
<output>6</output>
<gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(3/4) + 2</gadget>
<output>11/4 = around 2.75</output>
<gadget id="calculator">16 / (11/4)</gadget>
<output>64/11 = around 5.818182</output>
<gadget id="calculator">floor(64/11)</gadget>
<output>5</output>
<gadget id="calculator">min(6, 5)</gadget>
<output>5</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(1/3) + 1</gadget>
<output>4/3 = around 1.333333</output>
<gadget id="calculator">8 / (4/3)</gadget>
<output>6</output>
<gadget id="calculator">min(5, 6)</gadget>
<output>5</output>
<result>A</result> | A | 5 | A recipe requires 2 1/2 (mixed number) cups of flour 2 3/4 (mixed number) cups of sugar and 1 1/3 (mixed number) cups of milk to make one cake. Victor has 15 cups if flour, 16 cups of sugar and 8 cups of milk. What is the greatest number of cakes john can make using this recipe? | {
"A": "5",
"B": "6",
"C": "7",
"D": "8",
"E": "9"
} | min(min(divide(15, add(2, divide(1, 2))), floor(divide(16, add(divide(3, 4), 2)))), divide(8, add(divide(1, 3), 1))) | divide(n1,n4)|divide(n1,n0)|divide(n4,n5)|add(n1,#0)|add(n0,#1)|add(n0,#2)|divide(n11,#3)|divide(n9,#4)|divide(n10,#5)|floor(#8)|min(#7,#9)|min(#6,#10)| | "less work up front : go through each item and see what the greatest number of cakes you can make with each . the lowest of these will be the right answer . flour : 15 cups , we need 2.5 cups each . just keep going up the line to see how many cakes we can make : that means i can make 2 cakes with 5 cups , so 6 cakes overall with 15 cups . i ' ve already got the answer narrowed to either a or b . sugar : 16 cups , we need 2.75 cups each . same principle . i can make 2 cups with 5.5 cups , so to make 6 cakes i ' d need 16.5 cups . i do n ' t have that much sugar , so we ' re limited to 5 cakes . no need to even do milk because we ' re already at 5 . sugar will be the limiting factor . answer is a" | general |
math_qa__IBLQnKMHQXByB4lO | A meal cost $ 36.50 and there was no tax. If the tip was more than 10 pc but less than 15pc of the price, then the total amount paid should be: Choose the correct choice
A) 40 - 42 B) 39 - 41 C) 38 - 40 D) 37 - 39 E) 36 - 37 | <gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">36.5 * (3/20)</gadget>
<output>5.475</output>
<gadget id="calculator">5.475 + 36.5</gadget>
<output>41.975</output>
<result>A</result> | A | 40 | A meal cost $ 36.50 and there was no tax. If the tip was more than 10 pc but less than 15pc of the price, then the total amount paid should be: | {
"A": "40 - 42",
"B": "39 - 41",
"C": "38 - 40",
"D": "37 - 39",
"E": "36 - 37"
} | add(multiply(36.50, divide(15, const_100)), 36.50) | divide(n2,const_100)|multiply(n0,#0)|add(n0,#1)| | "10 % ( 36.5 ) = 3.65 15 % ( 36.5 ) = 5.475 total amount could have been 36.5 + 3.65 and 36.5 + 5.475 = > could have been between 40.15 and 41.975 = > approximately between 40 and 42 answer is a ." | general |
math_qa__c1xfTV5uC2Xj9zkf | Imagine an analog clock set to 12 o'clock. Note that the hour and minute hands overlap. How many times each day do both the hour and minute hands overlap? How would you determine the exact times of the day that this occurs? Choose the correct choice from the following choices
A) 11
B) 12
C) 22
D) 24
E) 44 | <gadget id="calculator">12 - 1</gadget>
<output>11</output>
<gadget id="calculator">11 * 2</gadget>
<output>22</output>
<result>C</result> | C | 22 | Imagine an analog clock set to 12 o'clock. Note that the hour and minute hands overlap. How many times each day do both the hour and minute hands overlap? How would you determine the exact times of the day that this occurs? | {
"A": "11",
"B": "12",
"C": "22",
"D": "24",
"E": "44"
} | multiply(subtract(12, const_1), const_2) | subtract(n0,const_1)|multiply(#0,const_2) | 22 times in a day . 12,1 hours 60 / 11 minutes , 2 hours 120 / 11 minutes , . . . so on till 12 ( 11 hours 660 / 11 minutes ) answer : c | physics |
math_qa__B44gWVaSmgyVl4QJ | Jamshid can paint a fence in 50 percent less time than Taimour can when each works alone. When they work together, they can paint the fence in 7 hours. How long would it take Taimour to paint the fence alone? Choose the correct answer: A) 6 hours B) 8 hours C) 14 hours D) 21 hours E) 32 hours | <gadget id="calculator">7 * 3</gadget>
<output>21</output>
<result>D</result> | D | 21 | Jamshid can paint a fence in 50 percent less time than Taimour can when each works alone. When they work together, they can paint the fence in 7 hours. How long would it take Taimour to paint the fence alone? | {
"A": "6 hours",
"B": "8 hours",
"C": "14 hours",
"D": "21 hours",
"E": "32 hours"
} | multiply(7, const_3) | multiply(n1,const_3)| | "i believe the answer is d . please see below for explanation . if jamshid can paint a dence in 50 percent less time then taimour we can infer the following rate j = 2 t if working together they can do the job in 8 hours we can infer 1 = 2 t + t * 7 = > 1 / 21 working alone taimour can do the job in 1 = 1 / 21 * hours = > 21 answer d" | physics |
math_qa__YxQbBTPtPch2Ypor | 12 buckets of water fill a tank when the capacity of each bucket is 81 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 9 litres? Choices.
A) 96 B) 110 C) 100 D) 90 E) 108 | <gadget id="calculator">81 * 12</gadget>
<output>972</output>
<gadget id="calculator">972 / 9</gadget>
<output>108</output>
<result>E</result> | E | 108 | 12 buckets of water fill a tank when the capacity of each bucket is 81 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 9 litres? | {
"A": "96",
"B": "110",
"C": "100",
"D": "90",
"E": "108"
} | divide(multiply(81, 12), 9) | multiply(n0,n1)|divide(#0,n2)| | "capacity of the tank = ( 12 ã — 81 ) litre number of buckets required of capacity of each bucket is 17 litre = 12 ã — 81 / 9 = 12 ã — 9 = 108 answer is e" | physics |
math_qa__kAQbFB6OJ8Z1HbEz | The number 83 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers? Choose the correct choice from the following options
A) 17 B) 16 C) 15 D) 14 E) 13 | <gadget id="calculator">4 + 3</gadget>
<output>7</output>
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">7 + 5</gadget>
<output>12</output>
<gadget id="calculator">12 + 3</gadget>
<output>15</output>
<result>C</result> | C | 15 | The number 83 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers? | {
"A": "17",
"B": "16",
"C": "15",
"D": "14",
"E": "13"
} | add(add(add(const_4, const_3), add(const_3, const_2)), 3) | add(const_3,const_4)|add(const_2,const_3)|add(#0,#1)|add(n1,#2) | 7 ^ 2 + 5 ^ 2 + 3 ^ 2 = 49 + 25 + 9 = 83 7 + 5 + 3 = 15 hence answer is c | geometry |
math_qa__spZY0dZItzFMl5Aj | A man buys an article for $110. and sells it for $125. Find the gain percent? Choose the correct choice from the following answers:
A) 10 %
B) 13.6 %
C) 25 %
D) 20 %
E) 30 % | <gadget id="calculator">110 / 100</gadget>
<output>11/10 = around 1.1</output>
<gadget id="calculator">125 / (11/10)</gadget>
<output>1_250/11 = around 113.636364</output>
<gadget id="calculator">(1_250/11) - 100</gadget>
<output>150/11 = around 13.636364</output>
<result>B</result> | B | 13.6 | A man buys an article for $110. and sells it for $125. Find the gain percent? | {
"A": "10 %",
"B": "13.6 %",
"C": "25 %",
"D": "20 %",
"E": "30 %"
} | subtract(divide(125, divide(110, const_100)), const_100) | divide(n0,const_100)|divide(n1,#0)|subtract(#1,const_100)| | "c . p . = $ 110 s . p . = $ 125 gain = $ 15 gain % = 15 / 110 * 100 = 13.6 % answer is b" | gain |
math_qa__EOPbr1gtBqDO7Bwr | The slant height of a cone is 10 cm and radius of the base is 5cm, find the curved surface of the cone?
Choose the correct option
A) 150
B) 155
C) 158
D) 157
E) 190 | <gadget id="calculator">pi * 5</gadget>
<output>5*pi = around 15.707963</output>
<gadget id="calculator">(5*pi) * 10</gadget>
<output>50*pi = around 157.079633</output>
<result>D</result> | D | 157 | The slant height of a cone is 10 cm and radius of the base is 5cm, find the curved surface of the cone? | {
"A": "150",
"B": "155",
"C": "158",
"D": "157",
"E": "190"
} | multiply(multiply(const_pi, 5), 10) | multiply(n1,const_pi)|multiply(n0,#0)| | "π * 10 * 5 = 157 answer : d" | geometry |
math_qa__uHllgzaNTqFPOi1d | Excluding stoppages, the speed of a train is 54 kmph and including stoppages it is 36 kmph. Of how many minutes does the train stop per hour?
Pick one:
A) 20 B) 17 C) 15 D) 18 E) 12 | <gadget id="calculator">36 / 54</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">60 * (2/3)</gadget>
<output>40</output>
<gadget id="calculator">60 - 40</gadget>
<output>20</output>
<result>A</result> | A | 20 | Excluding stoppages, the speed of a train is 54 kmph and including stoppages it is 36 kmph. Of how many minutes does the train stop per hour? | {
"A": "20",
"B": "17",
"C": "15",
"D": "18",
"E": "12"
} | subtract(const_60, multiply(const_60, divide(36, 54))) | divide(n1,n0)|multiply(#0,const_60)|subtract(const_60,#1)| | "t = 18 / 54 * 60 = 20 answer : a" | physics |
math_qa__ACSa6bhp2Aoypykd | A rectangular region has a fence along three sides and a wall along the fourth side. The fenced side opposite the wall is twice the length of each of the other two fenced sides. If the area of the rectangular region is 200 square feet, what is the total length of the fence, in feet? Choose the most appropriate option: A) 10 B) 20 C) 30 D) 40 E) 80 | <gadget id="calculator">1 + 1</gadget>
<output>2</output>
<gadget id="calculator">2 * 2</gadget>
<output>4</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">2 * 5</gadget>
<output>10</output>
<gadget id="calculator">10 + 10</gadget>
<output>20</output>
<gadget id="calculator">10 + 20</gadget>
<output>30</output>
<gadget id="calculator">5 + 10</gadget>
<output>15</output>
<gadget id="calculator">15 + 5</gadget>
<output>20</output>
<gadget id="calculator">200 / 20</gadget>
<output>10</output>
<gadget id="calculator">30 + 10</gadget>
<output>40</output>
<result>D</result> | D | 40 | A rectangular region has a fence along three sides and a wall along the fourth side. The fenced side opposite the wall is twice the length of each of the other two fenced sides. If the area of the rectangular region is 200 square feet, what is the total length of the fence, in feet? | {
"A": "10",
"B": "20",
"C": "30",
"D": "40",
"E": "80"
} | add(add(multiply(const_2, add(multiply(add(const_1, const_1), const_2), const_1)), add(multiply(const_2, add(multiply(add(const_1, const_1), const_2), const_1)), multiply(const_2, add(multiply(add(const_1, const_1), const_2), const_1)))), divide(200, add(add(add(multiply(add(const_1, const_1), const_2), const_1), multiply(const_2, add(multiply(add(const_1, const_1), const_2), const_1))), add(multiply(add(const_1, const_1), const_2), const_1)))) | add(const_1,const_1)|multiply(#0,const_2)|add(#1,const_1)|multiply(#2,const_2)|add(#3,#3)|add(#2,#3)|add(#4,#3)|add(#5,#2)|divide(n0,#7)|add(#6,#8) | two sides each = x the third = 2 x and the wall length is thus 2 x too x * 2 x = 2 x ^ 2 = 200 ie x ^ 2 = 100 ie x = 10 l = 20 w = 10 total lenght of fence = 2 * 10 + 20 = 40 my answer is d | geometry |
math_qa__y02VC6LRROyqz4iD | If x ¤ y = (x + y)^2 - (x - y)^2. Then √3 ¤ √3 =
Choose one:
A) 0 B) 5 C) 12 D) 15 E) 20 | <gadget id="calculator">3 ** (1/2)</gadget>
<output>sqrt(3) = around 1.732051</output>
<gadget id="calculator">(sqrt(3)) + (sqrt(3))</gadget>
<output>2*sqrt(3) = around 3.464102</output>
<gadget id="calculator">(2*sqrt(3)) ** 2</gadget>
<output>12</output>
<result>C</result> | C | 12 | If x ¤ y = (x + y)^2 - (x - y)^2. Then √3 ¤ √3 = | {
"A": "0",
"B": "5",
"C": "12",
"D": "15",
"E": "20"
} | power(add(sqrt(3), sqrt(3)), 2) | sqrt(n2)|add(#0,#0)|power(#1,n0)| | "x = √ 3 and y also = √ 3 applying the function ( √ 3 + √ 3 ) ^ 2 - ( √ 3 - √ 3 ) ^ 2 = ( 2 √ 3 ) ^ 2 - 0 = 4 x 3 = 12 . note : alternative approach is the entire function is represented as x ^ 2 - y ^ 2 = ( x + y ) ( x - y ) which can be simplified as ( x + y + x - y ) ( x + y - ( x - y ) ) = ( 2 x ) ( 2 y ) = 4 xy . substituting x = √ 3 and y = √ 3 you get the answer 12 . answer c" | general |
math_qa__doXiA4c201nHZASp | Hillary and Eddy are climbing to the summit of Mt. Everest from a base camp 5,000 ft from the summit. When they depart for the summit at 06:00, Hillary climbs at a rate of 800 ft/hr with Eddy lagging behind at a slower rate of 500 ft/hr. If Hillary stops 1000 ft short of the summit and then descends at a rate of 1,000 ft/hr, at what time do Hillary and Eddy pass each other on her return trip? Choose the correct option: A) 11.0 B) 12.0 C) 13.0 D) 14.0 E) 15.0 | <gadget id="calculator">500 / 100</gadget>
<output>5</output>
<gadget id="calculator">5 - 1</gadget>
<output>4</output>
<gadget id="calculator">800 / 1_000</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">4 / (4/5)</gadget>
<output>5</output>
<gadget id="calculator">500 / 1_000</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(4/5) - (1/2)</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">(1/2) + 1</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">(3/2) / (3/2)</gadget>
<output>1</output>
<gadget id="calculator">1 + 5</gadget>
<output>6</output>
<gadget id="calculator">6 + 6</gadget>
<output>12</output>
<result>B</result> | B | 12 | Hillary and Eddy are climbing to the summit of Mt. Everest from a base camp 5,000 ft from the summit. When they depart for the summit at 06:00, Hillary climbs at a rate of 800 ft/hr with Eddy lagging behind at a slower rate of 500 ft/hr. If Hillary stops 1000 ft short of the summit and then descends at a rate of 1,000 ft/hr, at what time do Hillary and Eddy pass each other on her return trip? | {
"A": "11.0",
"B": "12.0",
"C": "13.0",
"D": "14.0",
"E": "15.0"
} | add(6, add(divide(multiply(divide(subtract(divide(500, const_100), const_1), divide(800, const_1000)), subtract(divide(800, const_1000), divide(500, const_1000))), add(divide(500, const_1000), const_1)), divide(subtract(divide(500, const_100), const_1), divide(800, const_1000)))) | divide(n4,const_100)|divide(n3,const_1000)|divide(n4,const_1000)|add(#2,const_1)|subtract(#0,const_1)|subtract(#1,#2)|divide(#4,#1)|multiply(#6,#5)|divide(#7,#3)|add(#8,#6)|add(n1,#9) | solution : h stopped 1000 ft before reaching the final point , time taken to reach 4000 ft = 4000 / 800 = 5 hrs . this means she reached there at 11 : 00 . speed difference between them is 800 - 500 = 300 ft / hr so by the time h stops they have 1500 ft of distance so now here we use relative speed formula they both are travelling toward each other with speed of 1000 and 500 total 1500 ft / hr and distance bwn them is 1500 ft so time taken to meet = 1 hr from 11 : 00 means 12 : 00 is the answer . b | general |
math_qa__xUHSNQyAhtNqg4Jg | A car drives 60 miles on local roads at 20 mph, and 120 miles on the highway at 60 mph, what is the average speed of the entire trip?
Select the correct option.
A) 36 mph
B) 40 mph
C) 44 mph
D) 52 mph
E) 58 mph | <gadget id="calculator">60 + 120</gadget>
<output>180</output>
<gadget id="calculator">60 / 20</gadget>
<output>3</output>
<gadget id="calculator">120 / 60</gadget>
<output>2</output>
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">180 / 5</gadget>
<output>36</output>
<result>A</result> | A | 36 | A car drives 60 miles on local roads at 20 mph, and 120 miles on the highway at 60 mph, what is the average speed of the entire trip? | {
"A": "36 mph",
"B": "40 mph",
"C": "44 mph",
"D": "52 mph",
"E": "58 mph"
} | divide(add(60, 120), add(divide(60, 20), divide(120, 60))) | add(n0,n2)|divide(n0,n1)|divide(n2,n3)|add(#1,#2)|divide(#0,#3)| | "so the answer is plainly a . . . . we have a general relation for speed , time and distance : v ( velocity ) * t ( time ) = d ( distance ) for first part we have d = 60 miles , and v = 20 mph so we can obtain time : 20 * t = 60 or t = 60 / 20 = 3 hours the needed time to cover 60 miles in the same way we should divide 120 to 60 to find the needed time to cover 120 miles , so t = 2 hours so the total time for covering total distance would be 3 + 2 = 5 hours and total distance is 60 + 120 = 180 miles final stage : average speed is total distance divide to total time : 180 / 5 = 36 miles per hour . . . ." | physics |
math_qa__rgcam161WZxlpZh1 | How many kg of pure salt must be added to 100kg of 10% solution of salt and water to increase it to a 20% solution? Choices.
A) 6.7 B) 1.3 C) 9.6 D) 12.5 E) 7.9 | <gadget id="calculator">20 - 10</gadget>
<output>10</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">10 / (4/5)</gadget>
<output>25/2 = around 12.5</output>
<result>D</result> | D | 12.5 | How many kg of pure salt must be added to 100kg of 10% solution of salt and water to increase it to a 20% solution? | {
"A": "6.7",
"B": "1.3",
"C": "9.6",
"D": "12.5",
"E": "7.9"
} | divide(subtract(20, 10), subtract(const_1, divide(20, 100))) | divide(n2,n0)|subtract(n2,n1)|subtract(const_1,#0)|divide(#1,#2)| | "amount salt in 100 kg solution = 10 * 100 / 100 = 10 kg let x kg of pure salt be added then ( 10 + x ) / ( 100 + x ) = 20 / 100 100 + 10 x = 200 + 2 x 8 x = 100 x = 12.5 answer is d" | general |
math_qa__ru8Zb4BhhSnmVrkW | If a triangle in the xy-coordinate system has vertices at (-2 , -3), (4, -3) and (28, 7), what is the area of the triangle? Pick one:
A) 30 B) 36 C) 48 D) 60 E) 65 | <gadget id="calculator">28 + 2</gadget>
<output>30</output>
<gadget id="calculator">30 ** 2</gadget>
<output>900</output>
<gadget id="calculator">7 + 3</gadget>
<output>10</output>
<gadget id="calculator">10 ** 2</gadget>
<output>100</output>
<gadget id="calculator">900 + 100</gadget>
<output>1_000</output>
<gadget id="calculator">1_000 ** (1/2)</gadget>
<output>10*sqrt(10) = around 31.622777</output>
<gadget id="calculator">28 - 4</gadget>
<output>24</output>
<gadget id="calculator">24 ** 2</gadget>
<output>576</output>
<gadget id="calculator">576 + 100</gadget>
<output>676</output>
<gadget id="calculator">676 ** (1/2)</gadget>
<output>26</output>
<gadget id="calculator">4 + 2</gadget>
<output>6</output>
<gadget id="calculator">6 ** 2</gadget>
<output>36</output>
<gadget id="calculator">36 ** (1/2)</gadget>
<output>6</output>
<gadget id="calculator">((((10*sqrt(10)) + 26 + 6) / 2) * (((10*sqrt(10)) + 26 + 6) / 2 - (10*sqrt(10))) * (((10*sqrt(10)) + 26 + 6) / 2 - 26) * (((10*sqrt(10)) + 26 + 6) / 2 - 6)) ** (1/2)</gadget>
<output>sqrt(-10 + 5*sqrt(10))*sqrt(10 + 5*sqrt(10))*sqrt(16 - 5*sqrt(10))*sqrt(5*sqrt(10) + 16) = around 30</output>
<result>A</result> | A | 30 | If a triangle in the xy-coordinate system has vertices at (-2 , -3), (4, -3) and (28, 7), what is the area of the triangle? | {
"A": "30",
"B": "36",
"C": "48",
"D": "60",
"E": "65"
} | triangle_area_three_edges(sqrt(add(power(add(28, 2), const_2), power(add(7, 3), const_2))), sqrt(add(power(subtract(28, 4), const_2), power(add(7, 3), const_2))), sqrt(power(add(4, 2), const_2))) | add(n0,n4)|add(n1,n5)|add(n0,n2)|subtract(n4,n2)|power(#0,const_2)|power(#1,const_2)|power(#3,const_2)|power(#2,const_2)|add(#4,#5)|add(#6,#5)|sqrt(#7)|sqrt(#8)|sqrt(#9)|triangle_area_three_edges(#11,#12,#10) | ( - 2 , - 3 ) is in 3 rd quadrant , ( 4 , - 3 ) is in 4 th quadrant while ( 28,7 ) is in 1 st quadrant . also , y coordinate of ( - 2 , - 3 ) and ( 4 , - 3 ) is same so they lie on same horizontal line . so base of triangle = sqrt [ ( - 3 + 3 ) ^ 2 + ( 4 + 2 ) ^ 2 ] = 6 and height of triangle = 7 - ( - 3 ) = 10 so area of triangle = 1 / 2 * 6 * 10 = 30 hence option ( a ) , | geometry |
math_qa__lpOIOviiMiTcDash | A man can row upstream at 20 kmph and downstream at 80 kmph, and then find the speed of the man in still water?
Choose the correct option: A) 32 kmph B) 50 kmph C) 30 kmph D) 45 kmph E) 65 kmph | <gadget id="calculator">20 + 80</gadget>
<output>100</output>
<gadget id="calculator">100 / 2</gadget>
<output>50</output>
<result>B</result> | B | 50 | A man can row upstream at 20 kmph and downstream at 80 kmph, and then find the speed of the man in still water? | {
"A": "32 kmph",
"B": "50 kmph",
"C": "30 kmph",
"D": "45 kmph",
"E": "65 kmph"
} | divide(add(20, 80), const_2) | add(n0,n1)|divide(#0,const_2)| | "us = 20 ds = 80 m = ( 20 + 80 ) / 2 = 50 answer : b" | physics |
math_qa__pM70ORzpHpfNk9Da | A crate measures 7 feet by 8 feet by 12 feet on the inside. A stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides. What is the radius, in feet, of the pillar with the largest volume that could still fit in the crate?
Choose the correct choice from the following options:
A) 2 B) 4 C) 6 D) 7 E) 12 | <gadget id="calculator">8 * 12</gadget>
<output>96</output>
<gadget id="calculator">96 * 7</gadget>
<output>672</output>
<gadget id="calculator">672 / 12</gadget>
<output>56</output>
<gadget id="calculator">56 / 8</gadget>
<output>7</output>
<result>D</result> | D | 7 | A crate measures 7 feet by 8 feet by 12 feet on the inside. A stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides. What is the radius, in feet, of the pillar with the largest volume that could still fit in the crate? | {
"A": "2",
"B": "4",
"C": "6",
"D": "7",
"E": "12"
} | divide(divide(multiply(multiply(8, 12), 7), 12), 8) | multiply(n1,n2)|multiply(n0,#0)|divide(#1,n2)|divide(#2,n1) | we can find the radius of all the three cases of cylinders . the only crux to find the answer faster is that : voulme is pi * r ^ 2 * h . the volume is a function of r ^ 2 . so r has to be the highest to find the largest volume . so r = 7 for the surface 8 * 12 face . volume = 343 pi answer d | geometry |
math_qa__tBTgx15yObEjkpz5 | In a fuel station the service costs $2.30 per vehicle and every liter of fuel costs $0.70. Assuming that you fill up 4 mini-vans and 2 trucks, what will be the total cost, if a mini-van's tank is 65 liters and a truck's tank is 120% bigger and they are all empty? Choose the correct choice from the following choices.
A) $ 396 B) $ 400 C) $ 404 D) $ 408 E) $ 412 | <gadget id="calculator">120 * 65</gadget>
<output>7_800</output>
<gadget id="calculator">7_800 / 100</gadget>
<output>78</output>
<gadget id="calculator">78 + 65</gadget>
<output>143</output>
<gadget id="calculator">143 * 2</gadget>
<output>286</output>
<gadget id="calculator">286 * 0.7</gadget>
<output>200.2</output>
<gadget id="calculator">4 * 65</gadget>
<output>260</output>
<gadget id="calculator">260 * 0.7</gadget>
<output>182</output>
<gadget id="calculator">200.2 + 182</gadget>
<output>382.2</output>
<gadget id="calculator">4 + 2</gadget>
<output>6</output>
<gadget id="calculator">2.3 * 6</gadget>
<output>13.8</output>
<gadget id="calculator">382.2 + 13.8</gadget>
<output>396</output>
<result>A</result> | A | 396 | In a fuel station the service costs $2.30 per vehicle and every liter of fuel costs $0.70. Assuming that you fill up 4 mini-vans and 2 trucks, what will be the total cost, if a mini-van's tank is 65 liters and a truck's tank is 120% bigger and they are all empty? | {
"A": "$ 396",
"B": "$ 400",
"C": "$ 404",
"D": "$ 408",
"E": "$ 412"
} | add(add(multiply(multiply(add(divide(multiply(120, 65), const_100), 65), 2), 0.70), multiply(multiply(4, 65), 0.70)), multiply(2.30, add(4, 2))) | add(n2,n3)|multiply(n4,n5)|multiply(n2,n4)|divide(#1,const_100)|multiply(n1,#2)|multiply(n0,#0)|add(n4,#3)|multiply(n3,#6)|multiply(n1,#7)|add(#8,#4)|add(#9,#5)| | "the service cost of 4 vans and 2 trucks is 6 * 2.30 $ 13.80 the fuel in 4 vans is 4 * 65 = 260 liters the fuel in 2 trucks is 2 * 65 * 2.2 = 286 liters the total fuel ( vans + trucks ) = 546 liters the total fuel cost is 546 * 0.7 = $ 382.20 the total cost is $ 382.20 + $ 13.80 = $ 396 the answer is a ." | general |
math_qa__udVLJvG4DjxCO8N2 | log3 N+log5 N what is 3 digit number N that will be whole number
Answers:
A) 629 B) 729 C) 829 D) 125 E) 727 | <gadget id="calculator">5 ** 3</gadget>
<output>125</output>
<result>D</result> | D | 125 | log3 N+log5 N what is 3 digit number N that will be whole number | {
"A": "629",
"B": "729",
"C": "829",
"D": "125",
"E": "727"
} | power(5, 3) | power(n1,n0)| | "no of values n can take is 1 5 ^ 3 = 125 answer : d" | other |
math_qa__4qykJQ97lkgDzNeg | Find large number from below question The difference of two numbers is 1375. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder Choose the correct choice from the following answers
A) 1234 B) 1265 C) 1350 D) 1467 E) 1647 | <gadget id="calculator">1_375 - 15</gadget>
<output>1_360</output>
<gadget id="calculator">6 - 1</gadget>
<output>5</output>
<gadget id="calculator">1_360 / 5</gadget>
<output>272</output>
<gadget id="calculator">272 * 6</gadget>
<output>1_632</output>
<result>E</result> | E | 1,647 | Find large number from below question The difference of two numbers is 1375. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder | {
"A": "1234",
"B": "1265",
"C": "1350",
"D": "1467",
"E": "1647"
} | multiply(divide(subtract(1375, 15), subtract(6, const_1)), 6) | subtract(n0,n2)|subtract(n1,const_1)|divide(#0,#1)|multiply(n1,#2)| | "let the smaller number be x . then larger number = ( x + 1375 ) . x + 1375 = 6 x + 15 5 x = 1360 x = 272 large number = 272 + 1375 = 1647 e" | general |
math_qa__ZxJBwH7LJ2144Unm | 3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day must 6 pumps work to empty the tank in 1 day?
Choose the correct option:
A) 8
B) 10
C) 11
D) 12
E) 13 | <gadget id="calculator">3 * 8</gadget>
<output>24</output>
<gadget id="calculator">24 * 2</gadget>
<output>48</output>
<gadget id="calculator">48 / 6</gadget>
<output>8</output>
<result>A</result> | A | 8 | 3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day must 6 pumps work to empty the tank in 1 day? | {
"A": "8",
"B": "10",
"C": "11",
"D": "12",
"E": "13"
} | divide(multiply(multiply(3, 8), 2), 6) | multiply(n0,n1)|multiply(n2,#0)|divide(#1,n3)| | "3 pumps take 16 hrs total ( 8 hrs a day ) if 1 pump will be working then , it will need 16 * 3 = 48 hrs 1 pump need 48 hrs if i contribute 6 pumps then 48 / 6 = 8 hrs . answer : a" | physics |
math_qa__weZCm4GBuDP88cDA | At a garage sale, all of the items were sold at different prices. If the price of a radio sold at the garage sale was both the 18th highest price and the 25th lowest price among the prices of the items sold, how many items were sold at the garage sale?
Choose the correct choice from the following options:
A) 41
B) 42
C) 43
D) 44
E) 45 | <gadget id="calculator">25 + 18</gadget>
<output>43</output>
<gadget id="calculator">43 - 1</gadget>
<output>42</output>
<result>B</result> | B | 42 | At a garage sale, all of the items were sold at different prices. If the price of a radio sold at the garage sale was both the 18th highest price and the 25th lowest price among the prices of the items sold, how many items were sold at the garage sale? | {
"A": "41",
"B": "42",
"C": "43",
"D": "44",
"E": "45"
} | subtract(add(25, 18), const_1) | add(n0,n1)|subtract(#0,const_1)| | "there were 17 items sold at a higher price than the radio and 24 items sold at a lower price than the radio . including the radio , there were 17 + 24 + 1 = 42 items sold . the answer is b ." | other |
math_qa__SCUhfBw0yZbQRsLg | Find the value of 3.5 x [(3.6 x 0.48 x 2.50) / (0.12 x 0.09 x 0.5)] Choose the correct choice from the following answers:
A) 800
B) 500
C) 2800
D) 1600
E) none | <gadget id="calculator">3.6 * 0.48</gadget>
<output>1.728</output>
<gadget id="calculator">1.728 * 2.5</gadget>
<output>4.32</output>
<gadget id="calculator">0.12 * 0.09</gadget>
<output>0.0108</output>
<gadget id="calculator">0.0108 * 0.5</gadget>
<output>0.0054</output>
<gadget id="calculator">4.32 / 0.0054</gadget>
<output>800</output>
<gadget id="calculator">800 * 3.5</gadget>
<output>2_800</output>
<result>C</result> | C | 2,800 | Find the value of 3.5 x [(3.6 x 0.48 x 2.50) / (0.12 x 0.09 x 0.5)] | {
"A": "800",
"B": "500",
"C": "2800",
"D": "1600",
"E": "none"
} | multiply(divide(multiply(multiply(3.6, 0.48), 2.5), multiply(multiply(0.12, 0.09), 0.5)), 3.5) | multiply(n1,n2)|multiply(n4,n5)|multiply(n3,#0)|multiply(n6,#1)|divide(#2,#3)|multiply(n0,#4) | answer 3.5 x [ ( 3.6 x 0.48 x 2.50 ) / ( 0.12 x 0.09 x 0.5 ) ] = 3.5 x [ ( 36 x 48 x 250 ) / ( 12 x 9 x 5 ) ] = 3.5 x 4 x 4 x 50 = 2800 correct option : c | general |
math_qa__m7B2JhGLEeBQCuVN | Dacid obtained 91, 65, 82, 67 and 85 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
Choose the most appropriate option
A) 29 B) 78 C) 39 D) 37 E) 75 | <gadget id="calculator">91 + 65</gadget>
<output>156</output>
<gadget id="calculator">156 + 82</gadget>
<output>238</output>
<gadget id="calculator">238 + 67</gadget>
<output>305</output>
<gadget id="calculator">305 + 85</gadget>
<output>390</output>
<gadget id="calculator">10 / 2</gadget>
<output>5</output>
<gadget id="calculator">390 / 5</gadget>
<output>78</output>
<result>B</result> | B | 78 | Dacid obtained 91, 65, 82, 67 and 85 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks? | {
"A": "29",
"B": "78",
"C": "39",
"D": "37",
"E": "75"
} | divide(add(add(add(add(91, 65), 82), 67), 85), divide(const_10, const_2)) | add(n0,n1)|divide(const_10,const_2)|add(n2,#0)|add(n3,#2)|add(n4,#3)|divide(#4,#1)| | "average = ( 91 + 65 + 82 + 67 + 85 ) / 5 = 78 answer : b" | general |
math_qa__u4ldVWcVX5eWaJ1l | Harkamal purchased 8kg of grapes at the rate of 80 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper? Select the correct option:
A) 1000 B) 1055 C) 1065 D) 1135 E) 1080 | <gadget id="calculator">8 * 80</gadget>
<output>640</output>
<gadget id="calculator">9 * 55</gadget>
<output>495</output>
<gadget id="calculator">640 + 495</gadget>
<output>1_135</output>
<result>D</result> | D | 1,135 | Harkamal purchased 8kg of grapes at the rate of 80 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper? | {
"A": "1000",
"B": "1055",
"C": "1065",
"D": "1135",
"E": "1080"
} | add(multiply(8, 80), multiply(9, 55)) | multiply(n0,n1)|multiply(n2,n3)|add(#0,#1)| | "cost of 8 kg grapes = 80 × 8 = 640 . cost of 9 kg of mangoes = 55 × 9 = 495 . total cost he has to pay = 640 + 495 = 1135 . d )" | gain |
math_qa__r4k9zCHF6yWB0ENQ | A man can row his boat with the stream at 26 km/h and against the stream in 12 km/h. The man's rate is? Pick one
A) 1 kmph B) 4 kmph C) 5 kmph D) 7 kmph E) 8 kmph | <gadget id="calculator">26 - 12</gadget>
<output>14</output>
<gadget id="calculator">14 / 2</gadget>
<output>7</output>
<result>D</result> | D | 7 | A man can row his boat with the stream at 26 km/h and against the stream in 12 km/h. The man's rate is? | {
"A": "1 kmph",
"B": "4 kmph",
"C": "5 kmph",
"D": "7 kmph",
"E": "8 kmph"
} | divide(subtract(26, 12), const_2) | subtract(n0,n1)|divide(#0,const_2)| | "ds = 26 us = 12 s = ? s = ( 26 - 12 ) / 2 = 7 kmph answer : d" | gain |
math_qa__rSKgH3oNZPjeOW8q | A retailer bought a machine at a wholesale price of $117 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 of the machine? Options
A) 81
B) 100
C) 120
D) 135
E) 159 | <gadget id="calculator">117 * 20</gadget>
<output>2_340</output>
<gadget id="calculator">2_340 / 100</gadget>
<output>117/5 = around 23.4</output>
<gadget id="calculator">117 + (117/5)</gadget>
<output>702/5 = around 140.4</output>
<gadget id="calculator">(702/5) * 100</gadget>
<output>14_040</output>
<gadget id="calculator">3 * 3</gadget>
<output>9</output>
<gadget id="calculator">9 * 10</gadget>
<output>90</output>
<gadget id="calculator">14_040 / 90</gadget>
<output>156</output>
<result>E</result> | E | 159 | A retailer bought a machine at a wholesale price of $117 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 of the machine? | {
"A": "81",
"B": "100",
"C": "120",
"D": "135",
"E": "159"
} | divide(multiply(add(117, divide(multiply(117, 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)| | "my solution : wholesale price = 117 retail price , be = x he provides 10 % discount on retail price = x - 10 x / 100 this retail price = 20 % profit on wholesale price x - 10 x / 100 = 117 + 1 / 5 ( 117 ) x = 156 ; answer : e" | gain |
math_qa__ywm6zI8EoPblGklR | What sum of money put at C.I amounts in 2 years to Rs.8000 and in 3 years to Rs.9261? Choose the correct choice from the following options
A) 5969.72 B) 8877.72 C) 2877.72 D) 2678.72 E) 1011.72 | <gadget id="calculator">9_261 / 8_000</gadget>
<output>9_261/8_000 = around 1.157625</output>
<gadget id="calculator">(9_261/8_000) - 1</gadget>
<output>1_261/8_000 = around 0.157625</output>
<gadget id="calculator">(1_261/8_000) + 1</gadget>
<output>9_261/8_000 = around 1.157625</output>
<gadget id="calculator">(9_261/8_000) ** 2</gadget>
<output>85_766_121/64_000_000 = around 1.340096</output>
<gadget id="calculator">8_000 / (85_766_121/64_000_000)</gadget>
<output>512_000_000_000/85_766_121 = around 5_969.723173</output>
<result>A</result> | A | 5,969.72 | What sum of money put at C.I amounts in 2 years to Rs.8000 and in 3 years to Rs.9261? | {
"A": "5969.72",
"B": "8877.72",
"C": "2877.72",
"D": "2678.72",
"E": "1011.72"
} | divide(8000, power(add(subtract(divide(9261, 8000), const_1), const_1), const_2)) | divide(n3,n1)|subtract(#0,const_1)|add(#1,const_1)|power(#2,const_2)|divide(n1,#3) | 8000 - - - - 1261 100 - - - - ? = > 15.76 % x * 115.76 / 100 * 115.76 / 100 = 8000 x * 1.34 = 8000 x = 8000 / 1.34 = > 5969.72 answer : a | general |
math_qa__vH6njIXT9Bv0DUEV | If x and y are both odd prime numbers and x < y, how many distinct positive integer T factors does 2xy have? Choose the correct choice from the following options: A) 3 B) 4 C) 6 D) 8 E) 12 | <gadget id="calculator">1 + 1</gadget>
<output>2</output>
<gadget id="calculator">2 * 2</gadget>
<output>4</output>
<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<result>D</result> | D | 8 | If x and y are both odd prime numbers and x < y, how many distinct positive integer T factors does 2xy have? | {
"A": "3",
"B": "4",
"C": "6",
"D": "8",
"E": "12"
} | multiply(multiply(2, add(const_1, const_1)), add(const_1, const_1)) | add(const_1,const_1)|multiply(n0,#0)|multiply(#0,#1)| | since 2 xy prime t factors are x ^ 1 * y ^ 1 * 2 ^ 1 , its total number or factors must be ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 2 ^ 3 = 8 . thus , i think d would be the correct answer . | other |
math_qa__cnP8uaLelA4K99DP | Calculate the value of y: 5y^2-8y+55 = 59 Select the correct option
A) 7 B) 1 C) 2 D) 9 E) 8 | <gadget id="calculator">8 ** 2</gadget>
<output>64</output>
<gadget id="calculator">55 - 59</gadget>
<output>-4</output>
<gadget id="calculator">5 * (-4)</gadget>
<output>-20</output>
<gadget id="calculator">(-20) * 4</gadget>
<output>-80</output>
<gadget id="calculator">64 - (-80)</gadget>
<output>144</output>
<gadget id="calculator">144 ** (1/2)</gadget>
<output>12</output>
<gadget id="calculator">12 + 8</gadget>
<output>20</output>
<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">20 / 10</gadget>
<output>2</output>
<result>C</result> | C | 2 | Calculate the value of y: 5y^2-8y+55 = 59 | {
"A": "7",
"B": "1",
"C": "2",
"D": "9",
"E": "8"
} | divide(add(sqrt(subtract(power(8, const_2), multiply(multiply(5, subtract(55, 59)), const_4))), 8), multiply(5, 2)) | multiply(n0,n1)|power(n2,const_2)|subtract(n3,n4)|multiply(n0,#2)|multiply(#3,const_4)|subtract(#1,#4)|sqrt(#5)|add(n2,#6)|divide(#7,#0) | using the elimination method substitute options for x and find the correct option . answer : c | general |
math_qa__zzwqpTGzAKmfxdqS | The average (arithmetic mean) of all scores on a certain algebra test was 90. If the average of the 8 male students’ grades was 85, and the average of the female students’ grades was 92, how many female students took the test? Choose the correct choice from the following answers:
A) 8
B) 9
C) 10
D) 11
E) 20 | <gadget id="calculator">90 * 8</gadget>
<output>720</output>
<gadget id="calculator">85 * 8</gadget>
<output>680</output>
<gadget id="calculator">720 - 680</gadget>
<output>40</output>
<gadget id="calculator">92 - 90</gadget>
<output>2</output>
<gadget id="calculator">40 / 2</gadget>
<output>20</output>
<result>E</result> | E | 20 | The average (arithmetic mean) of all scores on a certain algebra test was 90. If the average of the 8 male students’ grades was 85, and the average of the female students’ grades was 92, how many female students took the test? | {
"A": "8",
"B": "9",
"C": "10",
"D": "11",
"E": "20"
} | divide(subtract(multiply(90, 8), multiply(85, 8)), subtract(92, 90)) | multiply(n0,n1)|multiply(n1,n2)|subtract(n3,n0)|subtract(#0,#1)|divide(#3,#2)| | "total marks of male = m total marks of female = f number of males = 8 number of females = f given : ( m + f ) / ( 8 + f ) = 90 - - - - - - - - - - - - - 1 also given , m / 8 = 85 thus m = 680 - - - - - - - - - 2 also , f / f = 92 thus f = 92 f - - - - - - - - - 3 put 2 and 3 in 1 : we get ( 680 + 92 f ) / ( 8 + f ) = 90 solving this we get f = 20 ans : e" | general |
math_qa__aUMgTtBbTKryJhD7 | A pipe can fill a cistern in 55 minutes. Find the time in which 1/11 part of the cistern will be filled? Choose the correct choice:
A) 5 min B) 2 min C) 3 min D) 1 min E) 10 min | <gadget id="calculator">1 / 11</gadget>
<output>1/11 = around 0.090909</output>
<gadget id="calculator">55 * (1/11)</gadget>
<output>5</output>
<result>A</result> | A | 5 | A pipe can fill a cistern in 55 minutes. Find the time in which 1/11 part of the cistern will be filled? | {
"A": "5 min",
"B": "2 min",
"C": "3 min",
"D": "1 min",
"E": "10 min"
} | multiply(55, divide(1, 11)) | divide(n1,n2)|multiply(n0,#0)| | "full cistern filled in = 55 minutes 1 / 11 part filled in = 55 * 1 / 11 = 5 minutes answer is a" | physics |
math_qa__crO5pbtCwYAx3HL4 | If the perimeter of a rectangular garden is 600 m, its length when its breadth is 95 m is? Pick one
A) 286 m B) 899 m C) 200 m D) 205 m E) 187 m | <gadget id="calculator">600 / 2</gadget>
<output>300</output>
<gadget id="calculator">300 - 95</gadget>
<output>205</output>
<result>D</result> | D | 205 | If the perimeter of a rectangular garden is 600 m, its length when its breadth is 95 m is? | {
"A": "286 m",
"B": "899 m",
"C": "200 m",
"D": "205 m",
"E": "187 m"
} | subtract(divide(600, const_2), 95) | divide(n0,const_2)|subtract(#0,n1) | 2 ( l + 95 ) = 600 = > l = 205 m answer : d | physics |
math_qa__rqfGqNXkmJYJAeZj | Two trains of equal are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 72 sec. The length of each train is? Choose the correct choice from the following answers.
A) 50 B) 26 C) 27 D) 28 E) 100 | <gadget id="calculator">46 - 36</gadget>
<output>10</output>
<gadget id="calculator">10 * 1_000</gadget>
<output>10_000</output>
<gadget id="calculator">10_000 / 3_600</gadget>
<output>25/9 = around 2.777778</output>
<gadget id="calculator">72 * (25/9)</gadget>
<output>200</output>
<gadget id="calculator">200 / 2</gadget>
<output>100</output>
<result>E</result> | E | 100 | Two trains of equal are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 72 sec. The length of each train is? | {
"A": "50",
"B": "26",
"C": "27",
"D": "28",
"E": "100"
} | divide(multiply(72, divide(multiply(subtract(46, 36), const_1000), const_3600)), const_2) | subtract(n0,n1)|multiply(#0,const_1000)|divide(#1,const_3600)|multiply(n2,#2)|divide(#3,const_2)| | "let the length of each train be x m . then , distance covered = 2 x m . relative speed = 46 - 36 = 10 km / hr . = 10 * 5 / 18 = 25 / 9 m / sec . 2 x / 72 = 25 / 9 = > x = 100 . answer : e" | general |
math_qa__019RpUN6YZY8PHbh | 6 workers should finish a job in 8 days. After 3 days came 4 workers join them. How many days D do they need to finish the same job?
Select:
A) 3
B) 4
C) 5
D) 6
E) 7 | <gadget id="calculator">6 * 8</gadget>
<output>48</output>
<gadget id="calculator">3 * 6</gadget>
<output>18</output>
<gadget id="calculator">48 - 18</gadget>
<output>30</output>
<gadget id="calculator">6 + 4</gadget>
<output>10</output>
<gadget id="calculator">30 / 10</gadget>
<output>3</output>
<result>A</result> | A | 3 | 6 workers should finish a job in 8 days. After 3 days came 4 workers join them. How many days D do they need to finish the same job? | {
"A": "3",
"B": "4",
"C": "5",
"D": "6",
"E": "7"
} | divide(subtract(multiply(6, 8), multiply(3, 6)), add(6, 4)) | add(n0,n3)|multiply(n0,n1)|multiply(n0,n2)|subtract(#1,#2)|divide(#3,#0)| | "let rate of one worker be r = > ( 6 * r ) * 8 = 1 ( rate * time = work ) = > r = 1 / 48 = > work remaining after 3 days 1 - ( 3 * 6 ) / 48 = 30 / 48 after 4 ppl joined in ( ( 6 + 4 ) * time ) / 48 = 30 / 48 time d = 3 days to finish the task imo a" | physics |
math_qa__0IutoREPRzwDVwm0 | What is the ratio between perimeters of two squares one having 11 times the diagonal then the other? Select: A) 3 : 8 B) 3 : 6 C) 3 : 7 D) 11 : 1 E) 3 : 3 | <gadget id="calculator">11 / 11</gadget>
<output>1</output>
<gadget id="calculator">11 / 1</gadget>
<output>11</output>
<result>D</result> | D | 11 | What is the ratio between perimeters of two squares one having 11 times the diagonal then the other? | {
"A": "3 : 8",
"B": "3 : 6",
"C": "3 : 7",
"D": "11 : 1",
"E": "3 : 3"
} | divide(11, divide(11, 11)) | divide(n0,n0)|divide(n0,#0)| | "d = 11 d d = d a √ 2 = 11 d a √ 2 = d a = 11 d / √ 2 a = d / √ 2 = > 11 : 1 answer : d" | geometry |
math_qa__ryXbDyaCPTwqi7OM | A student has to obtain 40% of the total marks to pass. He got 150 marks and failed by 50 marks. The maximum marks are? Select
A) 500 B) 650 C) 400 D) 575 E) 610 | <gadget id="calculator">150 + 50</gadget>
<output>200</output>
<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">200 / (2/5)</gadget>
<output>500</output>
<result>A</result> | A | 500 | A student has to obtain 40% of the total marks to pass. He got 150 marks and failed by 50 marks. The maximum marks are? | {
"A": "500",
"B": "650",
"C": "400",
"D": "575",
"E": "610"
} | divide(add(150, 50), divide(40, const_100)) | add(n1,n2)|divide(n0,const_100)|divide(#0,#1)| | "let the maximum marks be x then , 40 % of x = 150 + 50 40 x / 100 = 200 x = 500 answer is a" | general |
math_qa__2oHNUe2ATvOqZ6NA | David has $1,800 at the beginning of his trip, after spending money, he still has exactly $800 less than he spent on the trip. How much money does John still have?
Choose the correct choice from the following answers: A) $ 200 B) $ 500 C) $ 600 D) $ 800 E) $ 1,200 | <gadget id="calculator">100 * 10</gadget>
<output>1_000</output>
<gadget id="calculator">1_000 + 800</gadget>
<output>1_800</output>
<gadget id="calculator">1_800 + 800</gadget>
<output>2_600</output>
<gadget id="calculator">2_600 / 2</gadget>
<output>1_300</output>
<gadget id="calculator">1_300 - 800</gadget>
<output>500</output>
<result>B</result> | B | 500 | David has $1,800 at the beginning of his trip, after spending money, he still has exactly $800 less than he spent on the trip. How much money does John still have? | {
"A": "$ 200",
"B": "$ 500",
"C": "$ 600",
"D": "$ 800",
"E": "$ 1,200"
} | subtract(divide(add(add(multiply(const_100, const_10), 800), 800), const_2), 800) | multiply(const_10,const_100)|add(n1,#0)|add(n1,#1)|divide(#2,const_2)|subtract(#3,n1) | suppose total money spent = x not spend ( money he still has ) = x - 800 x + x - 800 = 1800 x = 1300 money not spend = 1300 - 800 = 500 answer : b | general |
math_qa__e7gCrA7gQObdr3G0 | Kamal was 4 times as old as his son 8 years ago. After 8 years, Kamal will be twice as old as his son. Find out the present age of Kamal. Select the correct option:
A) 30 B) 35 C) 40 D) 45 E) 50 | <gadget id="calculator">4 * 4</gadget>
<output>16</output>
<gadget id="calculator">16 / 2</gadget>
<output>8</output>
<gadget id="calculator">8 * 4</gadget>
<output>32</output>
<gadget id="calculator">32 + 8</gadget>
<output>40</output>
<result>C</result> | C | 40 | Kamal was 4 times as old as his son 8 years ago. After 8 years, Kamal will be twice as old as his son. Find out the present age of Kamal. | {
"A": "30",
"B": "35",
"C": "40",
"D": "45",
"E": "50"
} | add(multiply(divide(multiply(4, 4), const_2), const_4), 8) | multiply(n0,n0)|divide(#0,const_2)|multiply(#1,const_4)|add(n1,#2) | let age of the son before 8 years = x then , age of kamal before 8 years ago = 4 x after 8 years , kamal will be twice as old as his son ⇒ 4 x + 16 = 2 ( x + 16 ) ⇒ x = 8 present age of kamal = 4 x + 8 = 4 × 8 + 8 = 40 answer is c . | general |
math_qa__hVk7TmfPgN6gXUVZ | Find the least number of complete years in which a sum of money put out at 13% compound interest will be more than double of itself? Pick:
A) 5 B) 6 C) 7 D) 8 E) 9 | <gadget id="calculator">log(2)</gadget>
<output>log(2) = around 0.693147</output>
<gadget id="calculator">13 / 100</gadget>
<output>13/100 = around 0.13</output>
<gadget id="calculator">1 + (13/100)</gadget>
<output>113/100 = around 1.13</output>
<gadget id="calculator">log(113/100)</gadget>
<output>log(113/100) = around 0.122218</output>
<gadget id="calculator">log(2) / log(113/100)</gadget>
<output>log(2)/log(113/100) = around 5.671417</output>
<gadget id="calculator">(log(2)/log(113/100)) + 1</gadget>
<output>1 + log(2)/log(113/100) = around 6.671417</output>
<gadget id="calculator">floor(1 + log(2)/log(113/100))</gadget>
<output>6</output>
<result>B</result> | B | 6 | Find the least number of complete years in which a sum of money put out at 13% compound interest will be more than double of itself? | {
"A": "5",
"B": "6",
"C": "7",
"D": "8",
"E": "9"
} | floor(add(divide(log(const_2), log(add(const_1, divide(13, const_100)))), const_1)) | divide(n0,const_100)|log(const_2)|add(#0,const_1)|log(#2)|divide(#1,#3)|add(#4,const_1)|floor(#5)| | "6 years answer : b" | general |
math_qa__rB56gsayiwwbLOng | Kiran has 85 currency notes in all, some of which were of Rs. 100 denomination and the
remaining of Rs. 50 denomination. The total amount of all these currency notes was Rs.
5000. How much amount did she have in the denomination of Rs. 50?
A. B. C. None of these D.
Answer: Option B
Explanation: Select the correct option
A) 1900 B) 3500 C) 4000 D) 2000 E) 2500 | <gadget id="calculator">50 * 85</gadget>
<output>4_250</output>
<gadget id="calculator">5_000 - 4_250</gadget>
<output>750</output>
<gadget id="calculator">750 / 50</gadget>
<output>15</output>
<gadget id="calculator">85 - 15</gadget>
<output>70</output>
<gadget id="calculator">70 * 50</gadget>
<output>3_500</output>
<result>B</result> | B | 3,500 | Kiran has 85 currency notes in all, some of which were of Rs. 100 denomination and the
remaining of Rs. 50 denomination. The total amount of all these currency notes was Rs.
5000. How much amount did she have in the denomination of Rs. 50?
A. B. C. None of these D.
Answer: Option B
Explanation: | {
"A": "1900",
"B": "3500",
"C": "4000",
"D": "2000",
"E": "2500"
} | multiply(subtract(85, divide(subtract(5000, multiply(50, 85)), 50)), 50) | multiply(n0,n2)|subtract(n3,#0)|divide(#1,n2)|subtract(n0,#2)|multiply(n2,#3) | let the number of 50 – rupee notes be x . then , the number of 100 - rupee notes = ( 85 – x ) 50 x + 100 ( 85 – x ) = 5000 x + 2 ( 85 – x ) = 100 = x = 70 so , required amount = rs . ( 50 x 70 ) = rs . 3500 answer : b | general |
math_qa__6vUd1Iys4JAMPbIs | A man sells a car to his friend at 12% loss. If the friend sells it for Rs.54000 and gains 20%, the original C.P.of the car was :
Pick
A) rs . 21136.36 B) rs . 31136.36 C) rs . 51136.36 D) rs . 61136.36 E) none of these | <gadget id="calculator">54_000 * 100</gadget>
<output>5_400_000</output>
<gadget id="calculator">100 + 20</gadget>
<output>120</output>
<gadget id="calculator">5_400_000 / 120</gadget>
<output>45_000</output>
<gadget id="calculator">45_000 * 100</gadget>
<output>4_500_000</output>
<gadget id="calculator">100 - 12</gadget>
<output>88</output>
<gadget id="calculator">4_500_000 / 88</gadget>
<output>562_500/11 = around 51_136.363636</output>
<result>C</result> | C | 51,136.36 | A man sells a car to his friend at 12% loss. If the friend sells it for Rs.54000 and gains 20%, the original C.P.of the car was : | {
"A": "rs . 21136.36",
"B": "rs . 31136.36",
"C": "rs . 51136.36",
"D": "rs . 61136.36",
"E": "none of these"
} | divide(multiply(divide(multiply(54000, const_100), add(const_100, 20)), const_100), subtract(const_100, 12)) | add(n2,const_100)|multiply(n1,const_100)|subtract(const_100,n0)|divide(#1,#0)|multiply(#3,const_100)|divide(#4,#2)| | "explanation : s . p = rs . 54,000 . gain earned = 20 % c . p = rs . [ 100 / 120 ã — 54000 ] = rs . 45000 this is the price the first person sold to the second at at loss of 12 % . now s . p = rs . 45000 and loss = 12 % c . p . rs . [ 100 / 88 ã — 45000 ] = rs . 51136.36 correct option : c" | gain |
math_qa__xxsWa3P43PJIiPiQ | The breath of a rectangle is three - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 2025 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the length is 10 units?
Choose the correct answer.
A) 370 sq . units B) 270 sq . units C) 170 sq . units D) 470 sq . units E) 570 sq . units | <gadget id="calculator">2_025 ** (1/2)</gadget>
<output>45</output>
<gadget id="calculator">45 * 3</gadget>
<output>135</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">135 / 5</gadget>
<output>27</output>
<gadget id="calculator">10 * 27</gadget>
<output>270</output>
<result>B</result> | B | 270 | The breath of a rectangle is three - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 2025 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the length is 10 units? | {
"A": "370 sq . units",
"B": "270 sq . units",
"C": "170 sq . units",
"D": "470 sq . units",
"E": "570 sq . units"
} | rectangle_area(10, divide(multiply(square_edge_by_area(2025), const_3), add(const_4, const_1))) | add(const_1,const_4)|square_edge_by_area(n0)|multiply(#1,const_3)|divide(#2,#0)|rectangle_area(n1,#3) | given that the area of the square = 2025 sq . units = > side of square = √ 2025 = 45 units the radius of the circle = side of the square = 45 units breath of the rectangle = 3 / 5 * 45 = 27 units given that length = 10 units area of the rectangle = lb = 27 * 10 = 270 sq . units answer : b | geometry |
math_qa__DbzLjRaLvzx0Q8Lg | There are 3 workers in the factory A, B, C. The age of A is 4 more than the age of B and the age of B is 4 more than the age of C. If the sum of the square of the ages is 1202. What is the sum of their ages?
Choose the most appropriate option: A) 50 B) 55 C) 60 D) 65 E) 70 | <gadget id="calculator">4 ** 2</gadget>
<output>16</output>
<gadget id="calculator">16 + 16</gadget>
<output>32</output>
<gadget id="calculator">1_202 - 32</gadget>
<output>1_170</output>
<gadget id="calculator">1_170 / 3</gadget>
<output>390</output>
<gadget id="calculator">390 ** (1/2)</gadget>
<output>sqrt(390) = around 19.748418</output>
<gadget id="calculator">(sqrt(390)) * 3</gadget>
<output>3*sqrt(390) = around 59.245253</output>
<result>C</result> | C | 60 | There are 3 workers in the factory A, B, C. The age of A is 4 more than the age of B and the age of B is 4 more than the age of C. If the sum of the square of the ages is 1202. What is the sum of their ages? | {
"A": "50",
"B": "55",
"C": "60",
"D": "65",
"E": "70"
} | multiply(sqrt(divide(subtract(1202, add(power(4, const_2), power(4, const_2))), 3)), 3) | power(n1,const_2)|add(#0,#0)|subtract(n3,#1)|divide(#2,n0)|sqrt(#3)|multiply(n0,#4) | let age of b = x ; age of a = x + 4 ; age of c = x - 4 ; sum of squares of ages = > 3 x ^ 2 + 32 = > x = 19.7 = > 20 sum of ages = 60 answer : c | general |
math_qa__L9PlkHu60MDXkIMk | If 12 men can reap 120 acres of land in 36 days, how many acres of land can 54 men reap in 54 days? Choose the most appropriate option.
A) 186 B) 188 C) 810 D) 167 E) 861 | <gadget id="calculator">54 / 12</gadget>
<output>9/2 = around 4.5</output>
<gadget id="calculator">54 / 36</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">(9/2) * (3/2)</gadget>
<output>27/4 = around 6.75</output>
<gadget id="calculator">120 * (27/4)</gadget>
<output>810</output>
<result>C</result> | C | 810 | If 12 men can reap 120 acres of land in 36 days, how many acres of land can 54 men reap in 54 days? | {
"A": "186",
"B": "188",
"C": "810",
"D": "167",
"E": "861"
} | multiply(120, multiply(divide(54, 12), divide(54, 36))) | divide(n3,n0)|divide(n4,n2)|multiply(#0,#1)|multiply(n1,#2)| | "12 men 120 acres 36 days 54 men ? 54 days 120 * 54 / 12 * 54 / 36 10 * 54 * 3 / 2 54 * 15 = 810 answer : c" | physics |
math_qa__HbpKdDHILiG2ueu5 | Find the sum lend at C.I. at 5 p.c per annum will amount to Rs.500 in 2 years? Pick:
A) 221 B) 287 C) 453 D) 288 E) 171 | <gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">1 + (1/20)</gadget>
<output>21/20 = around 1.05</output>
<gadget id="calculator">(21/20) ** 2</gadget>
<output>441/400 = around 1.1025</output>
<gadget id="calculator">500 / (441/400)</gadget>
<output>200_000/441 = around 453.514739</output>
<result>C</result> | C | 453 | Find the sum lend at C.I. at 5 p.c per annum will amount to Rs.500 in 2 years? | {
"A": "221",
"B": "287",
"C": "453",
"D": "288",
"E": "171"
} | divide(500, power(add(const_1, divide(5, const_100)), const_2)) | divide(n0,const_100)|add(#0,const_1)|power(#1,const_2)|divide(n1,#2) | explanation : 500 = p ( 21 / 20 ) 2 p = 453.51 answer : c | general |
math_qa__rtabvnSugGmuR6dY | x varies inversely as square of y. Given that y=3 for x=1. The value of x for y = 4 will be equal to:
Select.
A) 3 B) 6 C) 1 / 9 D) 1 / 3 E) 9 / 16 | <gadget id="calculator">3 ** 2</gadget>
<output>9</output>
<gadget id="calculator">1 * 9</gadget>
<output>9</output>
<gadget id="calculator">4 ** 2</gadget>
<output>16</output>
<gadget id="calculator">9 / 16</gadget>
<output>9/16 = around 0.5625</output>
<result>E</result> | E | 0.5625 | x varies inversely as square of y. Given that y=3 for x=1. The value of x for y = 4 will be equal to: | {
"A": "3",
"B": "6",
"C": "1 / 9",
"D": "1 / 3",
"E": "9 / 16"
} | divide(multiply(1, power(3, const_2)), power(4, const_2)) | power(n0,const_2)|power(n2,const_2)|multiply(n1,#0)|divide(#2,#1)| | "explanation : solution : given x = k / y ^ 2 , where k is constant . now , y = 3 and x = 1 gives k = 9 . . ' . x = 9 / y ^ 2 = > x = 9 / 4 ^ 2 = 9 / 16 answer : e" | general |
math_qa__sOH0tI8XmdL3KNBi | In a sports club with 27 members, 17 play badminton and 19 play tennis and 2 do not play either. How many members play both badminton and tennis? Choose the correct choice from the following: A) 7 B) 8 C) 9 D) 10 E) 11 | <gadget id="calculator">17 + 19</gadget>
<output>36</output>
<gadget id="calculator">36 + 2</gadget>
<output>38</output>
<gadget id="calculator">38 - 27</gadget>
<output>11</output>
<result>E</result> | E | 11 | In a sports club with 27 members, 17 play badminton and 19 play tennis and 2 do not play either. How many members play both badminton and tennis? | {
"A": "7",
"B": "8",
"C": "9",
"D": "10",
"E": "11"
} | subtract(add(add(17, 19), 2), 27) | add(n1,n2)|add(n3,#0)|subtract(#1,n0)| | "let x play both badminton and tennis so 17 - x play only badminton and 19 - x play only tennis . 2 play none and there are total 30 students . hence , ( 17 - x ) + ( 19 - x ) + x + 2 = 27 38 - 2 x + x = 27 38 - x = 27 x = 11 so 8 members play both badminton and tennis . e" | other |
math_qa__vO0MceXiKf8JG8X2 | A & B can separately do a piece of work in 20 & 15 days. They worked together for 6 days, after which B was replaced by C. The work was finished in next 5 days. The no.of days in which C alone could do the work is
Choose the correct choice from the following
A) 10 days
B) 20 days
C) 30 days
D) 40 days
E) 50 days | <gadget id="calculator">1 / 20</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">1 / 15</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">(1/20) + (1/15)</gadget>
<output>7/60 = around 0.116667</output>
<gadget id="calculator">(7/60) * 6</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">1 - (7/10)</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(3/10) / 5</gadget>
<output>3/50 = around 0.06</output>
<gadget id="calculator">(3/50) - (1/20)</gadget>
<output>1/100 = around 0.01</output>
<gadget id="calculator">1 / (1/100)</gadget>
<output>100</output>
<gadget id="calculator">100 / 2</gadget>
<output>50</output>
<result>E</result> | E | 50 | A & B can separately do a piece of work in 20 & 15 days. They worked together for 6 days, after which B was replaced by C. The work was finished in next 5 days. The no.of days in which C alone could do the work is | {
"A": "10 days",
"B": "20 days",
"C": "30 days",
"D": "40 days",
"E": "50 days"
} | divide(inverse(subtract(divide(subtract(const_1, multiply(add(divide(const_1, 20), divide(const_1, 15)), 6)), 5), divide(const_1, 20))), const_2) | divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|multiply(n2,#2)|subtract(const_1,#3)|divide(#4,n3)|subtract(#5,#0)|inverse(#6)|divide(#7,const_2) | b worked for 6 days = > in 6 days b completed = 6 x 1 15 = 2 5 th work a worked for first 6 days and later 4 days = > in 10 days a completed = 10 x 1 20 = 1 2 of the work total work done by a and b = 2 5 + 1 2 = 4 + 5 10 = 9 10 balance work = 1 - 9 10 = 1 10 th of total work balance work was completed by c in 5 days c can do 1 / 10 of the work in 5 days . therefore c alone can do the work in 50 days . e | physics |
math_qa__Dv9c5mgzzF6eWaAI | 145 liters of a mixture of milk and water contains in the ratio 3:2. How much water should now be added so that the ratio of milk and water becomes 3:4?
Options:
A) 12 liters B) 32 liters C) 41 liters D) 50 liters E) 58 liters | <gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">145 / 5</gadget>
<output>29</output>
<gadget id="calculator">29 * 2</gadget>
<output>58</output>
<result>E</result> | E | 58 | 145 liters of a mixture of milk and water contains in the ratio 3:2. How much water should now be added so that the ratio of milk and water becomes 3:4? | {
"A": "12 liters",
"B": "32 liters",
"C": "41 liters",
"D": "50 liters",
"E": "58 liters"
} | multiply(divide(145, add(3, 2)), 2) | add(n1,n2)|divide(n0,#0)|multiply(n2,#1)| | "milk = 3 / 5 * 145 = 87 liters water = 58 liters 87 : ( 58 + p ) = 3 : 4 174 + 3 p = 348 = > p = 58 58 liters of water are to be added for the ratio become 3 : 4 . answer : e" | general |
math_qa__3weY9hDzpJvcbwZt | Edward's home have 3 taps,One tap, working alone at its maximum constant rate, can fill a certain sink in 270 seconds.A second tap working alone at its maximum constant rate, can fill a certain sink in 274 seconds. A third tap, working alone at its maximum constant rate, can fill the same sink in 276 seconds. If all taps work together at their respective maximum constant rates, the time it will take to fill the sink is closest to Answers:
A) 91 seconds B) 102 seconds C) 177 seconds D) 200 seconds E) 270 seconds | <gadget id="calculator">270 / 3</gadget>
<output>90</output>
<gadget id="calculator">274 / 3</gadget>
<output>274/3 = around 91.333333</output>
<gadget id="calculator">90 + (274/3)</gadget>
<output>544/3 = around 181.333333</output>
<gadget id="calculator">276 / 3</gadget>
<output>92</output>
<gadget id="calculator">(544/3) + 92</gadget>
<output>820/3 = around 273.333333</output>
<gadget id="calculator">(820/3) / 3</gadget>
<output>820/9 = around 91.111111</output>
<result>A</result> | A | 91 | Edward's home have 3 taps,One tap, working alone at its maximum constant rate, can fill a certain sink in 270 seconds.A second tap working alone at its maximum constant rate, can fill a certain sink in 274 seconds. A third tap, working alone at its maximum constant rate, can fill the same sink in 276 seconds. If all taps work together at their respective maximum constant rates, the time it will take to fill the sink is closest to | {
"A": "91 seconds",
"B": "102 seconds",
"C": "177 seconds",
"D": "200 seconds",
"E": "270 seconds"
} | divide(add(add(divide(270, 3), divide(274, 3)), divide(276, 3)), 3) | divide(n1,n0)|divide(n2,n0)|divide(n3,n0)|add(#0,#1)|add(#3,#2)|divide(#4,n0) | tap 1 : 270 secs tap 2 : 274 secs tap 3 : 276 secs considering the average of these 3 taps : 273.33 secs . so 1 tap can fill the tank in 273.33 secs , so 3 taps can fill the tank in 273.33 / 3 = 91.11 secs . closest answer is a . | physics |
math_qa__kW8bxhXzvqHIeQzp | The overall age of X and Y is 12 year greater than the overall age of Y and Z. Z is how many decades younger that X? Pick one.
A) 11
B) 15
C) 12
D) 17
E) 19 | <gadget id="calculator">12 / 1</gadget>
<output>12</output>
<result>C</result> | C | 12 | The overall age of X and Y is 12 year greater than the overall age of Y and Z. Z is how many decades younger that X? | {
"A": "11",
"B": "15",
"C": "12",
"D": "17",
"E": "19"
} | divide(12, const_1) | divide(n0,const_1)| | "c 12 ( x + y ) – ( y + z ) = 12 x – z = 12" | general |
math_qa__jfP9hajmNGIgQjXw | what is rate of interest if principal.amount be 400,simple interest 140 and time 2year. Choose the correct choice.
A) 10
B) 17.5
C) 25
D) 12
E) 14.5 | <gadget id="calculator">400 * 2</gadget>
<output>800</output>
<gadget id="calculator">140 / 800</gadget>
<output>7/40 = around 0.175</output>
<gadget id="calculator">(7/40) * 100</gadget>
<output>35/2 = around 17.5</output>
<result>B</result> | B | 17.5 | what is rate of interest if principal.amount be 400,simple interest 140 and time 2year. | {
"A": "10",
"B": "17.5",
"C": "25",
"D": "12",
"E": "14.5"
} | multiply(divide(140, multiply(400, 2)), const_100) | multiply(n0,n2)|divide(n1,#0)|multiply(#1,const_100)| | "s . i = ( p * r * t ) / 100 140 = 800 r / 100 r = 140 / 8 = 17.5 % answer b" | gain |
math_qa__qXGvdcUnjS0F6QIZ | The population of a village is 12000. It increases annually at the rate of 24% p.a. What will be its population after 2 years? Choose the correct choice from the following answers.
A) 14567 B) 18451 C) 18789 D) 18786 E) 14400 | <gadget id="calculator">24 / 100</gadget>
<output>6/25 = around 0.24</output>
<gadget id="calculator">1 + (6/25)</gadget>
<output>31/25 = around 1.24</output>
<gadget id="calculator">(31/25) ** 2</gadget>
<output>961/625 = around 1.5376</output>
<gadget id="calculator">12_000 * (961/625)</gadget>
<output>92_256/5 = around 18_451.2</output>
<result>B</result> | B | 18,451 | The population of a village is 12000. It increases annually at the rate of 24% p.a. What will be its population after 2 years? | {
"A": "14567",
"B": "18451",
"C": "18789",
"D": "18786",
"E": "14400"
} | multiply(12000, power(add(const_1, divide(24, const_100)), 2)) | divide(n1,const_100)|add(#0,const_1)|power(#1,n2)|multiply(n0,#2)| | "formula : ( after = 100 denominator ago = 100 numerator ) 12000 × 124 / 100 × 124 / 100 = 18451 b" | gain |
math_qa__YB0r38tUk9BljMwJ | A and B can do a piece of work in 10 days, B and C in 15 days, C and A in 12 days. How long will C take to do it? Answers: A) 70 days B) 55 days C) 24 days D) 40 days E) 11 days | <gadget id="calculator">10 * 3</gadget>
<output>30</output>
<gadget id="calculator">30 / 12</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">30 / 10</gadget>
<output>3</output>
<gadget id="calculator">30 / 15</gadget>
<output>2</output>
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">(5/2) + 5</gadget>
<output>15/2 = around 7.5</output>
<gadget id="calculator">(15/2) / 2</gadget>
<output>15/4 = around 3.75</output>
<gadget id="calculator">(15/4) - 3</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">30 / (3/4)</gadget>
<output>40</output>
<result>D</result> | D | 40 | A and B can do a piece of work in 10 days, B and C in 15 days, C and A in 12 days. How long will C take to do it? | {
"A": "70 days",
"B": "55 days",
"C": "24 days",
"D": "40 days",
"E": "11 days"
} | divide(multiply(10, const_3), subtract(divide(add(divide(multiply(10, const_3), 12), add(divide(multiply(10, const_3), 10), divide(multiply(10, const_3), 15))), const_2), divide(multiply(10, const_3), 10))) | multiply(n0,const_3)|divide(#0,n0)|divide(#0,n1)|divide(#0,n2)|add(#1,#2)|add(#4,#3)|divide(#5,const_2)|subtract(#6,#1)|divide(#0,#7)| | "2 c = 1 / 15 + 1 / 12 – 1 / 10 = 1 / 20 c = 1 / 40 = > 40 days answer : d" | physics |
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