euclaise/mathqa_programs huggingface dataset:
Problem: if ( 10 ^ 4 * 3.456789 ) ^ 10 is written as a single term , how many digits would be to the right of the decimal place ?
Options: a ) 12 , b ) 16 , c ) 20 , d ) 32 , e ) 48
Rationale: "3.456789 ^ 10 has 6 * 10 = 60 decimal places . 10 ^ 40 moves the decimal place to the right 40 places . ( 10 ^ 4 * 3.456789 ) ^ 10 has 60 - 40 = 20 digits after the decimal point . the answer is c ."
Answer: c
Python program:
a = 10 * 2
Problem: if each edge of cube increased by 30 % , the percentage increase in
Options: a ) 69 , b ) 72 , c ) 64 , d ) 61 , e ) 75
Rationale: "100 × ( 130 ) / 100 × ( 130 ) / 100 = 169 = > 69 % answer is a ."
Answer: a
Python program:
a = 100 + 30 
b = a ** 3
c = 100 ** 3
d = b - c
e = 100 ** 3
f = d / e
g = 100 * f
Problem: a certain drink of type a is prepared by mixing 4 parts milk with 3 parts fruit juice . another drink of type b is prepared by mixing 4 parts of fruit juice and 3 parts of milk . how many liters of fruit juice must be added to 63 liters of drink a to convert it to drink b ?
Options: a ) 7 , b ) 14 , c ) 21 , d ) 28 , e ) 35
Rationale: "in 63 liters of drink a , there are 36 liters of milk and 27 liters of juice . with 36 liters of milk , we need a total of 48 liters of juice to make drink b . we need to add 21 liters of juice . the answer is c ."
Answer: c
Python program:
a = 4 + 3 
b = 4 / a
c = b * 63
d = c * 4
e = d / 3
f = 4 + 3 
g = 3 / f
h = g * 63
i = e - h
Problem: james went on a diet 12 months ago when he weighed 222 pounds . if he now weighs 198 pounds and continues to lose at the same average monthly rate , in approximately how many months will he weigh 190 pounds ?
Options: a ) 3 , b ) 3.5 , c ) 4 , d ) 4.5 , e ) 5
Rationale: 222 - 198 = 24 pounds lost in 12 months 24 / 12 = 2 , so joe is losing weight at a rate of 2 pounds per month . . . . in approximately how many months will he weigh 190 pounds ? a simple approach is to just list the weights . now : 198 lbs in 1 month : 196 lbs in 2 months : 194 lbs in 3 months : 192 lbs in 4 months : 190 lbs answer : c
Answer: c
Python program:
a = 222 - 198
b = 198 - 190
c = a / b
d = 12 / c
Problem: the dimensions of a rectangular solid are 4 inches , 5 inches , and 9 inches . if a cube , a side of which is equal to one of the dimensions of the rectangular solid , is placed entirely within thespherejust large enough to hold the cube , what the ratio of the volume of the cube to the volume within thespherethat is not occupied by the cube ?
Options: a ) 2 : 5 , b ) 5 : 9 , c ) 5 : 16 , d ) 25 : 7 , e ) 32 : 25
Rationale: answer : b .
Answer: b
Python program:
a = 9 * 2
b = a + 2 
c = b + 1 
d = 10 / c
Problem: there are cats got together and decided to kill the mice of 999951 . each cat kills equal number of mice and each cat kills more number of mice than cats there were . then what are the number of cats ?
Options: a ) 941,1009 , b ) 993,1007 , c ) 991,1009 , d ) 791,1009 , e ) 931,1009
Rationale: "999951 can be written as 1000000 â € “ 49 = 10002 â € “ 72 ie of the form a 2 - b 2 = ( a + b ) ( a - b ) = ( 1000 + 7 ) * ( 1000 - 7 ) = ( 1007 ) * ( 993 ) given that number of cats is less than number if mice . so number of cats is 993 and number of mice were 1007 answer b"
Answer: b
Python program:
a = 100 * 10
b = 3 + 2 
c = a + b 
d = 999951 / c
Problem: a taxi company costs $ 2.75 for the first quarter - mile and 12.5 cents for each additional quarter mile . what is the maximum distance you can travel with $ 6.50 ?
Options: a ) 4 miles , b ) 5 3 / 4 miles , c ) 6 1 / 2 miles , d ) 7 3 / 4 miles , e ) 8 1 / 4 miles
Rationale: use reverse calculation - total cost = fixed cost ( for 1 / 4 miles ) + variable cost ( distance travelled ) or , 6.50 = 2.75 + 0.125 * d or , 3.75 = d / 8 or , d = 30 quarter miles so , total distance = ( 30 + 1 ) quarter miles so , distance = 31 / 4 = > 73 / 4 miles hence answer will be ( d )
Answer: d
Python program:
a = 6 - 5
b = a * 100
c = b / 12
d = c * const_0_25
e = d + const_0_25
Problem: claire has a total of 96 pets consisting of gerbils and hamsters only . one - quarter of the gerbils are male , and one - third of the hamsters are male . if there are 25 males altogether , how many gerbils does claire have ?
Options: a ) 84 , b ) 50 , c ) 54 , d ) 57 , e ) 60
Rationale: "g + h = 96 . . . 1 ; g / 4 + h / 3 = 25 . . . . 2 or 3 g + 4 h = 25 * 12 = 300 g = 96 - h or 3 ( 96 - h ) + 4 h = 300 h = 300 - 288 = 12 then g = 96 - 12 = 84 a"
Answer: a
Python program:
a = 96 - 25
b = a + 1
Problem: find 94 × × 97
Options: a ) 93 / 198 , b ) 93 / 12 , c ) 93 / 18 , d ) 93 / 10 , e ) 93 / 11
Rationale: "here both numbers are less than 100 . so they are deficient of - 6 and - 3 compared with 100 . so answer : c"
Answer: c
Python program:
a = 94 / 97
Problem: a 1200 m long train crosses a tree in 120 sec , how much time will i take to pass a platform 800 m long ?
Options: a ) 266 sec , b ) 200 sec , c ) 776 sec , d ) 166 sec , e ) 997 sec
Rationale: "l = s * t s = 1200 / 120 s = 10 m / sec . total length ( d ) = 2000 m t = d / s t = 2000 / 10 t = 200 sec answer : b"
Answer: b
Python program:
a = 1200 + 800 
b = 1200 / 120
c = a / b
Problem: at what rate percent of simple interest will a sum of money double itself in 11 years ?
Options: a ) 9.09 % , b ) 4.54 % , c ) 8 . 2 % , d ) 4.94 % , e ) 5.54 %
Rationale: "let sum = x . then , s . i . = x . rate = ( 100 * s . i . ) / ( p * t ) = ( 100 * x ) / ( x * 11 ) = 100 / 11 = 9.09 % answer : a"
Answer: a
Python program:
a = 100 / 11
Problem: if m and n are positive integers and m ^ 2 + n ^ 2 = 137 , what is the value of m ^ 3 + n ^ 3 ?
Options: a ) 72 , b ) 224 , c ) 320 , d ) 512 , e ) 1,395
Rationale: you need to integers which squared are equal 40 . which could it be ? let ' s start with the first integer : 1 ^ 2 = 1 2 ^ 2 = 4 3 ^ 2 = 9 4 ^ 2 = 16 5 ^ 2 = 25 6 ^ 2 = 36 7 ^ 2 = 49 8 ^ 2 = 64 9 ^ 2 = 81 10 ^ 2 = 100 11 ^ 2 = 121 stop . the integers ca n ' t be greater than 6 or we will score above 137 . the second integer need to be picked up the same way . 1 ^ 2 = 1 2 ^ 2 = 4 3 ^ 2 = 9 4 ^ 2 = 16 5 ^ 2 = 25 6 ^ 2 = 36 7 ^ 2 = 49 8 ^ 2 = 64 9 ^ 2 = 81 10 ^ 2 = 100 11 ^ 2 = 121 the only pair that matches is 11 ^ 2 + 4 ^ 2 = 137 . so 11 ^ 3 + 4 ^ 3 = 1395 . answer e . )
Answer: e
Python program:
a = math.gcd(137, 4)
Problem: if the product of the integers from 1 to n is divisible by 630 , what is the least possible value of n ?
Options: a ) 7 , b ) 14 , c ) 21 , d ) 28 , e ) 35
Rationale: "630 = 2 x 3 x 3 x 5 x 7 n must include at least up to the number 7 . the answer is a ."
Answer: a
Python program:
a = 630 / 3
b = 3 + 4 
c = a / b
d = 3 + 4 
e = c / d
f = e * 3
Problem: a monkey start climbing up a tree 22 ft tall . each hour it hops 3 ft and slips back 2 ft . how much time would it take the monkey to reach the top .
Options: a ) 15 hrs , b ) 18 hrs , c ) 20 hrs , d ) 17 hrs , e ) 16 hrs
Rationale: "if monkey hops 3 ft and slips back 2 ft in a hour , it means the monkey hops ( 3 ft - 2 ft ) = 1 ft / hr . similarly in 19 hrs it wil be 19 ft . bt since the height of the tree is 22 ft , so if the monkey hops up the tree in the next hr i . e 20 th hr then it reaches at the top of the tree . hence it takes 20 hrs for monkey to reach at the top answer : c"
Answer: c
Python program:
a = 3 - 2
b = 22 / a
c = b - 2
Problem: the first doughnut is priced at $ 1 and then if you purchase additional doughnuts as dozens then the price is $ 6 / dozen . what is the total number of doughnuts purchased if you paid $ 26 ?
Options: a ) 50 , b ) 52 , c ) 54 , d ) 56 , e ) 58
Rationale: "$ 26 = 4 * $ 6 + $ 2 the number of doughnuts is 4 * 12 + 2 = 50 the answer is a ."
Answer: a
Python program:
a = 26 / 6
b = a * 12
Problem: when you draw 2 dices together , find the probability of getting a total of 6 ?
Options: a ) 3 / 13 , b ) 2 / 31 , c ) 5 / 36 , d ) 7 / 41 , e ) 7 / 43
Rationale: s = { ( 1,1 ) , ( 1,2 ) , ( 1,3 ) , ( 1,4 ) , ( 1,5 ) , ( 1,6 ) , ( 4,1 ) , ( 4,2 ) , ( 4,3 ) , ( 4,4 ) , ( 4,5 ) , ( 4,6 ) , ( 2,1 ) , ( 2,2 ) , ( 2,3 ) , ( 2,4 ) , ( 2,5 ) , ( 2,6 ) , ( 5,1 ) , ( 5,2 ) , ( 5,3 ) , ( 5,4 ) , ( 5,5 ) , ( 5,6 ) , ( 3,1 ) , ( 3,2 ) , ( 3,3 ) , ( 3,4 ) , ( 3,5 ) , ( 3,6 ) , ( 6,1 ) , ( 6,2 ) , ( 6,3 ) , ( 6,4 ) , ( 6,5 ) , ( 6,6 ) } n ( s ) = 36 set of total of 6 , a = { ( 1,5 ) , ( 5,1 ) , ( 2,4 ) , ( 4,2 ) , ( 3,3 ) } ; n ( a ) = 5 p ( total of 6 ) = n ( a ) n ( s ) n ( a ) n ( s ) = 5 / 36 c
Answer: c
Python program:
a = 6 ** 2
b = 2 / a
c = 6 ** 2
d = 3 / c
e = b + d
Problem: elvin ' s monthly telephone bill is the sum of the charge for the calls he made during the month and a fixed monthly charge for internet service . elvin ' s total telephone bill for january was $ 50 and elvin ' s total telephone bill for february was 76 $ . if elvin ' s charge for the calls he made in february was twice the charge for the calls he made in january , what is elvin ' s fixed monthly charge for internet service ?
Options: a ) $ 5 , b ) $ 10 , c ) $ 14 , d ) $ 24 , e ) $ 28
Rationale: "bill = fixed charge + charge of calls made in jan , bill = fixed charge ( let , y ) + charge of calls made in jan ( let , x ) = $ 50 in feb , bill = fixed charge ( let , y ) + charge of calls made in feb ( then , 2 x ) = $ 76 i . e . x + y = 50 and 2 x + y = 76 take the difference if two equations i . e . ( 2 x + y ) - ( x + y ) = 76 - 50 i . e . x = 26 i . e . fixed monthly charge , y = 26 answer : d"
Answer: d
Python program:
a = 50 * 2
b = a - 76
Problem: a salesman ’ s terms were changed from a flat commission of 5 % on all his sales to a fixed salary of rs . 1300 plus 2.5 % commission on all sales exceeding rs . 4,000 . if his remuneration as per new scheme was rs . 600 more than that by the previous schema , his sales were worth ?
Options: a ) 12028 , b ) 12000 , c ) 12019 , d ) 12197 , e ) 18000
Rationale: [ 1300 + ( x - 4000 ) * ( 2.5 / 100 ) ] - x * ( 5 / 100 ) = 600 x = 18000 answer : c
Answer: c
Python program:
a = 5 / 100
b = 600 / a
Problem: a man took a loan at rate of 12 % per annum simple interest . after 3 years he had to pay 9000 interest . the principal amount borrowed by him was .
Options: a ) rs 14000 , b ) rs 25000 , c ) rs 16000 , d ) rs 17000 , e ) none of these
Rationale: explanation : s . i . = p â ˆ — r â ˆ — t / 100 = > p = s . i . â ˆ — 100 / r â ˆ — t = > p = 9000 â ˆ — 100 / 12 â ˆ — 3 = rs 25000 option b
Answer: b
Python program:
a = 9000 * 100
b = 12 * 3
c = a / b
Problem: tabby is training for a triathlon . she swims at a speed of 1 mile per hour . she runs at a speed of 9 miles per hour . she wants to figure out her average speed for these two events . what is the correct answer for her ?
Options: a ) 8 mph , b ) 5.25 mph , c ) 3.5 mph , d ) 5 mph , e ) 0.5 mph
Rationale: "( 1 mph + 9 mph ) / 2 = 5 mph correct option is : d"
Answer: d
Python program:
a = 1 + 9 
b = a / 2
Problem: suppose you want to buy 3 loaves of bread that cost $ 2.25 each and a jar of peanut butter that costs $ 2 . a jar of jelly is $ 2.75 , but you don â € ™ t need any jelly . you have $ 14 . how much money will you have left over ?
Options: a ) $ 1.50 , b ) $ 2.50 , c ) $ 5.25 , d ) $ 4.50 , e ) $ 5.50
Rationale: the jelly is extra information . 14.00 â € “ 3 x 2.25 â € “ 2.00 = 14.00 â € “ 6.75 â € “ 2.00 = 5.25 . you have $ 5.25 left . correct answer c
Answer: c
Python program:
a = 3 * 2
b = 14 - a
c = b - 2
Problem: a batsman scored 110 runs which included 3 boundaries and 8 sixes . what percent of his total score did he make by running between the wickets ?
Options: a ) 50 % , b ) 40 % , c ) 60 % , d ) 70 % , e ) 45.45 %
Rationale: "number of runs made by running = 110 - ( 3 x 4 + 8 x 6 ) = 110 - ( 60 ) = 50 now , we need to calculate 50 is what percent of 110 . = > 50 / 110 x 100 = 45.45 % answer : e"
Answer: e
Python program:
a = 3 * 8
b = 8 * 3
c = a + b 
d = 110 - c
e = d / 110
f = e * 100
Problem: a man can row 3.6 km / hr in still water . it takes him twice as long to row upstream as to row downstream . what is the rate of the current ?
Options: a ) 1.9 , b ) 1.7 , c ) 1.2 , d ) 1.5 , e ) 1.1
Rationale: "speed of boat in still water ( b ) = 3.6 km / hr . speed of boat with stream ( down stream ) , d = b + u speed of boat against stream ( up stream ) , u = b – u it is given upstream time is twice to that of down stream . ⇒ downstream speed is twice to that of upstream . so b + u = 2 ( b – u ) ⇒ u = b / 3 = 1.2 km / hr . answer : c"
Answer: c
Python program:
a = 3 * 6
b = a - 3
c = b / 3
Problem: two cars are traveling in the same direction along the same route . the red car travels at a constant speed of 30 miles per hour , and the black car is traveling at a constant speed of 50 miles per hour . if the red car is 20 miles ahead of the black car , how many hours will it take the black car to overtake the red car ?
Options: a ) 0.1 , b ) 0.6 , c ) 1 , d ) 1.2 , e ) 2
Rationale: "option c 20 + 30 t = 50 t t = 1"
Answer: c
Python program:
a = 50 - 30
b = 20 / a
Problem: the population of locusts in a certain swarm doubles every two hours . if 4 hours ago there were 1,000 locusts in the swarm , in approximately how many hours will the swarm population exceed 32,000 locusts ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 9
Rationale: "- 4 hours : 1,000 - 2 hours : 2,000 now : 4,000 + 2 hours : 8,000 + 4 hours : 16,000 + 6 hours : 32,000 answer : c"
Answer: c
Python program:
a = 4 ** 4
b = a / 2
c = math.log(b)
d = c * 2
e = d - 4
Problem: find the ratio in which rice at rs . 7.10 a kg be mixed with rice at rs . 5.70 a kg to produce a mixture worth rs . 6.30 a kg
Options: a ) 2 : 0 , b ) 3 : 4 , c ) 2 : 1 , d ) 2 : 2 , e ) 2 : 8
Rationale: "by the rule of alligation : cost of 1 kg rice of 1 st kind cost of 1 kg rice of 2 nd kind required ratio = 60 : 80 = 3 : 4 answer : b"
Answer: b
Python program:
a = 6 - 30
b = 7 - 10
c = a / b
Problem: in an election , candidate a got 75 % of the total valid votes . if 15 % of the total votes were declared invalid and the total numbers of votes is 560000 , find the number of valid vote polled in favour of candidate .
Options: a ) 357000 , b ) 357003 , c ) 277677 , d ) 699377 , e ) 267877
Rationale: "total number of invalid votes = 15 % of 560000 = 15 / 100 × 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 – 84000 = 476000 percentage of votes polled in favour of candidate a = 75 % therefore , the number of valid votes polled in favour of candidate a = 75 % of 476000 = 75 / 100 × 476000 = 35700000 / 100 = 357000 answer : a"
Answer: a
Python program:
a = 15 / 100
b = 1 - a
c = 560000 * b
d = 75 / 100
e = c * d
Problem: there is a 40 cm line marked at each centimeter and an insect is placed at every centimeter . 9 frogs are trained to jump a constant distance . the first one jumps 2 cm in every leap , the second one jumps 3 cm and so on until the 9 th one jumps 10 cm in every leap and they eat any insect that is available at that spot . if all of them start from start line and finish the entire 40 cm , how many insects were still left after the race was over ?
Options: a ) 0 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "only the prime numbers greater than 10 and less than 40 were left . that is 11 , 13 , 17 , 19 , 23 , 29 , 31 , and 37 . the total is 8 . the answer is d ."
Answer: d
Python program:
a = 10 + 2
Problem: the average salary of all the workers in a workshop is $ 1000 . the average salary of 5 technicians is $ 5000 and the average salary of the rest is $ 500 . the total number of workers in the shop is ?
Options: a ) 25 , b ) 20 , c ) 15 , d ) 30 , e ) 18
Rationale: "let the total number of workers be x 1000 x = 5000 * 5 + 500 ( x - 5 ) x = 25 answer is a"
Answer: a
Python program:
a = 5 * 5000
b = 500 * 5
c = a - b
d = 1000 - 500
e = c / d
Problem: you have been given a physical balance and 7 weights of 43 , 45 , 30 , 33 , 28 , 37 and 55 kgs . keeping weights on one pan and object on the other , what is the maximum you can weigh less than 145 kgs .
Options: a ) 145 , b ) 143 , c ) 147 , d ) 141 , e ) 142
Rationale: 55 + 43 + 45 = 143 answer : b
Answer: b
Python program:
a = 45 + 30 
b = a + 33 
c = b + 37
Problem: united telephone charges a base rate of $ 11.00 for service , plus an additional charge of $ 0.25 per minute . atlantic call charges a base rate of $ 12.00 for service , plus an additional charge of $ 0.20 per minute . for what number of minutes would the bills for each telephone company be the same ?
Options: a ) 2 minutes , b ) 10 minutes , c ) 20 minutes , d ) 40 minutes , e ) 60 minutes
Rationale: "lets take number of minutesx . given that , 11 + 0.25 x = 12 + 0.2 x - > 0.05 x = 2 - > x = 20 minutes ans c"
Answer: c
Python program:
a = 12 - 0
b = 0 - 25
c = a / b
Problem: if the ratio of a to b is 8 to 3 and the ratio of b to c is 1 to 5 , what is the ratio of a to c ?
Options: a ) 8 / 15 , b ) 1 / 3 , c ) 2 / 5 , d ) 4 / 5 , e ) 7 / 6
Rationale: "a : b = 8 : 3 - - 1 b : c = 1 : 5 = > b : c = 3 : 15 - - 2 from 1 and 2 , we get a : c = 8 : 15 answer a"
Answer: a
Python program:
a = 8 * 1
b = 3 * 5
c = a / b
Problem: the least number which when divided by 5 , 67 and 8 leaves a remainder 3 , but when divided by 9 leaves no remainder , is :
Options: a ) 1677 , b ) 1683 , c ) 2523 , d ) 3363 , e ) none of these
Rationale: solution l . c . m . of 5 , 6 , 7 , 8 = 840 . so , required number is of the form 840 k + 3 . least value of k for which ( 840 k + 3 ) is divisible by 9 is k = 2 . so , required number = ( 840 × 2 + 3 ) = 1683 . answer b
Answer: b
Python program:
a = 5 + 1 
b = 5 * a
c = 5 + 2 
d = b * c
e = d * 8
f = e + 3
Problem: the monthly incomes of a and b are in the ratio 5 : 2 . b ' s monthly income is 12 % more than c ' s monthly income . if c ' s monthly income is rs . 16000 , then find the annual income of a ?
Options: a ) rs . 537600 , b ) rs . 180000 , c ) rs . 201600 , d ) rs . 504000 , e ) none of these
Rationale: b ' s monthly income = 16000 * 112 / 100 = rs . 17920 b ' s monthly income = 2 parts - - - - > rs . 17920 a ' s monthly income = 5 parts = 5 / 2 * 17920 = rs . 44800 a ' s annual income = rs . 44800 * 12 = rs . 537600 answer : a
Answer: a
Python program:
a = 12 / 100
b = 1 + a 
c = 16000 * b
d = 5 / 2
e = c * d
f = e * 12
Problem: 1 , 13 , 35 , 67 , 109 , ____
Options: a ) 161 , b ) 154 , c ) 216 , d ) 158 , e ) none
Rationale: "1 , 13 , 35 , 67 , 109 , . . . . . 13 = 1 + 12 35 = 13 + 22 67 = 35 + 32 109 = 67 + 42 so 109 + 52 = 161 answer : a"
Answer: a
Python program:
a = negate - (
Problem: two cars start from the opposite places of a main road , 150 km apart . first car runs for 25 km and takes a right turn and then runs 15 km . it then turns left and then runs for another 25 km and then takes the direction back to reach the main road . in the mean time , due to minor break down the other car has run only 35 km along the main road . what would be the distance between two cars at this point ?
Options: a ) 65 , b ) 38 , c ) 20 , d ) 28 , e ) 21
Rationale: answer : a ) 65 km
Answer: a
Python program:
a = 150 - 35
b = 25 + 25 
c = a - b
Problem: a sum of money at simple interest amounts to rs . 820 in 3 years and to rs . 854 in 4 years . the sum is :
Options: a ) 647 , b ) 718 , c ) 654 , d ) 847 , e ) 976
Rationale: "s . i . for 1 year = rs . ( 854 - 820 ) = rs . 34 . s . i . for 3 years = rs . ( 34 x 3 ) = rs . 102 . principal = rs . ( 820 - 102 ) = rs . 718 . answer : b"
Answer: b
Python program:
a = 854 - 820
b = a * 3
c = b / 4
d = 820 - c
Problem: what is the least number . which should be added to 0.0568 to make it a perfect square ?
Options: a ) 0.0004 , b ) 0.0009 , c ) 0.0002 , d ) 0.0003 , e ) 0.0008
Rationale: "0.0568 + 0.0008 = 0.0576 ( 0.24 ) ^ 2 answer : e"
Answer: e
Python program:
a = 12 + 4 
b = a + 2 
c = b / 100
d = 12 + 4 
e = d + 2 
f = e / 100
g = c * f
h = g - 0
Problem: the average of first five multiples of 5 is :
Options: a ) 9 , b ) 15 , c ) 17 , d ) 8 , e ) 10
Rationale: "explanation : ( 5 ( 1 + 2 + 3 + 4 + 5 ) / 5 = 5 x 15 / 5 = 15 answer : b"
Answer: b
Python program:
a = 5 + 1
Problem: a cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.1 m and its walls are 5 cm thick . the thickness of the bottom is :
Options: a ) 90 cm , b ) 1 dm , c ) 1 m , d ) 1.1 cm , e ) none of these
Rationale: "explanation : let the thickness of the bottom be x cm . then , [ ( 330 - 10 ) × ( 260 - 10 ) × ( 110 - x ) ] = 8000 × 1000 = > 320 × 250 × ( 110 - x ) = 8000 × 1000 = > ( 110 - x ) = 8000 × 1000 / 320 = 100 = > x = 10 cm = 1 dm . answer : b"
Answer: b
Python program:
a = 3 * 3
b = a * 1
c = 8000 / 1000
d = b - c
Problem: a theater charges $ 12 for seats in the orchestra and $ 8 for seats in the balcony . on a certain night , a total of 380 tickets were sold for a total cost of $ 3,320 . how many more tickets were sold that night for seats in the balcony than for seats in the orchestra ?
Options: a ) 90 , b ) 110 , c ) 120 , d ) 130 , e ) 240
Rationale: "orchestra seats - a balcony seats - b a + b = 380 and 12 a + 8 b = 3320 solving equations simultaneously ( multiply equation 1 with 8 and subtract from second equation ) 4 a = 3320 - 8 * 380 = 3320 - 3040 = 280 i . e . a = 70 and b = 380 - 70 = 310 more seats in balcony than orchestra = b - a = 310 - 70 = 240 answer : option e"
Answer: e
Python program:
a = 12 * 380
b = 3 * 1000
c = 3 * 100
d = b + c 
e = 2 * 10
f = d + e 
g = a - f
h = 12 - 8
i = g / h
j = 12 * 380
k = 3 * 1000
l = 3 * 100
m = k + l 
n = 2 * 10
o = m + n 
p = j - o
q = 12 - 8
r = p / q
s = 380 - r
t = i - s
Problem: 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 6 ohms ?
Options: a ) 7 / 30 , b ) 11 / 30 , c ) 11 / 15 , d ) 30 / 11 , e ) 15 / 11
Rationale: 1 / r = 1 / x + 1 / y 1 / r = 1 / 5 + 1 / 6 = 11 / 30 r = 30 / 11 the answer is d .
Answer: d
Python program:
a = 6 * 5
b = 5 + 6 
c = a / b
Problem: in a practice paper at 2 iim . com , questions were given from 5 topics . out of the appearing students , 10 % passed in all topics while 10 % did not pass in any . of the remaining , 20 % passed in one topic only and 25 % in two topics only . if 24 % of the total students passed 4 topics only and 500 students passed in 3 topics only , find the total number of students who appeared in the examination ?
Options: a ) 2500 , b ) 2000 , c ) 1600 , d ) 4545 , e ) 6565
Rationale: detailed solution let the number of appearing students be 100 . pass only in 0 topic – 10 1 – 16 ( 20 % of 80 ) 2 – 20 ( 25 % of 80 ) 3 – 20 % ( 100 – ( 16 + 20 + 24 + 20 ) ) 4 – 24 % 5 – 20 % therefore , 20 % of x = 500 = ) x = 2500 correct answer : a
Answer: a
Python program:
a = 100 - 10
b = a - 10
c = 20 + 25 
d = b * c
e = d / 100
f = e + 24 
g = f + 10 
h = g + 10 
i = 100 - h
j = i / 100
k = 500 / j
Problem: a person buys an article at rs . 650 . at what price should he sell the article so as to make a profit of 10 % ?
Options: a ) 600 , b ) 715 , c ) 269 , d ) 261 , e ) 281
Rationale: "cost price = rs . 650 profit = 10 % of 650 = rs . 65 selling price = cost price + profit = 650 + 65 = rs . 715 answer : b"
Answer: b
Python program:
a = 10 / 100
b = 650 * a
c = 650 + b
Problem: wink , inc . follows a certain procedure that requires two tasks to be finished independently in order for a job to be done . on any given day , there is a 7 / 8 probability that task 1 will be completed on time , and a 1 / 5 probability that task 2 will be completed on time . on a certain day , what is the probability that task 1 will be completed on time , but task 2 will not ?
Options: a ) 1 / 20 , b ) 3 / 40 , c ) 13 / 40 , d ) 7 / 10 , e ) 13 / 22
Rationale: "p ( 1 and not 2 ) = 7 / 8 * ( 1 - 1 / 5 ) = 7 / 10 . answer : d ."
Answer: d
Python program:
a = 7 / 8
b = 1 / 7
c = 1 - b
d = a * c