euclaise/mathqa_programs huggingface dataset:
Problem: if john makes a contribution to a charity fund at school , the average contribution size will increase by 50 % reaching $ 75 per person . if there were 2 other contributions made before john ' s , what is the size of his donation ?
Options: a ) $ 125 , b ) $ 150 , c ) $ 200 , d ) $ 250 , e ) $ 450
Rationale: "cavg = average contribution before john cavg * 1.5 = 75 , therefore the average cont is $ 50 before john . if he needs to increase the average contribution by $ 25 , he must put in $ 25 for each of the 2 people . so $ 50 . but , he also has to put in the average for himself ( the threeth person ) , so add $ 75 . so $ 125 is your answer . answer a"
Answer: a
Python program:
a = 2 + 1 
b = a * 75
c = 2 + 1 
d = c * 50
e = b - d
f = e + 50
Problem: if 20 % of a number = 100 , then 120 % of that number will be ?
Options: a ) 20 , b ) 120 , c ) 360 , d ) 600 , e ) 820
Rationale: let the number x . then , 20 % of x = 100 x = ( 100 * 100 ) / 20 = 500 120 % of x = ( 120 / 100 * 500 ) = 600 . answer : d
Answer: d
Python program:
a = 120 * 100
b = a / 20
Problem: in what ratio should a variety of rice costing rs . 20 per kg be mixed with another variety of rice costing rs . 31.50 per kg to obtain a mixture costing rs . 23.75 per kg ?
Options: a ) 16 : 30 , b ) 30 : 14 , c ) 16 : 31 , d ) 31 : 15 , e ) 15 : 31
Rationale: "let us say the ratio of the quantities of cheaper and dearer varieties = x : y by the rule of allegation , x / y = ( 31.50 - 23.75 ) / ( 23.75 - 20 ) = 31 / 15 answer : d"
Answer: d
Python program:
a = 31 - 50
b = 31 - 50
c = a / b
d = 31 - 50
e = 31 - 50
f = d / e
g = 1 - f
h = c / g
Problem: n and m are each 3 - digit integers . each of the numbers 2 , 34 , 6 , 7 , and 8 is a digit of either n or m . what is the smallest possible positive difference between n and m ?
Options: a ) 39 , b ) 49 , c ) 58 , d ) 113 , e ) 131
Rationale: you have 6 digits : 2 , 3 , 4 , 6 , 7 , 8 each digit needs to be used to make two 3 digit numbers . this means that we will use each of the digits only once and in only one of the numbers . the numbers need to be as close to each other as possible . the numbers can not be equal so the greater number needs to be as small as possible and the smaller number needs to be as large as possible to be close to each other . the first digit ( hundreds digit ) of both numbers should be consecutive integers now let ' s think about the next digit ( the tens digit ) . to minimize the difference between the numbers , the tens digit of the greater number should be as small as possible and the tens digit of the smaller number should be as large as possible . so let ' s not use 2 and 8 in the hundreds places and reserve them for the tens places . now what are the options ? try and make a pair with ( 3 * * and 4 * * ) . make the 3 * * number as large as possible and make the 4 * * number as small as possible . 387 and 426 ( difference is 39 ) or try and make a pair with ( 6 * * and 7 * * ) . make the 6 * * number as large as possible and make the 7 * * number as small as possible . we get 684 and 723 ( difference is 39 ) a
Answer: a
Python program:
a = 2 - 8
b = a * 10
c = 100 + b 
d = c - 1
Problem: if three painters can complete three rooms in two hours , how many hours 5 painters would it take to do 20 rooms ?
Options: a ) 6 , b ) 9 , c ) 7 , d ) 8 , e ) 5
Rationale: "explanation : three painters can complete three rooms in two hours . so 20 rooms can be painted in 8 hrs by 5 painters answer : e ) 5 painters"
Answer: e
Python program:
a = 20 * 3
b = a * 3
c = 3 * 3
d = b / c
Problem: if anangletis defined as 1 percent of 1 degree , then how many anglets are there in a fifth circle ?
Options: a ) 0.36 , b ) 7200 , c ) 360 , d ) 3,600 , e ) 36,000
Rationale: "1 degree * 1 / 100 = 1 anglet so 1 degree = 100 anglets = > 72 degrees = 7200 anglets answer - b"
Answer: b
Python program:
a = 2 + 4 
b = 1 / a
c = 3600 / 10
d = c * 100
e = b * d
Problem: worker a takes 5 hours to do a job . worker b takes 10 hours to do the same job . how long it take both a & b , working together but independently , to do the same job ?
Options: a ) 20 / 9 , b ) 40 / 9 , c ) 50 / 9 , d ) 60 / 9 , e ) 10 / 3
Rationale: "one day work of a = 1 / 5 one day work of b = 1 / 10 so one day work of a and b together = 1 / 5 + 1 / 10 = 3 / 10 so total days required = 10 / 3 answer : e"
Answer: e
Python program:
a = 1 / 5
b = 1 / 10
c = a + b 
d = 1 / c
Problem: every day , the value of a stock rises by exactly two dollars in the morning , and then falls by exactly one dollar in the afternoon . if the stock ' s value at the start of the first day is $ 100 , on what day will the stock ' s value first reach $ 200 ?
Options: a ) 50 , b ) 99 , c ) 100 , d ) 101 , e ) 200
Rationale: note that each day the stock is worth $ 1 more than on the previous day , and that on the first day it rises to $ 102 and then falls to $ 101 . therefore , on the nth day , the stock ' s value rises to n + 101 dollars in the morning and falls to n + 100 dollars in the afternoon . the solution is therefore the smallest n for which n + 101 = 200 , or n = 99 . in particular , the stock will be $ 200 in the middle of day 99 , although not at the end of this day . correct answer b
Answer: b
Python program:
a = 200 - 100
b = 2 - 1
c = a / b
Problem: how many pieces of 75 cm can be cut from a rope 52.5 meters long ?
Options: a ) 30 , b ) 40 , c ) 60 , d ) none , e ) can not be determined
Rationale: "explanation : total pieces of 75 cm that can be cut from a rope of 52.5 meters long is = ( 52.5 meters ) / ( 75 cm ) = ( 52.5 meters ) / ( 0.75 meters ) = 70 answer : d"
Answer: d
Python program:
a = 52 / 5
Problem: bruce purchased 8 kg of grapes at the rate of 70 per kg and 10 kg of mangoes at the rate of 55 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) a ) 1040 , b ) b ) 1050 , c ) c ) 1055 , d ) d ) 1110 , e ) e ) 1075
Rationale: "cost of 8 kg grapes = 70 × 8 = 560 . cost of 10 kg of mangoes = 55 × 10 = 550 . total cost he has to pay = 560 + 550 = 1110 d"
Answer: d
Python program:
a = 8 * 70
b = 10 * 55
c = a + b
Problem: for a certain exam , a score of 86 was 5 standard deviations above mean and a score of 67 was 2.5 standard deviations above mean . what was the mean score for the exam ?
Options: a ) 50 , b ) 55 , c ) 48 , d ) 42 , e ) 49
Rationale: "mean + 5 sd = 86 mean + 2.5 sd = 67 by solving above equations we get , sd ( absolute value ) = 7.6 mean = 48 ans . c"
Answer: c
Python program:
a = 86 * 2
b = 67 * 5
c = a + b 
d = 5 + 3 
e = c / d
Problem: 162 students represent x percent of the boys at a school . if the boys at the school make up 50 % of the total school population of x students , what is x ?
Options: a ) 120 , b ) 150 , c ) 180 , d ) 250 , e ) 440
Rationale: "let b be the number of boys in the school . 162 = xb / 100 b = 0.5 x 16200 = 0.5 x ^ 2 x ^ 2 = 32400 x = 180 the answer is c ."
Answer: c
Python program:
a = 162 * 100
b = 50 / 100
c = a / b
d = math.sqrt(c)
Problem: if x , y , and z are positive integers , and 4 x = 5 y = 6 z , then the least possible value of x + y + z is
Options: a ) 15 , b ) 28 , c ) 37 , d ) 42 , e ) 60
Rationale: take lcm of 4,5 and 6 = 60 now 4 x = 60 = > x = 15 5 y = 60 = > y = 12 6 z = 60 = > z = 10 115 + 12 + 10 = 37 . option c .
Answer: c
Python program:
a = 4 * 5
b = a * 6
c = b / 2
d = c / 4
e = 4 * 5
f = e * 6
g = f / 2
h = g / 5
i = d + h 
j = 4 * 5
k = j * 6
l = k / 2
m = l / 6
n = i + m
Problem: what is the remainder when 3 ^ 30 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "the units digit of powers of 3 follow a repeating cycle of four : { 3 , 9 , 7 , 1 } 30 has the form 4 k + 2 , so the units digit of 3 ^ 30 is 9 . the remainder when dividing by 5 is 4 . the answer is e ."
Answer: e
Python program:
a = 5 / 2
b = 3 * 3
c = a - b
Problem: if two painters can complete four rooms in two hours , how many painters would it take to do 24 rooms in 8 hours ?
Options: a ) 7 , b ) 8 , c ) 4 , d ) 6 , e ) 1
Rationale: "explanation : two painters can complete four rooms in two hours . so 24 rooms can be painted in 8 hrs by 4 painters answer : c ) 4 painters"
Answer: c
Python program:
a = 8 * 3
b = a * 3
c = 3 * 3
d = b / c
Problem: a tank is filled by 3 pipes with uniform flow . the first two pipes operating simultaneously fill the tan in the same time during which the tank is filled by the third pipe alone . the 2 nd pipe fills the tank 5 hours faster than first pipe and 4 hours slower than third pipe . the time required by first pipe is
Options: a ) 13 hours , b ) 45 hours , c ) 15 hours , d ) 12 hours , e ) 11 hours
Rationale: if first pipe fills tank in x hrs , then second pipe fills tank in x - 5 hrs and 3 rd pipe fills tank in x - 9 hrs , then as per given condition 1 / x + 1 / ( x - 5 ) = 1 / ( x - 9 ) solving it , we get x = 15 hrs answer : c
Answer: c
Python program:
a = 5 + 4 
b = a * 2
c = 5 + 4 
d = c * 2
e = d ** 2
f = 5 + 4 
g = 5 * f
h = 4 * g
i = e - h
j = math.sqrt(i)
k = b + j 
l = k / 2
Problem: a train 210 m in length crosses a telegraph post in 13 seconds . the speed of the train is ?
Options: a ) 77 kmph , b ) 55 kmph , c ) 54 kmph , d ) 58 kmph , e ) 76 kmph
Rationale: s = 210 / 13 * 18 / 5 = 58 kmph answer : d
Answer: d
Python program:
a = 210 / 13
b = const_3_6 * a
Problem: a sum was put at simple interest at certain rate for 3 years . had it been put at 1 % higher rate it would have fetched rs . 75 more . the sum is : a . rs . 2,400 b . rs . 2,100 c . rs . 2,200 d . rs . 2,480
Options: a ) 2500 , b ) 2100 , c ) 2200 , d ) 2300 , e ) 2400
Rationale: "1 percent for 3 years = 75 1 percent for 1 year = 25 = > 100 percent = 2500 answer : a"
Answer: a
Python program:
a = 75 / 3
b = a * 100
Problem: alex takes a loan of $ 5,000 to buy a used truck at the rate of 2 % simple interest . calculate the annual interest to be paid for the loan amount .
Options: a ) 100 , b ) 150 , c ) 720 , d ) 200 , e ) 750
Rationale: "from the details given in the problem principle = p = $ 5,000 and r = 2 % or 0.02 expressed as a decimal . as the annual interest is to be calculated , the time period t = 1 . plugging these values in the simple interest formula , i = p x t x r = 5,000 x 1 x 0.02 = 100.00 annual interest to be paid = $ 100 answer : a"
Answer: a
Python program:
a = 2 * 100
b = math.sqrt(100)
c = a * b
d = c * 2
e = d / 100
Problem: during the first two weeks of january , the total rainfall in springdale was 40 inches . if the rainfall during the second week was 1.5 times the rainfall during the first week , what was the rainfall during the second week of january ?
Options: a ) 5 inches , b ) 6 inches , c ) 9 inches , d ) 10 inches , e ) 24 inches
Rationale: "total rainfall in 2 weeks = 40 inches . assume the rainfall in second week = 1 . x rainfall in first week = x total rainfall = 2.5 x = 40 inches x = 16 and 1.5 x = 24 rainfall during second week = 24 inches option e"
Answer: e
Python program:
a = 1 + 1 
b = 1 / 5
c = 40 * b
Problem: tom , working alone , can paint a room in 20 hours . peter and john , working independently , can paint the same room in 10 hours and 5 hours , respectively . tom starts painting the room and works on his own for two hour . he is then joined by peter and they work together for two hour . finally , john joins them and the three of them work together to finish the room , each one working at his respective rate . what fraction of the whole job was done by peter ?
Options: a ) 5 / 7 , b ) 7 / 8 , c ) 2 / 5 , d ) 3 / 5 , e ) 1 / 5
Rationale: "let the time when all three were working together be t hours . then : tom worked for t + 4 hour and has done 1 / 20 * ( t + 4 ) part of the job ; peter worked for t + 2 hour and has done 1 / 10 * ( t + 2 ) part of the job ; john worked for t hours and has done 1 / 5 * t part of the job : 1 / 20 * ( t + 4 ) + 1 / 10 * ( t + 2 ) + 1 / 5 * t = 1 - - > multiply by 20 - - > ( t + 4 ) + ( 2 t + 2 ) + 4 t = 20 - - > t = 2 ; hence peter has done 1 / 10 * ( 2 + 2 ) = 4 / 10 = 2 / 5 answer : c"
Answer: c
Python program:
a = 4 * 2
b = a + 1 
c = 4 / b
Problem: a van takes 5 hours to cover a distance of 450 km . what speed in kph should the van maintain to cover the same distance in 3 / 2 of the previous time ?
Options: a ) 56 , b ) 60 , c ) 64 , d ) 68 , e ) 72
Rationale: "( 3 / 2 ) * 5 = 7.5 hours 450 / 7.5 = 60 kph the answer is b ."
Answer: b
Python program:
a = 3 / 2
b = a * 5
c = 450 / b
Problem: what is the compound interest paid on a sum of rs . 4500 for the period of 2 years at 10 % per annum .
Options: a ) 945 , b ) 620 , c ) 610 , d ) 600 , e ) none of these
Rationale: "solution = interest % for 1 st year = 10 interest % for 2 nd year = 10 + 10 % of 10 = 10 + 10 * 10 / 100 = 11 total % of interest = 10 + 11 = 21 total interest = 21 % 4500 = 4500 * ( 21 / 100 ) = 945 answer a"
Answer: a
Python program:
a = 10 / 100
b = 1 + a 
c = b ** 2
d = 4500 * c
e = d - 4500
Problem: at veridux corporation , there are 250 employees . of these , 90 are female , and the rest are males . there are a total of 40 managers , and the rest of the employees are associates . if there are a total of 145 male associates , how many female managers are there ?
Options: a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 35
Rationale: "250 employees : 90 male , 160 female 40 managers , 210 associates 145 male associates implies 65 female associates which means the remaining 25 females must be managers c . 25"
Answer: c
Python program:
a = 40 * 1
Problem: if 10 parallel lines in a plane is intersected by a family of another 8 parallel lines , how many parallelograms are there in the network thus formed ?
Options: a ) 80 , b ) 63 , c ) 120 , d ) 160 , e ) 1260
Rationale: "parallelogram can formed by 2 horizontal and 2 vertical lines for horizontal 10 c 2 for vertical 8 c 2 total parallelogram is 10 c 2 * 8 c 2 = 45 * 28 = 1260 answer : e"
Answer: e
Python program:
a = 10 - 1
b = 10 * a
c = b / 2
d = 8 - 1
e = 8 * d
f = e / 2
g = c * f
Problem: on rainy mornings , mo drinks exactly n cups of hot chocolate ( assume that n is an integer ) . on mornings that are not rainy , mo drinks exactly 5 cups of tea . last week mo drank a total of 22 cups of tea and hot chocolate together . if during that week mo drank 8 more tea cups than hot chocolate cups , then how many rainy days were there last week ?
Options: a ) 2 , b ) 4 , c ) 3 , d ) 5 , e ) 6
Rationale: "t = the number of cups of tea c = the number of cups of hot chocolate t + c = 22 t - c = 8 - > t = 15 . c = 7 . mo drinks 5 cups of tea a day then number of days that are not rainy = 15 / 5 = 3 so number of rainy days = 7 - 3 = 4 b is the answer ."
Answer: b
Python program:
a = 4 + 3 
b = 22 + 8 
c = b / 2
d = c / 5
e = a - d
Problem: two cars a and b start from boston and new york respectively simultaneously and travel towards each other at constant speeds along the same route . after meeting at a point between boston and new york the two cars a and b proceed to their respective destinations of new york and boston . car a reaches new york 10 minutes after the two cars have met and car b reaches boston 90 minutes after they have met . how long did car a take to cover the distance between boston and new york ?
Options: a ) 1 hour , b ) 1 hour 10 minutes , c ) 2 hours 30 minutes , d ) 50 minutes , e ) 2 hours 10 minutes
Rationale: "both cars leave at the same time both cars travel at constant speed stealing a useful piece of information from paragkan : if two objects a and b start from opposite points and , after having met en route , reach their respective destinations in a and b mins ( or any other measure of time ) respectively , then the ratio of their speeds ratio of speed : ( a / b ) = sq . rt ( b / a ) sq . rt ( b / a ) sq . rt ( 90 / 10 ) sq . rt ( 3 / 2 ) so , for every three units of distance a travels , b travels two . because we know the ratio of speed and the time it took b to travel the distance a has n ' t yet covered , we can find the time it took a to cover the distance b did in 90 minutes . 90 * ( 2 / 3 ) where 2 / 3 represents the lesser amount of time it took a to travel the distance b did in 90 minutes . = 60 minutes . therefore , a took 10 minutes to travel the first portion then 60 minutes to travel the distance b did in 90 minutes . a spent ( 10 + 60 ) = 50 minutes on the road . d . 50 minutes"
Answer: d
Python program:
a = 10 / 90
b = math.sqrt(a)
c = b * 90
d = c + 10
Problem: 70 % of a number is added to 120 , the result is the same number . find the number ?
Options: a ) 300 , b ) 400 , c ) 1687 , d ) 997 , e ) 121
Rationale: "( 70 / 100 ) * x + 120 = x 2 x = 800 x = 400 answer : b"
Answer: b
Python program:
a = 120 / 100
b = 120 / a
Problem: two spherical balls lie on the ground touching . if one of the balls has a radius of 4 cm , and the point of contact is 6 cm above the ground , what is the radius of the other ball ?
Options: a ) 10 cm , b ) 12 cm , c ) 14 cm , d ) 16 cm , e ) 18 cm
Rationale: similar triangle properties . . 2 / r + 4 = 4 / r - 4 giving r = 14 . answer : c
Answer: c
Python program:
a = 4 + 6 
b = a + 4
Problem: 1370 , 1320 , 1070 , - 180 ?
Options: a ) - 6430 , b ) - 6530 , c ) - 6630 , d ) - 6730 , e ) - 6830
Rationale: 1370 , 13201070 , - 180 , ? 1370 - 50 * ( 5 ^ 0 ) = 1320 1320 - 50 * ( 5 ^ 1 ) = 1070 1070 - 50 * ( 5 ^ 2 ) = - 180 - 180 - 50 * ( 5 ^ 3 ) = - 6430 answer : a .
Answer: a
Python program:
a = negate - (
Problem: mary and mike enter into a partnership by investing $ 650 and $ 350 respectively . at the end of one year , they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business . if mary received $ 600 more than mike did , what was the profit made by their business in that year ?
Options: a ) $ 3000 , b ) $ 3200 , c ) $ 3300 , d ) $ 3400 , e ) $ 4000
Rationale: "explanatory answer let the profit made during the year be $ 3 x therefore , $ x would have been shared equally and the remaining $ 2 x would have been shared in the ratio 6.5 : 3.5 i . e . , 65 % of 2 x would go to mary and 35 % of 2 x would go to mike . hence , mary would get ( 65 - 35 ) % of 2 x more than mike or 30 % of 2 x = $ 600 i . e . , ( 30 / 100 ) * 2 x = 600 or 2 x = 2000 . hence , the profit made by the company during the year $ 3 x = $ 3000 . answer : a"
Answer: a
Python program:
a = 650 / 1000
b = 350 / 1000
c = a - b
d = 1 / 3
e = 1 - d
f = c * e
g = 600 / f
Problem: a train 150 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train . find the speed of the train .
Options: a ) 45 kmph , b ) 50 kmph , c ) 85 kmph , d ) 60 kmph , e ) 70 kmph
Rationale: "explanation : let the speed of the train be x kmph . speed of the train relative to man = ( x + 5 ) kmph = ( x + 5 ) × 5 / 18 m / sec . therefore 150 / ( ( x + 5 ) × 5 / 18 ) = 6 < = > 30 ( x + 5 ) = 2700 < = > x = 85 speed of the train is 85 kmph . answer : option c"
Answer: c
Python program:
a = 6 * const_0_2778
b = 150 / a
c = b - 5
Problem: a , b and c start a business each investing 20,000 . after 5 months a withdrew 10000 , b withdrew 15000 and c invests 5000 more . at the end of the year , a total profit of 58000 was recorded . find the share of b .
Options: a ) 20,000 , b ) 21,200 , c ) 28,200 , d ) 13,500 , e ) none of these
Rationale: ratio of the capitals of a , b and c = 20000 ã — 5 + 10000 ã — 7 : 20000 ã — 5 + 5000 ã — 7 : 20000 ã — 5 + 25000 ã — 7 = 170000 : 135000 : 275000 = 170 : 135 : 275 . b â € ™ s share = ( 58000 ã — 135 â  „ 580 ) = 13500 answer d
Answer: d
Python program:
a = 12 - 5
b = a * 15000
c = 100 * 100
d = 2 * c
e = d * 5
f = b + e 
g = 100 * 10
h = f / g
Problem: in a college , the ratio of the number of boys to girls is 8 : 4 . if there are 200 girls , the total number of students in the college is
Options: a ) 420 , b ) 520 , c ) 600 , d ) 720 , e ) 820
Rationale: "explanation : let the boy are 8 x and girls are 4 x = > 4 x = 200 = > x = 50 total students = 8 x + 4 x = 12 x = 12 ( 50 ) = 600 option c"
Answer: c
Python program:
a = 200 / 4
b = a * 8
c = 200 + b
Problem: a certain bag contains 60 balls — 22 white , 18 green , 5 yellow , 6 red , and 9 purple . if a ball is to be chosen at random , what is the probability that the ball will be neither red nor purple ?
Options: a ) 0.09 , b ) 0.15 , c ) 0.54 , d ) 0.75 , e ) 0.91
Rationale: according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 22 + 18 + 5 ) / 60 = 45 / 60 = 0.75 . answer : d .
Answer: d
Python program:
a = 22 + 18 
b = a + 5 
c = b / 60
Problem: a and b start a business , with a investing the total capital of rs . 50000 , on the condition that b pays a interest @ 10 % per annum on his half of the capital . a is a working partner and receives rs . 1500 per month from the total profit and any profit remaining is equally shared by both of them . at the end of the year , it was found that the income of a is twice that of b . find the total profit for the year ?
Options: a ) 59028 , b ) 27777 , c ) 29999 , d ) 59000 , e ) 27772
Rationale: "interest received by a from b = 10 % of half of rs . 50000 = 10 % * 25000 = 2500 . amount received by a per annum for being a working partner = 1500 * 12 = rs . 18000 . let ' p ' be the part of the remaining profit that a receives as his share . total income of a = ( 2500 + 18000 + p ) total income of b = only his share from the remaining profit = ' p ' , as a and b share the remaining profit equally . income of a = twice the income of b ( 2500 + 18000 + p ) = 2 ( p ) p = 20500 total profit = 2 p + 18000 = 2 * 20500 + 18000 = 59000 . answer : d"
Answer: d
Python program:
a = 50000 / 2
b = a / 10
c = b * 3
d = c * 4
e = d + 1500
Problem: on a certain date , pat invested $ 6000 at x percent annual interest , compounded annually . if the total value of the investment plus interest at the end of 10 years will be $ 24000 , in how many years total will the total value of the investment plus interest increase to $ 48000 ?
Options: a ) 15 , b ) 16 , c ) 18 , d ) 20 , e ) 24
Rationale: 24,000 = 6,000 ( 1 + x ) ^ 10 4 = ( 1 + x ) ^ 10 = 2 ^ 2 ( 1 + x ) ^ 10 = ( ( 1 + x ) ^ 5 ) ^ 2 = 2 ^ 2 therefore , ( 1 + x ) ^ 5 = 2 48,000 = 6000 ( 1 + x ) ^ n ( 1 + x ) ^ n = 8 ( 1 + x ) ^ n = 2 ^ 3 ( 1 + x ) ^ n = ( ( 1 + x ) ^ 5 ) ^ 3 = ( 1 + x ) ^ 15 therefore , n = 15 . the answer is a .
Answer: a
Python program:
a = 24000 + 48000 
b = a / 6000
c = b + 3
Problem: equal amount of water were poured into two empty jars of different capacities , which made one jar 1 / 6 full and other jar 1 / 5 full . if the water in the jar with lesser capacity is then poured into the jar with greater capacity , what fraction of the larger jar will be filled with water ?
Options: a ) 1 / 7 , b ) 2 / 7 , c ) 1 / 3 , d ) 7 / 12 , e ) 2 / 3
Rationale: "same amount of water made bigger jar 1 / 6 full , thenthe same amount of water ( stored for a while in smaller jar ) were added to bigger jar , so bigger jar is 1 / 6 + 1 / 6 = 2 / 6 = 1 / 3 full . answer : c ."
Answer: c
Python program:
a = 2 / 6
Problem: abel can complete a work in 10 days , ben in 14 days and carla in 15 days . all of them began the work together , but abel had to leave after 2 days and ben 3 days before the completion of the work . how long did the work last ?
Options: a ) 6 , b ) 7 , c ) 7 10 / 29 , d ) 9 , e ) 10
Rationale: "abel in the 2 days that he worked completed 1 / 5 of the job = 4 / 5 remains then if ben had to leave 3 days before the completion , this means that carla had to work alone for these 3 days in which she completed 1 / 5 of the job . now together , ben and carla completed the job in ( 1 / 14 + 1 / 15 ) ( t ) = 3 / 5 29 / 210 ( t ) = 3 / 5 - - - > t = 126 / 29 therefore , these 4 10 / 29 days worked plus the 3 days that carla had to work by herself add to 7 10 / 29 days answer : c"
Answer: c
Python program:
a = 2 + 4 
b = a * 3
Problem: what is the smallest positive integer that can be multiplied by 432 to make it a perfect square ?
Options: a ) 2 , b ) 3 , c ) 5 , d ) 7 , e ) 11
Rationale: "432 = 2 ^ 4 * 3 ^ 2 * 3 therefore the smallest integer to multiplied to 1008 to make it a perfect square is 3 . answer b ."
Answer: b
Python program:
a = 3 + 4