euclaise/mathqa_programs huggingface dataset:
Problem: jerry went to a shop and bought things worth rs . 35 , out of which 30 % went on sales tax on taxable purchases . if the tax rate was 6 % , then what was the cost of the tax free items ?
Options: a ) 19 , b ) 19.7 , c ) 21.3 , d ) 21.5 , e ) 29.7
Rationale: "total cost of the items he purchased = rs . 35 given that out of this rs . 35 , 30 % is given as tax = > total tax incurred = 30 % = rs . 30 / 100 let the cost of the tax free items = x given that tax rate = 6 % ∴ ( 35 − 30 / 100 − x ) 6 / 100 = 30 / 100 ⇒ 6 ( 35 − 0.3 − x ) = 30 ⇒ ( 35 − 0.3 − x ) = 5 ⇒ x = 35 − 0.3 − 5 = 29.7 e )"
Answer: e
Python program:
a = 30 / 100
b = 100 / 6
c = a * b
d = 30 / 100
e = c + d 
f = 35 - e
Problem: how long does a train 110 m long running at the speed of 36 km / hr takes to cross a bridge 132 m length ?
Options: a ) 82.1 sec , b ) 12.1 sec , c ) 24.2 sec , d ) 13.1 sec , e ) 12.15 sec
Rationale: "speed = 36 * 5 / 18 = 10 m / sec total distance covered = 110 + 132 = 242 m . required time = 242 / 10 = 24.2 sec . answer : c"
Answer: c
Python program:
a = 110 + 132 
b = 36 * const_0_2778
c = a / b
Problem: kathleen can paint a room in 3 hours , and anthony can paint an identical room in 5 hours . how many hours would it take kathleen and anthony to paint both rooms if they work together at their respective rates ?
Options: a ) 8 / 15 , b ) 4 / 3 , c ) 15 / 8 , d ) 9 / 4 , e ) 15 / 4
Rationale: "kat - - - 3 hrs - - - 1 room ; so rate is work / time = 1 / 3 anthony - - - 5 hrs - - - 1 room ; rate = 1 / 5 rate of kat and anthony together = 1 / 3 + 1 / 5 = 8 / 15 but we are told that they both paint 2 rooms which are identical . so ; work is 2 rooms , rate is 8 / 15 , total time required for both of them together to complete the work = 2 / ( 8 / 15 ) = 30 / 8 = 15 / 4 hence answer = e"
Answer: e
Python program:
a = 1 / 3
b = 1 / 5
c = a + b 
d = 1 / c
e = d * 3
Problem: 1200 men have provisions for 15 days . if 200 more men join them , for how many days will the provisions last now ?
Options: a ) 12.85 , b ) 12.62 , c ) 12.5 , d ) 12.24 , e ) 12.1
Rationale: "1200 * 15 = 1400 * x x = 12.85 . answer : a"
Answer: a
Python program:
a = 15 * 1200
b = 1200 + 200 
c = a / b
Problem: the average ( arithmetic mean ) of 4 positive integers is 50 . if the average of 2 of these integers is 35 , what is the greatest possible value that one of the other 2 integers can have ?
Options: a ) 55 , b ) 65 , c ) 100 , d ) 109 , e ) 129
Rationale: "a + b + c + d = 200 a + b = 70 c + d = 130 greatest possible = 129 ( just less than 1 ) answer = e"
Answer: e
Python program:
a = 50 * 4
b = 35 * 2
c = a - b
Problem: what will be the compound interest on a sum of rs . 21,000 after 3 years at the rate of 12 % p . a . ?
Options: a ) rs . 8503.49 , b ) rs . 9720 , c ) rs . 10123.20 , d ) rs . 10483.20 , e ) none
Rationale: "amount = [ 21000 * ( 1 + 12 / 100 ) 3 ] = 21000 * 28 / 25 * 28 / 25 * 28 / 25 = rs . 29503.49 c . i . = ( 29503.49 - 21000 ) = rs . 8503.49 answer : a"
Answer: a
Python program:
a = 4 * 100
b = a * 100
c = 12 / 100
d = 1 + c 
e = d ** 3
f = b * e
g = 4 * 100
h = g * 100
i = f - h
Problem: a man swims downstream 72 km and upstream 45 km taking 10 hours each time ; what is the speed of the current ?
Options: a ) 1.55 , b ) 1.85 , c ) 1.65 , d ) 1.35 , e ) 1.15
Rationale: "72 - - - 10 ds = 7.2 ? - - - - 1 45 - - - - 10 us = 4.5 ? - - - - 1 s = ? s = ( 7.2 - 4.5 ) / 2 = 1.35 answer : d"
Answer: d
Python program:
a = 45 / 10
b = 72 / 10
c = a + b 
d = c / 2
Problem: the length of a rectangle is twice its breadth . if its length is decreased by 5 cm and breadth is increased by 5 cm , the area of the rectangle is increased by 65 sq . cm . find the length of the rectangle .
Options: a ) 12 cm , b ) 14 cm , c ) 16 cm , d ) 18 cm , e ) 20 cm
Rationale: "explanation : let breadth = x . then , length = 2 x . then , ( 2 x - 5 ) ( x + 5 ) - 2 x * x = 65 = > 5 x - 25 = 65 = > x = 16 . length of the rectangle = 16 cm . answer : option c"
Answer: c
Python program:
a = 100 / 3
Problem: find the amount on rs . 6000 in 2 years , the rate of interest being 4 % per first year and 5 % for the second year ?
Options: a ) 5568 , b ) 6369 , c ) 5460 , d ) 5635 , e ) 6552
Rationale: "6000 * 104 / 100 * 105 / 100 = > 6552 answer : e"
Answer: e
Python program:
a = 100 + 4 
b = 6000 * a
c = b / 100
d = 100 + 5 
e = c * d
f = e / 100
Problem: an aeroplane covers a certain distance at a speed of 320 kmph in 4 hours . to cover the same distance in 1 2 / 3 hours , it must travel at a speed of :
Options: a ) 520 , b ) 620 , c ) 820 , d ) 768 , e ) 720
Rationale: "distance = ( 240 x 5 ) = 1280 km . speed = distance / time speed = 1280 / ( 5 / 3 ) km / hr . [ we can write 1 2 / 3 hours as 5 / 3 hours ] required speed = ( 1280 x 3 / 5 ) km / hr = 768 km / hr answer d ) 768 km / hr"
Answer: d
Python program:
a = 320 * 4
b = 2 / 3
c = 1 + b 
d = a / c
e = d / 2
Problem: a customer bought a product at the shop . however , the shopkeeper increased the price of the product by 20 % so that the customer could not buy the required amount of the product . the customer managed to buy only 70 % of the required amount . what is the difference in the amount of money that the customer paid for the second purchase compared to the first purchase ?
Options: a ) 16 % , b ) 18 % , c ) 20 % , d ) 22 % , e ) 24 %
Rationale: let x be the amount of money paid for the first purchase . the second time , the customer paid 0.7 ( 1.2 x ) = 0.84 x . the difference is 16 % . the answer is a .
Answer: a
Python program:
a = 20 / 100
b = a + 1 
c = 70 / 100
d = b * c
e = 1 - d
f = e * 100
Problem: a group of men decided to do a work in 10 days , but 5 of them became absent . if the rest of the group did the work in 12 days , find the original number of men ?
Options: a ) 15 , b ) 20 , c ) 30 , d ) 25 , e ) 18
Rationale: original number of men = 5 * 12 / ( 12 - 10 ) = 30 answer is c
Answer: c
Python program:
a = 5 * 12
b = 12 - 10
c = a / b
Problem: george can do a piece of work in 8 hours . paul can do the same work in 10 hours , hari can do the same work in 12 hours . george , paul and hari start the same work at 9 am , while george stops at 11 am , the remaining two complete the work . what time will the work complete ?
Options: a ) 12 : 00 pm , b ) 1 : 00 pm , c ) 2 : 00 pm , d ) 3 : 00 pm , e ) 4 : 00 pm
Rationale: ( ( 1 / 8 ) + ( 1 / 10 ) + ( 1 / 12 ) ) 2 + ( ( 1 / 10 ) + ( 1 / 12 ) ) ( x - 2 ) = 1 x = 4 hrs work started at 9 am . . takes 4 hrs to complete 9 am + 4 hrs = 1 : 00 pm answer : b
Answer: b
Python program:
a = 1 / 10
b = 1 / 12
c = a + b 
d = 1/(c)
e = 1 / 8
f = 1 / 10
g = e + f 
h = 1 / 12
i = g + h 
j = i * 2
k = 1 - j
l = d * k
m = l + 11 
n = m - 12
Problem: if x and y are both odd prime numbers and x < y , how many distinct positive integer factors does 2 xy have ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 12
Rationale: the solution should be the same for all numbers that fulfill the condition above . as x and y are odd prime numbers , they must be > 2 . also , they must be distinct as x < y . i choose x = 3 and y = 5 : how many factors does 2 x 3 x 5 = 30 have : 1 , 2 , 3 , 5 , 6 , 10 , 15 , 30 = 8 distinct positive integer factors . hence , the correct answer is d .
Answer: d
Python program:
a = 1 + 1 
b = 2 * a
c = 1 + 1 
d = b * c
Problem: if 3 cats can kill 3 rats in 3 minutes , how long will it take 100 cats to kill 100 rats ?
Options: a ) 1 minutes , b ) 2 minutes , c ) 3 minutes , d ) 4 minutes , e ) 5 minutes
Rationale: "it will take 3 minutes for 100 cats to kill 100 rats . 1 cat can kill 1 rat in 3 minutes , so 100 cats can kill 100 rats in 3 minutes answer c"
Answer: c
Python program:
a = 3 * 1
Problem: hammers and wrenches are manufactured at a uniform weight per hammer and a uniform weight per wrench . if the total weight of two hammers and three wrenches is one - third that of 6 hammers and 5 wrenches , then the total weight of one wrench is how many times that of one hammer ?
Options: a ) 1 / 4 , b ) 2 / 3 , c ) 1 , d ) 3 / 2 , e ) 2
Rationale: "x be the weight of a hammer and y be the weight of a wrench . ( 2 x + 3 y ) = 1 / 3 * ( 7 x + 5 y ) 3 ( 2 x + 3 y ) = ( 7 x + 5 y ) 6 x + 9 y = 7 x + 5 y 4 y = x y = x / 4 ans - a"
Answer: a
Python program:
a = 3 * 2
b = 6 - a
c = 3 * 2
d = c - 5
e = b / d
Problem: a certain quantity of 80 % solution is replaced with 25 % solution such that the new concentration is 35 % . what is the fraction of the solution that was replaced ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 9 / 11
Rationale: "let ' s say that the total original mixture a is 100 ml the original mixture a thus has 50 ml of alcohol out of 100 ml of solution you want to replace some of that original mixture a with another mixture b that contains 25 ml of alcohol per 100 ml . thus , the difference between 80 ml and 25 ml is 55 ml per 100 ml of mixture . this means that every time you replace 100 ml of the original mixture a by 100 ml of mixture b , the original alcohol concentration will decrease by 25 % . the question says that the new mixture , let ' s call it c , must be 35 % alcohol , a decrease of only 45 % . therefore , 45 out of 55 is 9 / 11 and e is the answer ."
Answer: e
Python program:
a = 35 - 25
b = 80 - 35
c = a / b
d = c + 1 
e = 1/(d)
Problem: the number of diagonals of a polygon of n sides is given by the formula c = n ( n - 3 ) / 2 . if a polygon has twice as many diagonals as sides , how many sides does it have ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: c = n ( n - 3 ) c = 2 * n 2 n = n ( n - 3 ) = > 2 = n - 3 = > n = 5 answer b
Answer: b
Python program:
a = 3 + 2
Problem: 5358 x 53 = ?
Options: a ) 272258 , b ) 272358 , c ) 283974 , d ) 274258 , e ) 274358
Rationale: "5358 x 51 = 5358 x ( 50 + 3 ) = 5358 x 50 + 5358 x 3 = 267900 + 16074 = 283974 . c )"
Answer: c
Python program:
a = 5358 / 53
b = a * 100
Problem: 80 is increased by 50 % . find the final number .
Options: a ) 100 , b ) 110 , c ) 120 , d ) 30 , e ) 160
Rationale: "final number = initial number + 50 % ( original number ) = 80 + 50 % ( 80 ) = 80 + 40 = 120 . answer c"
Answer: c
Python program:
a = 50 / 100
b = 80 * a
c = 80 + b
Problem: the total age of a and b is 12 years more than the total age of b and c . c is how many years younger than a ?
Options: a ) 12 , b ) 81 , c ) 77 , d ) 66 , e ) 73
Rationale: "( a + b ) - ( b + c ) = 12 a - c = 12 answer : a"
Answer: a
Python program:
a = 12 * 1
Problem: in a bag , there are 2400 ball , and their colors are red , green blue . . the ratio of the balls are 15 : 13 : 17 . then how many red color balls are available in the bag ?
Options: a ) 900 , b ) 1600 , c ) 750 , d ) 890 , e ) 1010
Rationale: red : green : blue = 15 + 13 + 17 = 45 ; ratio of the red balls = 15 / 40 simplify = 3 / 8 * 2400 = 900 . answer = a
Answer: a
Python program:
a = 15 + 13 
b = a + 17 
c = 17 / b
d = c * 2400
Problem: the average age of 39 students in a group is 10 years . when teacher ’ s age is included to it , the average increases by one . what is the teacher ’ s age in years ?
Options: a ) 50 , b ) 55 , c ) 60 , d ) can not be determined , e ) none of these
Rationale: "age of the teacher = ( 40 × 11 – 39 × 10 ) years = 50 years . answer a"
Answer: a
Python program:
a = 39 + 1
Problem: an alloy is to contain copper and zinc in the ratio 9 : 4 . the zinc required to be melted with 24 kg of copper is ?
Options: a ) 12 kg , b ) 8.3 kg , c ) 10.7 kg , d ) 15.5 kg , e ) 7 kg
Rationale: "let the required quantity of copper be x kg 9 : 4 : : 24 : x 9 x = 4 * 24 x = 10 2 / 3 kg = 32 / 3 = 10.7 kg answer is c"
Answer: c
Python program:
a = 24 * 4
b = a / 9
Problem: two trains of equal lengths take 9 sec and 15 sec respectively to cross a telegraph post . if the length of each train be 120 m , in what time will they cross other travelling in opposite direction ?
Options: a ) 10 , b ) 11.3 , c ) 13 , d ) 14 , e ) 15
Rationale: "speed of the first train = 120 / 9 = 13.3 m / sec . speed of the second train = 120 / 15 = 8 m / sec . relative speed = 13.3 + 8 = 21.3 m / sec . required time = ( 120 + 120 ) / 21.3 = 11.3 sec . answer : option b"
Answer: b
Python program:
a = 120 * 2
b = speed + ( 
c = a / b
Problem: trains a and b start simultaneously from stations 350 miles apart , and travel the same route toward each other on adjacent parallel tracks . if train a and train b travel at a constant rate of 40 miles per hour and 30 miles per hour , respectively , how many miles will train a have traveled when the trains pass each other , to the nearest mile ?
Options: a ) 112 , b ) 133 , c ) 150 , d ) 167 , e ) 200
Rationale: since we know the distance ( 350 ) and the combined rate ( 70 ) , we plug it into the formula : distance = rate * time 350 = 70 * time we can solve for the time they will meet cause we added the rate of train a and train b together . so the time will be 350 / 70 from dividing 70 on both sides to isolate time in the equation above . time will be 5 hours so now you can plug that in for train a ’ s distance . distance = rate * time distance = 40 * 5 distance = 200 according to answer choice e .
Answer: e
Python program:
a = 40 + 30 
b = 350 / a
c = 40 * b
Problem: harold works at a resort from the beginning of march to the end of september . during the month of august this past year , he made 6 times the average ( arithmetic mean ) of his monthly totals in tips for the other months . his total tips for august were what fraction of his total tips for all of the months he worked ?
Options: a ) 1 / 3 , b ) 2 / 5 , c ) 3 / 7 , d ) 1 / 2 , e ) 4 / 7
Rationale: the time from beginning of march to the end of september is 7 months . if x is the average monthly tip for all months other than august then his august month tip will be 6 * x his total tip for the 7 months = 6 * ( average tip for the months other than august ) + 6 x = 12 x august tips as a fraction of total tips = 6 x / 12 x = 1 / 2 . so d
Answer: d
Python program:
a = 6 * 1
b = 6 * 1
c = 6 * 1
d = b + c 
e = a / d
Problem: for how many values of n , is | | | n - 5 | - 10 | - 5 | = 2 ? ( those ls are mods )
Options: a ) 0 , b ) 2 , c ) 4 , d ) 8 , e ) more than 8
Rationale: i think its 8 | | | n - 5 | - 10 | - 5 | = 2 let | n - 5 | = a which makes above | | a - 10 | - 5 | = 2 let | a - 10 | = b which makes | b - 5 | = 2 now for the above b can take 3 , 7 for every b = 3 a can have 13 , 7 and for b = 7 a can have 17 and 3 so ' a ' has four solutions 13 , 7 , 17 and 3 for a = 13 ; x has 18 or - 8 thus has 2 for every combination hence 4 x 2 = 8 answer d
Answer: d
Python program:
a = 2 ** 3
Problem: mr . kramer , the losing candidate in a two - candidate election , received 942,568 votes , which was exactly 42 percent of all votes cast . approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast ?
Options: a ) 10 % , b ) 12 % , c ) 14 % , d ) 17 % , e ) 20 %
Rationale: "let me try a simpler one . lets assume that candidate got 42 % votes and total votes is 100 . candidate won = 42 remaining = 58 to get 50 % , candidate requires 8 votes from 100 which is 8 % and 8 votes from 58 . 8 / 58 = . 137 = 13.7 % which is approx 14 % . hence the answer is c ."
Answer: c
Python program:
a = 50 / 100
b = 42 / 100
c = a - b
d = 42 / 100
e = 1 - d
f = c / e
g = f * 100
Problem: a certain bus driver is paid a regular rate of $ 15 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 976 in total compensation , how many total hours did he work that week ?
Options: a ) 56 , b ) 51 , c ) 59 , d ) 54 , e ) 52
Rationale: "for 40 hrs = 40 * 15 = 600 excess = 976 - 600 = 376 for extra hours = . 75 ( 15 ) = 11.25 + 15 = 26.25 number of extra hrs = 376 / 26.25 = 14.3 = 14 approx . total hrs = 40 + 14 = 54 answer d"
Answer: d
Python program:
a = 15 * 40
b = 976 - a
c = 100 + 75 
d = 15 * c
e = d / 100
f = b / e
g = 40 + f
Problem: in a class , 6 students can speak tamil , 15 can speak gujarati and 6 can speak h . if two students can speak two languages and one student can speak all the 3 languages , then how many students are there in the class ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: t = 6 g = 15 h = 6 students can speak two languages ( suppose tamil & gujarati ) = 2 student can speak all the three languages = 1 student can speak only tamil language = 6 - 2 - 1 = 3 student can speak only gujarati language = 15 - 2 - 1 = 12 student can speak only h language = 6 - 1 = 5 so , total number of student = 2 + 1 + 3 + 12 + 5 = 23 answer : d
Answer: d
Python program:
a = 6 + 15 
b = 6 + a 
c = b - 3
d = c - 2
Problem: what should be the least number to be added to the 3198 number to make it divisible by 8 ?
Options: a ) 12 , b ) 17 , c ) 2 , d ) 77 , e ) 26
Rationale: "answer : 2 option : c"
Answer: c
Python program:
a = 8 - reminder
Problem: 10 % people of a village in sri lanka died by bombardment , 20 % of the remainder left the village on account of fear . if now the population is reduced to 3168 , how much was it in the beginning ?
Options: a ) a ) 3800 , b ) b ) 4200 , c ) c ) 4400 , d ) d ) 4500 , e ) e ) 4600
Rationale: "x * ( 90 / 100 ) * ( 80 / 100 ) = 3168 x = 4400 answer : c"
Answer: c
Python program:
a = 100 - 10
b = a / 100
c = 100 - 20
d = c / 100
e = b * d
f = 3168 / e
g = math.floor(f)
Problem: 60 men shake hands with each other . maximum no of handshakes without cyclic handshakes .
Options: a ) 190 , b ) 200 , c ) 210 , d ) 1770 , e ) 230
Rationale: "1 st person will shake hand with 59 people 2 nd person will shake hand with 58 people 3 rd person will shake hand with 57 people . . . . . . total no . of handshakes = 59 + 58 + 57 + . . . + 3 + 2 + 1 = 19 * ( 19 + 1 ) / 2 = 1770 or , if there are n persons then no . of shakehands = nc 2 = 60 c 2 = 1770 answer : d"
Answer: d
Python program:
a = 60 - 1
b = 60 / 2
c = a * b
Problem: what is the difference between the c . i . on rs . 4000 for 1 1 / 2 years at 4 % per annum compounded yearly and half - yearly ?
Options: a ) s . 2.04 , b ) s . 2.08 , c ) s . 1.63 , d ) s . 2.83 , e ) s . 2.42
Rationale: "c . i . when interest is compounded yearly = [ 4000 * ( 1 + 4 / 100 ) * ( 1 + ( 1 / 2 * 4 ) / 100 ] = 4000 * 26 / 25 * 51 / 50 = rs . 4243.2 c . i . when interest is compounded half - yearly = [ 4000 * ( 1 + 2 / 100 ) 2 ] = ( 4000 * 51 / 50 * 51 / 50 * 51 / 50 ) = rs . 4244.83 difference = ( 4244.83 - 4243.2 ) = rs . 1.63 . answer : c"
Answer: c
Python program:
a = 2 / 100
b = 1 + a 
c = 2 / 100
d = 1 + c 
e = b * d
f = 2 / 100
g = 1 + f 
h = e * g
i = 4000 * h
j = 2 / 100
k = 1 + j 
l = 4 / 100
m = 1 + l 
n = k * m
o = 4000 * n
p = i - o
Problem: 657.987 - ? + 56.84 = 324.943
Options: a ) a ) 899.015 , b ) b ) 752.804 , c ) c ) 389.884 , d ) d ) 629.906 , e ) of these
Rationale: "explanation : 389.884 answer : option c"
Answer: c
Python program:
a = 657 / 987
b = a * 56
c = 1 / 3
d = 657 / 987
e = d * 56
f = c * e
g = b - f
Problem: approximately what percentage of the world ’ s forested area is represented by finland given that finland has 53.42 million hectares of forested land of the world ’ s 8.076 billion hectares of forested land .
Options: a ) 0.0066 % , b ) 0.066 % , c ) 0.66 % , d ) 6.6 % , e ) 66 %
Rationale: since 1 billion is 1000 million soc changing all quantities to million finland forest area = 53.42 million hect . worlds ' s forest area = 8.076 billion hect . % = 53.42 * 100 / 8.076 * 1000 = 0.66 % answer c
Answer: c
Python program:
a = 53 / 42
b = a / 3
c = 10 - 1
d = b / c
Problem: two stations a and b are 65 km apart on a straight line . one train starts from a at 7 a . m . and travels towards b at 20 kmph . another train starts from b at 8 a . m . and travels towards a at a speed of 25 kmph . at what time will they meet ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 8
Rationale: suppose they meet x hours after 7 a . m . distance covered by a in x hours = 20 x km . distance covered by b in ( x - 1 ) hours = 25 ( x - 1 ) km . therefore 20 x + 25 ( x - 1 ) = 65 45 x = 90 x = 2 . so , they meet at 9 a . m . answer : option a
Answer: a
Python program:
a = 65 - 20
b = 25 + 20 
c = a / b
d = 8 + c
Problem: divide rs . 800 among a , b and c so that a receives 1 / 3 as much as b and c together and b receives 2 / 3 as a and c together . a ' s share is ?
Options: a ) s . 800 , b ) s . 200 , c ) s . 600 , d ) s . 500 , e ) s . 900
Rationale: "a + b + c = 800 a = 1 / 3 ( b + c ) ; b = 2 / 3 ( a + c ) a / ( b + c ) = 1 / 3 a = 1 / 4 * 800 = > 200 answer : b"
Answer: b
Python program:
a = 800 / 3
Problem: x and y invested in a business . they earned some profit which they divided in the ratio of 2 : 3 . if x invested rs . 60,000 . the amount invested by y is
Options: a ) rs . 45,000 , b ) rs . 50,000 , c ) rs . 60,000 , d ) rs . 90,000 , e ) none
Rationale: "solution suppose y invested rs . y then , 60000 / y = 2 / 3 â € ¹ = â € º y = ( 60000 ã — 3 / 2 ) . â € ¹ = â € º y = 90000 . answer d"
Answer: d
Python program:
a = 1 + 4 
b = a * 1000
c = b * 2
d = c / 3
Problem: salesperson a ' s compensation for any week is $ 360 plus 6 percent of the portion of a ' s total sales above $ 1,000 for that week . salesperson b ' s compensation for any week is 10 percent of a ' s total sales for that week . for what amount of total weekly sales would both salepeople earn the same compensation ?
Options: a ) $ 21,000 , b ) $ 18,000 , c ) $ 15,00 , d ) $ 4,500 , e ) $ 15,000
Rationale: sometime , setting up an equation is an easy way to go with : 360 + 0.06 ( x - 1000 ) = 0.1 x x = 15,000 ans : e
Answer: e
Python program:
a = 6 / 100
b = a * 1000
c = 360 - b
d = 10 / 100
e = 6 / 100
f = d - e
g = c / f
h = 6 / 100
i = h * 1000
j = 360 - i
k = 10 / 100
l = 6 / 100
m = k - l
n = j / m
o = g + n 
p = o / 1000
Problem: what is the smallest positive integer k such that the product of 61347 x k is a perfect square ?
Options: a ) 3 , b ) 9 , c ) 15 , d ) 25 , e ) 63
Rationale: "a perfect square , is just an integer that can be written as the square of some other integer . for example 16 = 4 ^ 2 , is a perfect square . now , 61347 = 13 ^ 2 * 11 ^ 2 * 3 , so if k = 3 then 61347 k = ( 13 * 11 * 3 ) ^ 2 , which is a perfect square ( basically the least positive value of k must complete only the power of 7 to even power as powers of other primes are already even ) . answer : a ."
Answer: a
Python program:
a = 3 + 4
Problem: the total age of a and b is 13 years more than the total age of b and c . c is how many years younger than a . ?
Options: a ) 16 , b ) 12 , c ) 15 , d ) 20 , e ) 13
Rationale: "( a + b ) - ( b - c ) = 13 a - c = 13 answer is e"
Answer: e
Python program:
a = 13 * 1
Problem: a pupil ' s marks were wrongly entered as 67 instead of 45 . due to that the average marks for the class got increased by half . the number of pupils in the class is :
Options: a ) 30 , b ) 80 , c ) 44 , d ) 25 , e ) 26
Rationale: "let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 . x / 2 = ( 67 - 45 ) = > x / 2 = 22 = > x = 44 . answer : c"
Answer: c
Python program:
a = 67 - 45
b = a * 2
Problem: how long does a train 100 m long traveling at 60 kmph takes to cross a bridge of 170 m in length ?
Options: a ) sec , b ) sec , c ) sec , d ) sec , e ) sec
Rationale: "d = 100 + 170 = 270 m s = 60 * 5 / 18 = 50 / 3 t = 270 * 3 / 50 = 16.2 sec answer : d"
Answer: d
Python program:
a = 100 + 170 
b = 60 * const_0_2778
c = a / b
Problem: a marketing survey of anytown found that the ratio of trucks to sedans to motorcycles was 3 : 7 : 2 , respectively . given that there are 9,100 sedans in anytown , how many motorcycles are there ?
Options: a ) 1260 , b ) 2600 , c ) 3600 , d ) 4200 , e ) 5200
Rationale: let the total number of trucks = 3 x total number of sedans = 7 x total number of motorcycles = 2 x total number of sedans = 9100 = > 7 x = 9100 = > x = 1300 total number of motorcycles = 2 x = 2 * 1300 = 2600 answer b
Answer: b
Python program:
a = 3 * 3
b = a * 1000
c = b + 100 
d = c / 7
e = d * 2