euclaise/mathqa_programs huggingface dataset:
Problem: today joelle opened an interest - bearing savings account and deposited $ 5,000 . if the annual interest rate is 5 percent compounded interest , and she neither deposits nor withdraws money for exactly 2 years , how much money will she have in the account ?
Options: a ) $ 6512.50 , b ) $ 7512.50 , c ) $ 5512.50 , d ) $ 4512.50 , e ) $ 5250.00
Rationale: "interest for 1 st year = 5000 * 5 / 100 = 250 interest for 2 nd year = 5250 * 5 / 100 = 262.50 total = 5000 + 250 + 262.50 = 5512.50 answer : c"
Answer: c
Python program:
a = 3 * 2
b = a * 100
c = b * 10
d = 3 * 2
e = d * 100
f = e * 10
g = f * 5
h = g / 100
i = c + h 
j = 3 * 2
k = j * 100
l = k * 10
m = 3 * 2
n = m * 100
o = n * 10
p = o * 5
q = p / 100
r = l + q 
s = r * 5
t = s / 100
u = i + t
Problem: if the sides of a triangle are 30 cm , 26 cm and 10 cm , what is its area ?
Options: a ) 120 , b ) 110 , c ) 130 , d ) 140 , e ) 150
Rationale: "the triangle with sides 30 cm , 26 cm and 10 cm is right angled , where the hypotenuse is 30 cm . area of the triangle = 1 / 2 * 26 * 10 = 130 cm 2 answer : option c"
Answer: c
Python program:
a = 26 * 10
b = a / 2
Problem: a store owner estimates that the average price of type a products will increase by 15 % next year and that the price of type b products will increase by 18 % next year . this year , the total amount paid for type a products was $ 4600 and the total price paid for type b products was $ 8400 . according to the store owner ' s estimate , and assuming the number of products purchased next year remains the same as that of this year , how much will be spent for both products next year ?
Options: a ) $ 15,202 , b ) $ 15,325 , c ) $ 16,000 , d ) $ 16,225 , e ) $ 17,155
Rationale: "cost of type a products next year = 1.15 * 4600 = 5290 cost of type b products next year = 1.18 * 8400 = 9912 total 5290 + 9912 = 15202 answer : a"
Answer: a
Python program:
a = 3 / 4
b = a * 1000
Problem: when positive integer n is divided by positive integer p , the quotient is 18 , with a remainder of 7 . when n is divided by ( p + 2 ) , the quotient is 10 and the remainder is 3 . what is the value of n ?
Options: a ) 151 , b ) 331 , c ) 511 , d ) 43 , e ) 87
Rationale: "n / p = 18 7 / p = 18 p + 7 n / ( p + 2 ) = 10 1 / ( p + 2 ) = 10 p + 20 + 3 solving these two equations we get p = 2 n = 43 answer is d"
Answer: d
Python program:
a = 10 * 2
b = a + 3 
c = b - 7
d = 18 - 10
e = c / d
f = 18 * e
Problem: ashok borrowed some money at the rate of 6 % p . a . for the first two years , at the rate of 9 % p . a . for the next 3 years and at the rate of 14 % p . a . for the period beyond 5 years . if he pays a total interest of 11400 / - at the end of 9 years , how much money did he borrow ?
Options: a ) 16060 , b ) 14000 , c ) 18000 , d ) 12000 , e ) none of these
Rationale: we have , si = p × r × t / 100 ∴ 11400 = p × 6 × 2 / 100 + p × 9 × 3 / 100 + p × 14 × 4 / 100 or , 12 p + 27 p + 56 p = 11400 × 100 or , 95 p = 11400 × 100 ∴ p = 12000 answer d
Answer: d
Python program:
a = 9 - 3
b = a - 2
c = 14 * b
d = c / 100
e = 6 * 2
f = e / 100
g = 9 * 3
h = g / 100
i = f + h 
j = d + i 
k = 11400 / j
Problem: ` ` i am 8 times as old as you were when i was as old as you are ` ` , said a man to his son . find out their present ages if the sum of the their ages is 75 years .
Options: a ) 23 , b ) 24 , c ) 25 , d ) 26 , e ) 27
Rationale: present age of boy x and previous age of boy y so present age of dad : 8 y and previous age is x so the gap between duration must be same so 8 y - x = x - y - - > x = 9 y / 2 and x + 8 y = 75 ( given ) - - > 9 y / 2 + y = 75 so y = 6 and and x = 27 therefore fathers age is 8 y = 8 * 6 = 48 and child ' s age = x = 27 answer : e
Answer: e
Python program:
a = 8 + 1 
b = 8 * 2
c = a / b
d = c + 1 
e = 75 / d
f = 75 - e
Problem: ada and paul received their scores on 3 tests . on the first test , ada ' s score was 10 points higher than paul ' s score . on the second test , ada ' s score was 4 points higher than paul ' s score . if paul ' s average ( arithmetic mean ) score on the 3 tests was 4 points higher than ada ' s average score on the 3 tests , then paul ' s score on the third test was how many points higher than ada ' s score ?
Options: a ) 9 , b ) 14 , c ) 17 , d ) 23 , e ) 26
Rationale: my take is option d ( 23 ) i followed a simple approach ( explained below ) : test 1 : ada ' s score = paul ' s score + 10 test 2 : ada ' s score = paul ' s score + 4 avg . of paul ' s score = 4 points higher than avg . of ada ' s score this implies that : sum of paul ' s score [ 3 tests ] = 12 points higher than sum of ada ' s score [ 3 tests ] ( 12 points higher since 3 points were given in terms of average of 3 scores ) so , paul needs to score 23 points higher than ada in test 3 , since paul needs to compensate for the lower score in test 1 and test 2 ( 26 = 10 + 4 + 12 ) e
Answer: e
Python program:
a = 4 * 3
b = a + 10 
c = b + 4
Problem: the simple interest on a certain sum of money for 3 years at 8 % per annum is half the compound interest on $ 4000 for 2 years at 10 % per annum . the sum placed on simple interest is ?
Options: a ) $ 1250 , b ) $ 1300 , c ) $ 1750 , d ) $ 2015 , e ) $ 1452
Rationale: c . i . = 4000 * ( 1 + 10 / 100 ) ^ 2 - 4000 = 4000 * 11 / 10 * 11 / 10 - 4000 = $ 840 sum = 420 * 100 / 3 * 8 = $ 1750 answer is c
Answer: c
Python program:
a = 10 / 100
b = 1 + a 
c = b ** 2
d = 4000 * c
e = d - 4000
f = e / 2
g = 8 / 100
h = 3 * g
i = f / h
Problem: teas worth rs . 126 per kg and rs . 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . if the mixture is worth rs 156 per kg , the price of the third variety per kg will be ?
Options: a ) rs . 147.50 , b ) rs . 785.50 , c ) rs . 178.50 , d ) rs . 258.50 , e ) none of these
Rationale: "explanation : since first and second varieties are mixed in equal proportions . so , their average price = rs . ( 126 + 135 ) / 2 . = > rs . 130.50 . so , the mixture is formed by mixing two varieties , one at rs . 130.50 per kg and the other at say , rs . x per kg in the ratio 2 : 2 , i . e . , 1 : 1 . we have to find x . by the rule of alligation , we have : cost of 1 kg cost of 1 kg of 1 st kind of 2 nd kind ( rs . 130.50 ) ( rs . x ) \ / mean price ( rs . 156 ) / \ x â ˆ ’ 156 22.50 = > x â ˆ ’ ( 156 / 22.50 ) = 1 . = > x â ˆ ’ 156 = 22.50 . = > x = 178.50 rs . answer : c"
Answer: c
Python program:
a = 1 + 1 
b = a + 2 
c = 156 * b
d = 126 + 135 
e = c - d
f = e / 2
Problem: in a company with 48 employees , some part - time and some full - time , exactly ( 1 / 3 ) of the part - time employees and ( 1 / 4 ) of the full - time employees take the subway to work . what is the greatest possible number of employees who take the subway to work ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: "let part time emp = x let full time emp = y then , 48 = x + y . . . . . . . . . ( 1 ) ( 1 / 3 ) x + ( 1 / 4 ) y = no . of ppl taking the subway 4 x + 3 y / 12 = no . of ppl taking the subway using 1 x / 12 + 3 * 48 / 12 = no . of ppl taking the subway so , the minimum value of x has to be 12 . hence to maximize the no . put 36 for x 36 / 12 + 12 / 4 = 15 answer : d"
Answer: d
Python program:
a = 48 * 3
b = 3 * 4
c = a / b
d = 3 * 4
e = 48 - d
f = 48 * 3
g = 3 * 4
h = f / g
i = e / h
j = c + i
Problem: what is the maximum number of pieces of birthday cake of size 3 ” by 3 ” that can be cut from a cake 21 ” by 21 ” ?
Options: a ) 5 , b ) 7 , c ) 49 , d ) 20 , e ) 25
Rationale: "the prompt is essentially asking for the maximum number of 3 x 3 squares that can be cut from a larger 21 by 21 square . since each ' row ' and each ' column ' of the larger square can be sub - divided into 7 ' pieces ' each , we have ( 7 ) ( 7 ) = 49 total smaller squares ( at maximum ) . c"
Answer: c
Python program:
a = 21 * 21
b = 3 * 3
c = a / b
Problem: in a certain company , the ratio of the number of managers to the number of non - managers in any department must always be greater than 7 : 37 . in the company , what is the maximum number of non - managers in a department that has 9 managers ?
Options: a ) 44 , b ) 45 , c ) 46 , d ) 47 , e ) 48
Rationale: "9 / 7 * 37 = 47.6 the answer is d ."
Answer: d
Python program:
a = 37 * 9
b = a / 7
c = math.floor(b)
Problem: a train covers a distance of 12 km in 10 min . if it takes 7 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 177 m , b ) 189 m , c ) 140 m , d ) 178 m , e ) 188 m
Rationale: "speed = ( 12 / 10 * 60 ) km / hr = ( 72 * 5 / 18 ) m / sec = 20 m / sec . length of the train = 20 * 7 = 140 m . answer : c"
Answer: c
Python program:
a = 12 / 10
b = a - 7
c = 12 / b
Problem: in a class of 78 students 41 are taking french , 22 are taking german . of the students taking french or german , 9 are taking both courses . how many students are not enrolled in either course ?
Options: a ) 26 , b ) 27 , c ) 24 , d ) 18 , e ) 11
Rationale: "explanation : you could solve this by drawing a venn diagram . a simpler way is to realize that you can subtract the number of students taking both languages from the numbers taking french to find the number taking only french . likewise find those taking only german . then we have : total = only french + only german + both + neither 78 = ( 41 - 9 ) + ( 22 - 9 ) + 9 + neither . not enrolled students = 24 answer : c"
Answer: c
Python program:
a = 41 + 22 
b = a - 9
c = 78 - b
Problem: if ( n + 2 ) ! / n ! = 182 , n = ?
Options: a ) 2 / 131 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "( n + 2 ) ! / n ! = 182 rewrite as : [ ( n + 2 ) ( n + 1 ) ( n ) ( n - 1 ) ( n - 2 ) . . . . ( 3 ) ( 2 ) ( 1 ) ] / [ ( n ) ( n - 1 ) ( n - 2 ) . . . . ( 3 ) ( 2 ) ( 1 ) ] = 132 cancel out terms : ( n + 2 ) ( n + 1 ) = 132 from here , we might just test the answer choices . since ( 14 ) ( 13 ) = 182 , we can see that n = 12 e"
Answer: e
Python program:
a = 4 + 4 
b = a - 1
Problem: in what ratio must tea at rs . 64 per kg be mixed with tea at rs . 74 per kg so that the mixture must be worth rs . 69 per kg ?
Options: a ) 1 : 1 , b ) 3 : 2 , c ) 4 : 3 , d ) 5 : 3 , e ) none
Rationale: "required ratio = 500 : 500 = 1 : 1 answer a"
Answer: a
Python program:
a = 74 - 69
b = 69 - 64
c = a / b
Problem: 36 . a 240 m long train crosses a platform of equal length in 27 s . what is the speed of the train in km / h ?
Options: a ) 48 , b ) 60 , c ) 56 , d ) 64 , e ) 68
Rationale: by the formula , speed = distance / time = ( 240 + 240 ) / 27 x ( 18 / 5 ) = 480 / 27 x 18 / 5 = 64 km / h answer : d
Answer: d
Python program:
a = 2 * 240
b = a / 27
c = 3600 / 1000
d = b * c
Problem: the base of a triangular field is three times its altitude . if the cost of cultivating the field at rs . 24.68 per hectare be rs . 333.18 , find its base and height .
Options: a ) 100 m
b ) 125 m
c ) 150 m
d ) 278 m
e ) 300 m
Rationale: sol . area of the field = total cost / rate = ( 333.18 / 25.6 ) hectares = 13.5 hectares ( 13.5 x 10000 ) m ^ 2 = 135000 m ^ 2 . let altitude = x metres and base = 3 x metres . then , ( 1 / 2 ) * 3 x * x = 135000 < = > x ^ 2 = 90000 < = > x = 300 . base = 900 m and altitude = 300 m . ans : e
Answer: e
Python program:
a = 333 / 18
b = a * 1000
c = b / 3
d = c / 10
e = 3 / 2
f = d / e
Problem: a , b and c enter into a partnership by investing $ 11000 , $ 15000 and $ 23000 respectively . at the end of 8 months , b receives $ 1540 as his share . find the share of a .
Options: a ) $ 811 , b ) $ 922 , c ) $ 1033 , d ) $ 1144 , e ) $ 1255
Rationale: "the ratio of capital of a , b and c = 11000 : 15000 : 23000 = 11 : 15 : 23 a ' s share = ( 11 / 15 ) * 1560 = $ 1144 the answer is d ."
Answer: d
Python program:
a = 15000 * 8
b = a / 100
c = 1540 / b
d = 11000 * c
e = d * 8
f = e / 100
Problem: if each year the population of the country grows by 30 % , how many years will elapse before the population of the country doubles ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 3 , e ) 7
Rationale: "till year 2000 , population is 100 . year 2001 : population becomes 130 . . . . . . . . . . . . . 1 year elapsed year 2002 : population becomes 169 . . . . . . . . . . . . . 2 year elapsed year 2004 : population > 200 . . . . . . . . . . . . . . . . . . 3 year elapsed answer : d"
Answer: d
Python program:
a = 4 + 4
Problem: if the median of a list of numbers is m , the first quartile of the list is the median of the numbers in the list that are less than m . what is the first quartile of the list of numbers 42 , 24 , 30 , 34 , 26 , 36 , 33 and 35 ?
Options: a ) 33 , b ) 28 , c ) 27 , d ) 24 , e ) 23
Rationale: "it is given that a quartile is the middle number of all numbers less than median . . so lets arrange the number in ascending order - 42 , 24 , 30 , 34 , 26 , 36 , 33 and 35 24 , 26 , 30 , 33 , 34 , 35 , 36 , 42 . . . numbers less than median are 24 , 26 , 30 , 33 . . the median of these numbers = center of 26 and 30 = 28 b"
Answer: b
Python program:
a = 24 + 26 
b = a / 2
Problem: how many integers are divisible by 3 between 20 ! and 20 ! + 20 inclusive ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "b - 7 20 ! is divisible by 3 there are 6 numbers between 10 ! and 10 ! + 20 that are divisible by 3 . hence 7"
Answer: b
Python program:
a = 20 / 3
b = a + 1
Problem: the speed of a boat in still water is 20 km / hr and the rate of current is 5 km / hr . the distance travelled downstream in 27 minutes is :
Options: a ) 9.25 , b ) 5.25 , c ) 7.25 , d ) 6.25 , e ) 11.25
Rationale: "explanation : speed downstream = ( 20 + 5 ) kmph = 25 kmph distance travelled = ( 25 * ( 27 / 60 ) ) km = 11.25 km . answer : e"
Answer: e
Python program:
a = 27 / const_60
b = 20 + 5 
c = a * b
Problem: if 4 people are selected from a group of 10 married couples , what is the probability that none of them would be married to each other ?
Options: a ) 1 / 33 , b ) 2 / 63 , c ) 1 / 3 , d ) 43 / 62 , e ) 11 / 12
Rationale: "if we are to select 4 people from 10 couples without any restriction , how many ways can we make the selection ? 20 ! / 4 ! 16 ! = 4845 if we are to select 4 people from 10 couples with restriction that no married couple can both make it to the group , only a representative ? 10 ! / 4 ! 6 ! = 210 but we know that to select a person from each couple , take 2 possibilities 210 * 2 * 2 * 2 * 2 = 3360 probability = desired / all possibilities = 3360 / 4845 = 43 / 62 answer : d"
Answer: d
Python program:
a = 10 * 2
b = 10 * 2
c = a / b
d = 4 * 4
e = 10 * 2
f = e - 1
g = d / f
h = c * g
i = 4 * 4
j = i - 2
k = 4 * 4
l = j / k
m = h * l
n = 4 * 4
o = n - 2
p = o - 2
q = 4 * 4
r = q - 1
s = p / r
t = m * s
Problem: what is the least number of square tiles required to pave the floor of a room 50 m 00 cm long and 11 m 25 cm broad ?
Options: a ) 724 , b ) 804 , c ) 814 , d ) 9000 , e ) none
Rationale: solution length of largest tile = h . c . f . of 5000 cm & 1125 cm = 25 cm . area of each tile = ( 25 x 25 ) cm 2 ∴ required number of tiles = [ 5000 x 1125 / 25 x 25 ] = 9000 . answer d
Answer: d
Python program:
a = 11 * 100
b = a + 25 
c = 50 * 100
d = b * c
e = 25 ** 2
f = d / e
Problem: in a fuel station the service costs $ 1.75 per car , every liter of fuel costs 0.65 $ . assuming that a company owns 12 cars and that every fuel tank contains 65 liters and they are all empty , how much money total will it cost to fuel all cars ?
Options: a ) 320 $ , b ) 380 $ , c ) 420 $ , d ) 450 $ , e ) 528 $
Rationale: "total cost = ( 1.75 * 12 ) + ( 0.65 * 12 * 65 ) = 21 + 507 = > 528 hence answer will be ( e ) 528"
Answer: e
Python program:
a = 0 * 65
b = a * 12
Problem: if the average of 37 , 69 , 47 and x is 46.5 , what is x ?
Options: a ) 37 , b ) 41 , c ) 50 , d ) 59 , e ) 33
Rationale: "x = 33 because : ( 37 + 69 + 47 + x ) / 4 = 46.5 ( 37 + 69 + 47 + x ) / 4 * 4 = 46.5 * 4 ( 37 + 69 + 47 + x ) = 186 ( 37 + 69 + 47 + x ) - 153 = 186 - 153 x = 33 therefore , the answer is e , 33 ."
Answer: e
Python program:
a = 37 * 2
b = 37 * 2
c = 69 - b
d = c * 37
e = a + d
Problem: joe ’ s average ( arithmetic mean ) test score across 4 equally weighted tests was 60 . he was allowed to drop his lowest score . after doing so , his average test score improved to 65 . what is the lowest test score that was dropped ?
Options: a ) 20 , b ) 45 , c ) 55 , d ) 65 , e ) 80
Rationale: "the arithmetic mean of 4 equally weighted tests was 60 . so what we can assume is that we have 4 test scores , each 60 . he dropped his lowest score and the avg went to 65 . this means that the lowest score was not 60 and other three scores had given the lowest score 5 each to make it up to 60 too . when the lowest score was removed , the other 3 scores got their 5 back . so the lowest score was 3 * 5 = 15 less than 60 . so the lowest score = 60 - 15 = 45 answer ( b )"
Answer: b
Python program:
a = 60 * 4
b = 65 * 3
c = a - b
Problem: if the number 992 , 132,24 x is divisible by 11 , what must be the value of x ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 0
Rationale: multiplication rule of 11 : ( sum of digits at odd places - sum of digits at even places ) should be divisible by 11 given number : 992 , 132,24 x sum of digits at odd places = 9 + 2 + 3 + 2 + x = 16 + x ( i ) sum of digits at even places = 9 + 1 + 2 + 4 = 16 ( ii ) ( i ) - ( ii ) = 16 + x - 16 = x - 0 hence x should be = 0 to make this a multiple of 11 ( 0 ) option e
Answer: e
Python program:
a = 3 * 10
b = a + 1 
c = b * 2
d = c * 4
e = d * 11
Problem: in kaya ' s teacher ' s desk there are 9 pink highlighters , 8 yellow highlighters , and 5 blue highlighters . how many highlighters are there in all ?
Options: a ) 11 , b ) 22 , c ) 77 , d ) 33 , e ) 88
Rationale: add the numbers of highlighters . 9 + 8 + 5 = 22 . answer is b .
Answer: b
Python program:
a = 9 + 8 
b = a + 5
Problem: a metal company ' s old machine makes bolts at a constant rate of 100 bolts per hour . the company ' s new machine makes bolts at a constant rate of 150 bolts per hour . if both machines start at the same time and continue making bolts simultaneously , how many minutes will it take the two machines to make a total of 500 bolts ?
Options: a ) 36 , b ) 72 , c ) 120 , d ) 144 , e ) 180
Rationale: "old machine 100 bolts in 60 mins so , 5 / 3 bolts in 1 min new machine 150 bolts in 60 mins so , 5 / 2 bolts in 1 min together , 5 / 3 + 5 / 2 = 25 / 6 bolts in 1 min so , for 500 bolts 500 * 6 / 25 = 120 mins ans c"
Answer: c
Python program:
a = 100 / const_60
b = 150 / const_60
c = a + b 
d = 500 / c
Problem: the average mark of a class of thirty two students is 75 . if 3 students whose marks are 28 and 34 are removed , then find the approximate average mark of the remaining students of the class .
Options: a ) 71 , b ) 74 , c ) 78 , d ) 70 , e ) 80
Rationale: exp . total mark of 32 students = 75 * 32 = 2400 , total mark after the removal of 2 students = 2400 – ( 28 + 34 ) = 2400 – 62 = 2338 approximate average mark = 2338 / ( 32 - 2 ) = 2338 / 30 = 78 answer : c
Answer: c
Python program:
a = 34 - 2
b = 75 * a
c = b - 28
d = c - 34
e = 34 - 2
f = e - 3
g = d / f
Problem: a can do a piece of work in 6 days , and b can do it in 5 days . if c , who can do the work in 12 days , joins them , how long will they take to complete the work ?
Options: a ) 2 days , b ) 3.5 days , c ) 2.2 days , d ) 4 days , e ) 5.7 days
Rationale: a , b , and c do the work in = 6 * 5 * 12 / 6 * 5 + 5 * 12 + 6 * 12 = 360 / 162 = 2.2 days answer is c
Answer: c
Python program:
a = 1 / 12
b = 1 / 6
c = 1 / 5
d = b + c 
e = a + d 
f = 1 / e
Problem: the average age of 20 students of a class is 20 years . out of these , the average age of 5 students is 14 years and that of the other 9 students is 16 years , the age of the 20 th student is
Options: a ) 186 , b ) 120 , c ) 152 , d ) 220 , e ) 220
Rationale: "explanation : age of the 20 th student = [ 20 * 20 - ( 14 * 5 + 16 * 9 ) ] = ( 400 - 214 ) = 186 years . answer : a"
Answer: a
Python program:
a = 20 * 20
b = 5 * 14
c = 9 * 16
d = b + c 
e = a - d
Problem: tom , working alone , can paint a room in 6 hours . peter and john , working independently , can paint the same room in 3 hours and 5 hours , respectively . tom starts painting the room and works on his own for one hour . he is then joined by peter and they work together for an 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 ) 19 / 35 , b ) 23 / 42 , c ) 27 / 55 , d ) 31 / 63 , e ) 35 / 74
Rationale: "tom paints 1 / 6 of the room in the first hour . tom and peter paint 1 / 6 + 1 / 3 = 1 / 2 of the room in the next hour for a total of 4 / 6 . the three people then paint the remaining 2 / 6 in a time of ( 2 / 6 ) / ( 21 / 30 ) = 10 / 21 hours peter worked for 31 / 21 hours so he painted 31 / 21 * 1 / 3 = 31 / 63 of the room . the answer is d ."
Answer: d
Python program:
a = 4 * 5
b = a + 1 
c = 4 / b
Problem: little roshini had $ 10.50 . he spent some money on sweets and gave to his two friends $ 3.40 each . how much money was spent for sweets ?
Options: a ) $ 4.70 , b ) $ 4.80 , c ) $ 3.85 , d ) $ 3.80 , e ) $ 3.70
Rationale: roshini spent and gave to his two friends a total of x + 3.40 + 3.40 = $ 3.65 money spent for sweet = 10.50 - 6.80 = $ 3.70 correct answer is e ) $ 3.70
Answer: e
Python program:
a = 2 * 3
b = 10 - 5
Problem: a company has two types of machines , type r and type s . operating at a constant rate a machine of r does a certain job in 36 hours and a machine of type s does the job in 9 hours . if the company used the same number of each type of machine to do job in 12 hours , how many machine r were used ?
Options: a ) 3 , b ) 4 , c ) 18 / 5 , d ) 9 , e ) 12
Rationale: "yes there is a typo in the question , i got the same ques on my gmat prep last week , and the questions goes as : a company has two types of machines , type r and type s . operating at a constant rate a machine of r does a certain job in 36 hours and a machine of type s does the job in 9 hours . if the company used the same number of each type of machine to do job in 2 hours , how many machine r were used ? so for a job to be done in 2 hours r = 1 / 2 r _ a ( rate of machine r ) = 1 / 36 r _ s ( rate of machine s ) = 1 / 9 lets say x machines are used to attain the desired rate , thus x / 36 + x / 9 = 1 / 2 ( desired r = 1 / 2 i . e . to complete the job in 2 hours ) ( x + 4 x ) / 36 = 1 / 2 5 x / 36 = 1 / 2 x = 18 / 5 . qa = 18 / 5 ( answer c )"
Answer: c
Python program:
a = 1 / 36
b = 1 / 2
c = a + b 
d = 9 * c
e = 1 / d
Problem: a batsman makes a score of 110 runs in the 11 th inning and thus increases his average by 5 . find his average after 11 th inning .
Options: a ) 40 , b ) 50 , c ) 60 , d ) 45 , e ) 56
Rationale: "let the average after 11 th inning = x then , average after 10 th inning = x - 5 10 ( x - 5 ) + 110 = 11 x x = 110 - 50 = 60 answer is c"
Answer: c
Python program:
a = 11 * 5
b = 110 - a
c = b + 5
Problem: if the population of a certain country increases at the rate of one person every 15 seconds , by how many persons does the population increase in 1 hour ?
Options: a ) 100 , b ) 120 , c ) 150 , d ) 180 , e ) 240
Rationale: "answer = 4 * 60 = 240 answer is e"
Answer: e
Python program:
a = const_60 / 15
b = a * 1
Problem: the difference of two numbers is 8 and one - fourth of their sum is 6 . find the numbers .
Options: a ) 16,8 , b ) 10,2 , c ) 17,6 , d ) 14,10 , e ) 12,4
Rationale: "let numbers be x and y . equation ( i ) : x - y = 8 equation ( ii ) : ( x + y ) / 4 = 6 solve system of equations : x = 16 , y = 8 a is the correct answer ."
Answer: a
Python program:
a = 10 / 2
b = a * 6
c = 10 / 2
d = c * 6
e = 8 + d 
f = e / 2
g = b - f
h = 10 / 2
i = g + h
Problem: a retailer bought a shirt at wholesale and marked it up 80 % to its initial price of $ 45 . by how many more dollars does he need to increase the price to achieve a 100 % markup ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "x is the buy price . x + 80 % x = 1,8 x is the sale price = 45 so x , the buy price becomes 45 / 1,8 = 25 % 100 mark up means x + 100 % x = 2 x so 50 . 50 - 45 = 5 answer : e"
Answer: e
Python program:
a = 80 / 100
b = 1 + a 
c = 45 / b
d = c * 2
e = d - 45