euclaise/mathqa_programs huggingface dataset:
Problem: bruce purchased 8 kg of grapes at the rate of 70 per kg and 8 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 ) 1000 , d ) d ) 1065 , e ) e ) 1075
Rationale: "cost of 8 kg grapes = 70 × 8 = 560 . cost of 8 kg of mangoes = 55 × 8 = 440 . total cost he has to pay = 560 + 440 = 1000 c"
Answer: c
Python program:
a = 8 * 70
b = 8 * 55
c = a + b
Problem: the sum of the ages of 4 children born at the intervals of 3 years each is 36 years . what is the age of the youngest child ?
Options: a ) 22 , b ) 18 , c ) 4.5 , d ) 99 , e ) 38
Rationale: "let x = the youngest child . each of the other four children will then be x + 3 , x + 6 , x + 9 we know that the sum of their ages is 36 so , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) = 36 therefore the youngest child is 4.5 years old answer : c"
Answer: c
Python program:
a = 4 / 3
b = 36 / a
c = 4 - 1
d = c * 3
e = b - d
f = e / 3
Problem: a pump can fill a tank with water in 4 hours . because of a leak , it took 20 hours to fill the tank . the leak can drain all the water of the tank in ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 4 , e ) 2
Rationale: p - - > pump , l - - - > leak pipe - - - - - - - - - - p - - - - - - - - - l - - - - - - - - - - - - ( p - l ) - - time - - - - - - - - - 4 - - - - - - - - - x - - - - - - - - - - - - - 20 * rate - - - - - - - - - 5 - - - - - - - - - x - - - - - - - - - - - - - 1 work - - - - - - - 20 - - - - - - - - - 20 - - - - - - - - - - - 20 time required to empty the tank if leakage present = 20 / ( ( 5 ) - 1 ) = ( 20 ) / ( 4 ) = 5 ans - c
Answer: c
Python program:
a = 1 / 4
b = 1 / 20
c = a - b
d = 1 / c
Problem: suppose 5 monkeys take 5 minutes to eat 5 bananas . how many monkeys would it take to eat 15 bananas in 15 minutes ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 5 , e ) 13
Rationale: "one monkey takes 5 min to eat 1 banana , so in 15 mins 1 monkey will eat 3 bananas , so for 15 bananas in 15 min we need 15 / 3 = 5 monkeys answer : d"
Answer: d
Python program:
a = 15 / 5
b = 15 / a
Problem: what is the decimal equivalent of ( 1 / 4 ) ^ 6 ?
Options: a ) 0.0016 , b ) 0.0625 , c ) 0.16 , d ) 0.0002 , e ) 0.5
Rationale: "( 1 / 4 ) ^ 6 = 1 / 4096 = 0.0002 answer : d"
Answer: d
Python program:
a = 1 / 4
b = a ** 6
Problem: 3 men and 8 women complete a task in same time as 6 men and 2 women do . how much fraction of work will be finished in same time if 2 men and 2 women will do that task .
Options: a ) 3 / 7 , b ) 3 / 10 , c ) 3 / 18 , d ) 3 / 16 , e ) 3 / 11
Rationale: "3 m + 8 w = 6 m + 2 w 3 m = 6 w 1 m = 2 w therefore 3 m + 8 w = 14 w 2 m + 2 w = 6 w answer is 6 / 14 = 3 / 7 answer : a"
Answer: a
Python program:
a = 8 - 2
b = 6 - 3
c = a / b
d = c * 2
e = d + 2 
f = 8 - 2
g = 6 - 3
h = f / g
i = 6 * h
j = i + 2 
k = e / j
Problem: what is the remainder when the number 14 ^ 2 * 15 ^ 8 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 4 , e ) 5
Rationale: "14 ^ 2 has units digit 6 15 ^ 8 has units digit 5 thus 14 ^ 2 * 15 ^ 8 has units digit 0 and will be divisible by 5 . the remainder will be zero answer : ( a )"
Answer: a
Python program:
a = 5 / 5
Problem: rahul played weel in this season . his current batting averagge is 52 . if he score 78 runs in today match . his batting average will become 54 . how many matches had he played in this season .
Options: a ) 8 , b ) 12 , c ) 9 , d ) 6 , e ) 5
Rationale: "52 x + 78 = 54 ( x + 1 ) = > 2 x = 24 = > x = 12 answer : b"
Answer: b
Python program:
a = 78 - 54
b = 54 - 52
c = a / b
Problem: a container holding 12 ounces of a solution that is 1 part alcohol to 2 parts water is added to a container holding 9 ounces of a solution that is 1 part alcohol to 2 parts water . what is the ratio of alcohol to water in the resulting solution ?
Options: a ) 1 : 2 , b ) 3 : 7 , c ) 3 : 5 , d ) 4 : 7 , e ) 7 : 3
Rationale: "container 1 has 12 ounces in the ratio 1 : 2 or , x + 2 x = 12 gives x ( alcohol ) = 4 and remaining water = 8 container 2 has 9 ounces in the ratio 1 : 2 or , x + 2 x = 9 gives x ( alcohol ) = 3 and remaining water = 6 mixing both we have alcohol = 4 + 3 and water = 8 + 6 ratio thus alcohol / water = 7 / 14 = 1 / 2 answer a"
Answer: a
Python program:
a = 1 + 2 
b = 1 / a
c = 12 * b
d = 1 + 2 
e = 1 / d
f = 9 * e
g = c + f 
h = 12 + 9 
i = 1 + 2 
j = 1 / i
k = 12 * j
l = 1 + 2 
m = 1 / l
n = 9 * m
o = k + n 
p = h - o
q = g / p
Problem: some of the 50 % solution of acid was removed and this was replaced with an equal amount of 20 % solution of acid . as a result , a 35 % solution of acid was obtained . what fraction of the original solution was replaced ?
Options: a ) 1 / 3 , b ) 1 / 2 , c ) 2 / 3 , d ) 3 / 5 , e ) 4 / 7
Rationale: let x be the fraction of the original solution that was replaced . 0.5 * ( 1 - x ) + 0.2 ( x ) = 0.35 0.3 x = 0.15 x = 1 / 2 the answer is b .
Answer: b
Python program:
a = 50 + 20 
b = 35 / a
Problem: there are 202 lights which are functional and each is controlled by a separate on / off switch . two children a and b start playing with the switches . a starts by pressing every third switch till he reaches the end . b , thereafter , presses every fifth switch till he too reaches the end . if all switches were in off position at the beggining , how many lights are switched on by the end of this operation ?
Options: a ) 93 , b ) 94 , c ) 92 , d ) 96 , e ) 95
Rationale: "editing my solution : number of switches = 202 number of switches turned on by a : 3 , 6 , . . . 201 = 67 number of switches turned on by b : 5 , 10 , . . . . 200 = 40 few switches are turned on by a and later turned off by b : lcm ( 3,5 ) = 15 x = 15 , 30 , . . . . 90 = 6 . subtract the above 6 switches from both a and b as they are turned off . number of switches that are turned on = ( 67 - 6 ) + ( 40 - 6 ) = 95 answer : e"
Answer: e
Python program:
a = 202 / 3
b = math.floor(a)
c = 1 + 4 
d = 202 / c
e = math.floor(d)
f = b + e 
g = 1 + 4 
h = 3 * g
i = 202 / h
j = math.floor(i)
k = j * 2
l = f - k
Problem: the maximum number of students among them 1048 pens and 828 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :
Options: a ) 4 , b ) 8 , c ) 16 , d ) 1911 , e ) none of these
Rationale: "explanation : required number of students = h . c . f of 1048 and 828 = 4 . answer : a"
Answer: a
Python program:
a = math.gcd(1048, 828)
Problem: marts income is 40 percent more than tims income and tims income is 40 percent less than juans income . what percentage of juans income is marts income
Options: a ) 124 % , b ) b ) 120 % , c ) c ) 96 % , d ) d ) 80 % , e ) e ) 84 %
Rationale: "m = ( 140 / 100 ) t t = ( 60 / 100 ) j = > m = ( 84 / 100 ) j answer e ."
Answer: e
Python program:
a = 100 + 40 
b = 100 - 40
c = 100 / b
d = c * 100
e = a / d
f = e * 100
Problem: if all the 6 are replaced by 9 , then the algebraic sum of all the numbers from 1 to 100 ( both inclusive ) varies by
Options: a ) 330 , b ) 340 , c ) 350 , d ) 360 , e ) 370
Rationale: 1 11 21 . . . . . . . 91 2 12 22 . . . . . . . . 92 3 13 23 . . . . . . . . 93 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . there are total 20 occurrence of 6 . once place at 6 th row in every column and tens place in 6 th column and diff of 6 and 9 is 3 so 3 * 1 * 10 + 3 * 10 * 10 = 330 answer : a
Answer: a
Python program:
a = 9 - 6
b = a * 10
c = b * 10
d = 9 - 6
e = d * 10
f = c + e
Problem: a boy is travelling from his home to school at 3 km / hr and reached 7 min late . next day he traveled at 12 km / hr and reached 8 min early . distance between home and school ?
Options: a ) 1 km , b ) 3 km , c ) 4 km , d ) 5 km , e ) 6 km
Rationale: "let the distance be x t 1 = x / 3 hr t 2 = x / 12 hr difference in time = 7 + 8 = 15 = 1 / 4 hr x / 3 - x / 12 = 1 / 4 x / 4 = 1 / 4 x = 1 km answer is a"
Answer: a
Python program:
a = 7 / const_60
b = 8 / const_60
c = a + b 
d = 1 / 12
e = c / d
Problem: if f ( x ) = 2 x ^ 2 + y , and f ( 2 ) = 20 , what is the value of f ( 5 ) ?
Options: a ) 104 , b ) 60 , c ) 62 , d ) 50 , e ) 25
Rationale: "f ( x ) = 2 x ^ 2 + y f ( 2 ) = 20 = > 2 * ( 2 ) ^ 2 + y = 20 = > 8 + y = 20 = > y = 12 f ( 5 ) = 2 * ( 5 ) ^ 2 + 12 = 62 answer c"
Answer: c
Python program:
a = 2 ** 2
b = a * 2
c = 20 - b
d = 5 ** 2
e = 2 * d
f = c + e
Problem: in a 100 member association consisting of men and women , exactly 20 % of men and exactly 25 % women are homeowners . what is the least number of members who are homeowners ?
Options: a ) 21 , b ) 47 , c ) 45 , d ) 43 , e ) 41
Rationale: "solution simple out of 100 20 % are male i . e 20 and 25 % are female i . e 25 , so total homeowner is 45 . now min number homeowner is 20 and max is 45 so question ask us to find least and 21 has least value among all option . so ans is 21 . answer : a"
Answer: a
Python program:
a = 25 / 100
b = a * 20
c = 25 / 100
d = c * 20
e = b * d
f = 100 - 20
g = f / 20
h = e + g
Problem: of the land owned by a farmer , 90 percent was cleared for planting . of the cleared land , 10 percent was planted with grapes and 80 percent of the cleared land was planted with potato . if the remaining 450 acres of cleared land was planted with tomato , how many acres did the farmer own ?
Options: a ) 3500 , b ) 4500 , c ) 5500 , d ) 5250 , e ) 5000
Rationale: 10 % od 90 % = 9 % , 80 % 0 f 90 % = 72 % so the remaining 90 - 9 - 72 = 9 % = 450 acres or 10 % of 90 % = 9 % - - > 450 / 9 * 100 = 5000 acres answer ( e )
Answer: e
Python program:
a = 100 - 10
b = a - 80
c = b / 100
d = 90 / 100
e = c * d
f = 450 / e
Problem: the ages of 2 persons differ by 18 years . if 12 years ago the elder one be 6 times as old as the younger one , find the present age of elder person .
Options: a ) 33.6 , b ) 47 , c ) 50.4 , d ) 52.4 , e ) 47.9
Rationale: "age of the younger person = x age of the elder person = x + 18 6 ( x - 12 ) = x + 18 - 12 x = 15.6 age of elder person = 15.6 + 18 = 33.6 answer is a"
Answer: a
Python program:
a = 2 * 18
b = 18 - 1
c = a / b
d = c + 18 
e = d - 2
Problem: david obtained 36 , 35 , 42 , 57 and 55 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology what are his average marks ?
Options: a ) 75 , b ) 45 , c ) 87 , d ) 165 , e ) 11
Rationale: "explanation : average = ( 36 + 35 + 42 + 57 + 55 ) / 5 = 225 / 5 = 45 . answer : b"
Answer: b
Python program:
a = 36 + 35 
b = a + 42 
c = b + 57 
d = c + 55 
e = 2 + 3 
f = d / e
Problem: find the smallest number of five digits exactly divisible by 32 , 40,56 and 64 .
Options: a ) 11020 , b ) 11030 , c ) 11040 , d ) 11060 , e ) 11080
Rationale: "smallest number of five digits is 10000 . required number must be divisible by l . c . m . of 32,40 , 56,64 i . e 2240 , on dividing 10000 by 2240 , we get 1200 as remainder . therefore , required number = 10000 + ( 2240 â € “ 1200 ) = 11040 . answer is c ."
Answer: c
Python program:
a = 100 * 100
b = 10 * a
c = b - 100
d = c + 40
Problem: find compound interest on $ 16000 at 15 % per annum for 2 years 4 months , compounded annually .
Options: a ) 6109 , b ) 6209 , c ) 6218 , d ) 6107 , e ) 6100
Rationale: "time = 2 years 4 months = 2 ( 4 / 12 ) years = 2 ( 1 / 3 ) years . amount = $ [ 16000 x ( 1 + ­ ( 15 / 100 ) ) 2 x ( 1 + ( ( 1 / 3 ) * 15 ) / 100 ) ] = $ [ 16000 * ( 23 / 20 ) * ( 23 / 20 ) * ( 21 / 20 ) ] = $ 22218 . : . c . i . = rs . ( 22218 - 16000 ) = $ 6218 answer c ."
Answer: c
Python program:
a = 15 / 100
b = 16000 * a
c = 15 / 100
d = 16000 * c
e = 16000 + d 
f = 15 / 100
g = e * f
h = b + g 
i = 15 / 100
j = 16000 * i
k = 16000 + j 
l = 15 / 100
m = 16000 * l
n = 16000 + m 
o = 15 / 100
p = n * o
q = k + p 
r = 15 / 100
s = r / 3
t = q * s
u = h + t
Problem: the average score in an examination of 10 students of a class is 60 . if the scores of the top 5 students are not considered , the average score of the remaining students falls by 5 . the pass mark was 40 and the maximum mark was 100 . it is also known that none of the students failed . if each of the top 5 scorers had distinct integral scores , the maximum possible score of the topper is . . . . . .
Options: a ) 99 , b ) 100 , c ) 87 , d ) 95 , e ) 90
Rationale: detailed solution 10 students have scored 600 marks amongst them , and no one is allowed to score lesser than 40 or higher than 100 . the idea now is to maximize what the highest scorer gets . the 5 least scores have an average of 55 , which means that they have scored 55 x 5 = 275 marks amongst them . this leaves 325 marks to be shared amongst the top 5 students . lets call them a , b , c , d and e . now , in order to maximize what the top scorer “ e ” gets , all the others have to get the least possible scores ( and at the same time , they should also get distinct integers . ) the least possible score of the top 5 should be at least equal to the highest of the bottom 5 . now we want to make sure that the highest of the bottom 5 is the least possible . this can be done by making all scores equal to 55 . if some scores are less than 55 , some other scores have to be higher than 55 to compensate and make the average 55 . thus the highest score is the least only when the range is 0 . so now , we have the lowest value that the top 5 can score , which is 55 . the others have to get distinct integer scores , and as few marks as possible , so that “ e ” gets the maximum . so , 55 + 56 + 57 + 58 + e = 325 e = 99 marks . answer choice ( a )
Answer: a
Python program:
a = 10 * 60
b = 60 - 5
c = b * 5
d = a - c
e = 60 - 5
f = d - e
g = 60 - 5
h = g + 1 
i = f - h
j = 60 - 5
k = j + 2 
l = i - k
m = 60 - 5
n = m + 3 
o = l - n
Problem: 5 + 3 + 2 = 151022 9 + 2 + 4 = 183652 8 + 6 + 3 = 482466 5 + 4 + 5 = 202541 then ; 7 + 2 + 5 = ?
Options: a ) 253547 , b ) 143681 , c ) 143547 , d ) 147614 , e ) 255547
Rationale: c 143547
Answer: c
Python program:
a = 7 * 2
b = a * 10
c = b + 3 
d = c * 1000
e = 5 * 100
f = d + e 
g = 7 * 5
h = 7 * 2
i = g + h 
j = i - 2
k = f + j
Problem: on a map , 1.5 inches represent 24 miles . how many miles approximately is the distance if you measured 45 centimeters assuming that 1 - inch is 2.54 centimeters ?
Options: a ) 174.2 , b ) 212 , c ) 283 , d ) 296 , e ) 282.4
Rationale: "1.5 inch = 2.54 * 1.5 cm . so , 2.54 * 1.5 represents 24 miles . so for 45 cm . : 45 / ( 2.54 * 1.5 ) = x / 24 - - - > x = 24 * 45 / ( 3.81 ) = 283 answer will be c ."
Answer: c
Python program:
a = 45 / 2
b = 24 / 1
c = a * b
Problem: a labourer was engaged for 25 days on the condition that for every day , he works , he will be paid rs . 2 and for every day , he is absent he will be fined 50 p . if he receives only rs . 37 • 50 , find the no . of days he was absent is _____
Options: a ) 3 days , b ) 4 days , c ) 5 days , d ) 6 days , e ) 7 days
Rationale: if a labour worked for 25 days he should get 50 rs . but in this he is getting 13 rs less . if he do n ' t go for work for 1 day he will loose 2.5 rs then no of days ( absent ) = 13 / 2.5 = 5.2 . means he was absent for 5 days answer : c
Answer: c
Python program:
a = 50 / 100
b = 37 + a 
c = 50 - b
d = 50 / 100
e = d + 2 
f = c / e
Problem: a cycle is bought for rs . 930 and sold for rs . 1210 , find the gain percent ?
Options: a ) 70 % , b ) 30 % , c ) 40 % , d ) 50 % , e ) 80 %
Rationale: "explanation : 930 - - - - 280 100 - - - - ? = > 30 % answer : b"
Answer: b
Python program:
a = 1210 - 930
b = a / 930
c = b * 100
Problem: bob finishes the first half of an exam in two - sixth the time it takes him to finish the second half . if the whole exam takes him an hour , how many minutes does he spend on the first half of the exam ?
Options: a ) 15 , b ) 24 , c ) 27 , d ) 36 , e ) 40
Rationale: many times , it is easiest to think of problems like this conceptually ( as opposed to formulaically ) . conceptually , if the first half of the exam takes 2 / 6 ' s the time of the second half ( 6 / 6 ' s ) , we can see that the hour the entire exam took to finish can be broken down into eight ' s . ( another way to look at this problem is via ratio ' s - first half is 2 : 8 and the second half is 6 : 8 ) . with each sixth of an hour being 15 / 2 minutes ( 60 / 8 ) , the first half of the exam would have taken 15 minutes . correct answer is a .
Answer: a
Python program:
a = 2 + 4 
b = 2 / a
c = b * const_60
d = const_60 - c
Problem: 4 , 10 , ( ? ) , 82 , 244 , 730
Options: a ) 26 , b ) 24 , c ) 40 , d ) 48 , e ) 28
Rationale: "4 × 3 - 2 = 10 10 × 3 - 2 = 28 28 × 3 - 2 = 82 82 × 3 - 2 = 244 244 × 3 - 2 = 730 answer is e ."
Answer: e
Python program:
a = negate - (
Problem: the capacity of a cylindrical tank is 246.4 litres . if the height is 4 metres , what is the diameter of the base ?
Options: a ) 1.4 metres , b ) 2.8 metres , c ) 28 metres , d ) 14 metres , e ) none of these
Rationale: capacity ( volume ) of a cylindrical tank = π r 2 h ( here r = radius and h = height of the tank ) now , from the question , 246.4 × 0.001 = 22 ⁄ 7 × r 2 × 4 [ ∵ 1 litre = 1000 cm 3 = 0.001 m 3 ] or , 0.2464 × 7 / 22 × 4 = r 2 or , r = 0.14 m or , diameter = 2 r = 0.28 m answer e
Answer: e
Python program:
a = 246 * 4
b = 4 * 100
c = a / b
d = 3 + 4 
e = c * d
f = const_60 / 3
g = f + 2 
h = e / g
i = math.sqrt(h)
j = i * 2
Problem: calculate the ratio between x and y if 80 % of x equal to 20 % of y ?
Options: a ) 1 : 1 , b ) 3 : 1 , c ) 4 : 5 , d ) 4 : 3 , e ) 4 : 1
Rationale: explanation : 80 x = 20 y x : y = 80 : 20 = 4 : 1 answer : e
Answer: e
Python program:
a = 80 / 20
Problem: a cistern which could be filled in 9 hours takes one hour more to be filled owing to a leak in its bottom . if the cistern is full in what time will the leak empty it ?
Options: a ) 76 hrs , b ) 99 hrs , c ) 55 hrs , d ) 90 hrs , e ) 11 hrs
Rationale: "1 / 9 - 1 / x = 1 / 10 = > 90 hrs answer : d"
Answer: d
Python program:
a = 1 / 9
b = 1 / 10
c = a - b
d = 1/(c)
Problem: how many odd numbers between 10 and 1600 are the squares of integers ?
Options: a ) 9 , b ) 12 , c ) 15 , d ) 18 , e ) 21
Rationale: "the numbers are the squares of 5 , 7 , 9 , . . . , 39 which includes 18 numbers . the answer is d ."
Answer: d
Python program:
a = 10 + 4
Problem: aaron will jog from home at 6 miles per hour and then walk back home by the same route at 12 miles per hour . how many miles from home can aaron jog so that he spends a total of 3 hours jogging and walking ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 15 , e ) 11
Rationale: "xyt / ( x + y ) x = 6 , y = 12 t = 3 6 * 12 * 3 / 6 + 12 = 12 answer : a"
Answer: a
Python program:
a = 6 * 12
b = a * 3
c = 6 * 12
d = b / c
Problem: if n is the greatest positive integer for which 2 ^ n is a factor of 6 ! , then n = ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "6 ! = 720 e . 2 ^ 10 = 512 ( 720 / 512 ) - this is not a factor of 6 ! d . 2 ^ 8 = 256 ( 720 / 256 ) - this is not a factor of 6 ! c . 2 ^ 6 = 64 ( 720 / 64 ) - this is not a factor of 6 ! b . 2 ^ 4 = 16 ( 720 / 16 ) - this is a factor of 6 ! b is answer"
Answer: b
Python program:
a = 6 / 2
b = a - 1
Problem: andrew travelling to 7 cities . gasoline prices varied from city to city . $ 1.75 , $ 1.61 , $ 1.79 , $ 2.11 , $ 1.96 , $ 2.09 , $ 1.85 . what is the median gasoline price ?
Options: a ) $ 1 , b ) $ 1.85 , c ) $ 1.92 , d ) $ 2.13 , e ) $ 2.15
Rationale: "ordering the data from least to greatest , we get : $ 1.61 , $ 1.75 , $ 1.79 , $ 1.85 , $ 1.96 , $ 2.09 , $ 2.11 the median gasoline price is $ 1.85 . ( there were 3 states with higher gasoline prices and 3 with lower prices . ) b"
Answer: b
Python program:
a = 1 + 75 
b = a + 1 
c = b + 2 
d = c + 1 
e = d + 2 
f = e + 1 
g = f / 7
h = min(g)
Problem: find the value of a / b + b / a , if a and b are the roots of the quadratic equation x 2 + 9 x + 3 = 0 ?
Options: a ) 28.3 , b ) 1.45 , c ) 2.78 , d ) 6.84 , e ) 7.23
Rationale: "a / b + b / a = ( a 2 + b 2 ) / ab = ( a 2 + b 2 + a + b ) / ab = [ ( a + b ) 2 - 2 ab ] / ab a + b = - 9 / 1 = - 9 ab = 3 / 1 = 3 hence a / b + b / a = [ ( - 9 ) 2 - 2 ( 3 ) ] / 3 = 56 / 4 = 28.3 . a )"
Answer: a
Python program:
a = negate ** (
b = a / 2
c = b - 3
Problem: if 20 men can build a water fountain 56 metres long in 6 days , what length of a similar water fountain can be built by 35 men in 3 days ?
Options: a ) 40 m , b ) 44 m , c ) 47 m , d ) 49 m , e ) 50 m
Rationale: explanation : let the required length be x metres more men , more length built ( direct proportion ) less days , less length built ( direct proportion ) men 20 : 35 days 6 : 3 : : 56 : x therefore ( 20 x 6 x x ) = ( 35 x 3 x 56 ) x = ( 35 x 3 x 56 ) / 120 = 49 hence , the required length is 49 m . answer : d
Answer: d
Python program:
a = 20 * 6
b = 56 / a
c = 35 * 3
d = b * c
Problem: each factor of 230 is inscribed on its own plastic ball , and all of the balls are placed in a jar . if a ball is randomly selected from the jar , what is the probability that the ball is inscribed with a multiple of 46 ?
Options: a ) 1 / 16 , b ) 5 / 42 , c ) 1 / 8 , d ) 3 / 16 , e ) 1 / 4
Rationale: "so the # of factors 230 has 8 ( see below ) ; so out of 8 factors only two are multiples of 46 : 46 and 230 , itself ; so , the probability is 2 / 8 = 1 / 4 . answer : e ."
Answer: e
Python program:
a = math.comb(46, 1)
b = a / 46
c = 3 ** 2
d = b / c
Problem: a certain psychologist charges $ 25 more for the first hour of therapy than for each additional hour . if the total charge to a patient who receives 5 hours of therapy is $ 250 , what is the total charge to a patient who receives only 2 hours of therapy ?
Options: a ) $ 115 , b ) $ 135 , c ) $ 150 , d ) $ 165 , e ) $ 192
Rationale: "let the charge for first hour = x + 25 then charge for each additional hour = x x + 25 + 4 x = 250 = > 5 x = 225 = > x = 45 total charge for patient for 3 hours of therapy = x + 25 + x = 2 x + 25 = 115 $ answer a"
Answer: a
Python program:
a = 250 - 25
b = a / 5
c = b * 2
d = c + 25
Problem: there are 8 stores in town that had a total of 23 visitors on a particular day . however , only 12 people went shopping that day ; some people visited more than one store . if 8 people visited exactly two stores each , and everyone visited at least one store , what is the largest number of stores anyone could have visited ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "8 people visited 2 stores each for 16 visits . to maximize the number of stores that one person visited , let ' s assume that 3 people visited 1 store each . the number of remaining visits is 23 - 16 - 3 = 4 , which is the maximum that one person could have visited . the answer is c ."
Answer: c
Python program:
a = 8 * 2
b = 23 - a
c = 12 - 8
d = c - 1
e = b - d
Problem: if difference between compound interest and simple interest on a sum at 10 % p . a . for 2 years is rs . 61 then sum is
Options: a ) s . 6100 , b ) s . 5100 , c ) s . 5800 , d ) s . 6000 , e ) s . 6200
Rationale: "p ( r / 100 ) ^ 2 = c . i - s . i p ( 10 / 100 ) ^ 2 = 61 6100 answer : a"
Answer: a
Python program:
a = 10 / 100
b = 10 / 100
c = a * b
d = 61 / c
Problem: a sum of money at simple interest amounts to rs . 815 in 4 years and to rs . 854 in 5 years . the sum is :
Options: a ) 659 , b ) 698 , c ) 780 , d ) 910 , e ) none
Rationale: "sol . s . i . for 1 year = rs . ( 854 - 815 ) = rs . 39 . s . i . for 4 years = rs . ( 39 * 4 ) = rs . 156 . â ˆ ´ principal = rs . ( 815 - 156 ) = rs . 659 answer a"
Answer: a
Python program:
a = 854 - 815
b = a * 4
c = b / 5
d = 815 - c
Problem: according to the directions on a can of frozen orange juice concentrate , 1 can of concentrate is to be mixed with 4 cans of water to make orange juice . how many 12 ounce cans of concentrate are required to prepare 120 6 - ounce servings of orange juice ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: 1 x 12 ounce can of concentrate + 4 x 12 ounce cans of water = 60 ounces of the mixture . 60 ounces of mixture gives ( 60 / 6 ) = 10 servings . thus 1 x 12 ounce can of concentrate is used to produce 10 servings of the mixture . to make 120 servings of the mixture , we need 120 / 10 = 12 cans of the concentrate . the answer is b .
Answer: b
Python program:
a = 120 * 6
b = 4 + 1 
c = a / b
d = c / 12