euclaise/mathqa_programs huggingface dataset:
Problem: working together at their respective constant rates , machine a and machine b can produce 1,800 units in 8 hours . working alone , machine b would complete that same output in 50 % more time . if machine a were to work on its own for an 8 - hour shift , what percent of the 1,800 unit total would it produce ?
Options: a ) 25 , b ) 33 , c ) 30 , d ) 67 , e ) 75
Rationale: "1 / a + 1 / b = 1 / t 1 / a + 1 / 12 = 1 / 8 ( 50 % more of 8 is 12 ) 1 / a = 1 / 24 machine a can produce 1800 units in 24 hrs , so it can produce 1800 * 8 / 24 = 600 units is 8 hrs . 600 is 30 % of 1800 . c is the answer"
Answer: c
Python program:
a = 4 * 4
b = a * 100
c = b / 8
d = 4 * 4
e = d * 100
f = 8 * 50
g = f / 100
h = 8 + g 
i = e / h
j = c - i
k = j * 8
l = 4 * 4
m = l * 100
n = k / m
o = n * 100
Problem: a coin is tossed 6 times . what is the probability of getting exactly 5 heads ?
Options: a ) 3 / 8 , b ) 3 / 16 , c ) 5 / 16 , d ) 3 / 32 , e ) 7 / 64
Rationale: "the number of possible outcomes is 2 ^ 6 = 64 there are 6 ways to get exactly 5 heads . p ( exactly 5 heads ) = 6 / 64 = 3 / 32 the answer is d ."
Answer: d
Python program:
a = 1 / 2
b = a ** 5
c = math.comb(6, 5)
d = 1 / 2
e = c * d
f = b * e
Problem: at a supermarket , john spent 1 / 4 of his money on fresh fruits and vegetables , 1 / 3 on meat products , and 1 / 6 on bakery products . if he spent the remaining $ 6 on candy , how much did john spend at the supermarket ?
Options: a ) $ 24 , b ) $ 80 , c ) $ 90 , d ) $ 120 , e ) $ 180
Rationale: "let ' s let t = total number of dollars spent at the supermarket . with this variable we can set up an equation and determine t . we are given that john spent 1 / 4 of his money on fresh fruits and vegetables , or ( 1 / 4 ) t , 1 / 3 on meat products , or ( 1 / 3 ) t , and 1 / 6 on bakery products , or ( 1 / 6 ) t . we are also given that he spent the remaining $ 6 on candy . since we know where all his money was allocated , we can sum these values together and set the sum to t . so we have : ( 1 / 4 ) t + ( 1 / 3 ) t + ( 1 / 6 ) t + 6 = t to get rid of the fractions we can multiply the entire equation by 12 , and we obtain : 3 t + 4 t + 2 t + 72 = 12 t 9 t + 72 = 12 t 72 = 3 t t = 24 john spent $ 24 at the supermarket . answer : a"
Answer: a
Python program:
a = 1 / 6
b = 1 / 3
c = a + b 
d = 1 / 4
e = c + d 
f = 1 - e
g = 6 / f
Problem: a and b are two multiples of 14 , and q is the set of consecutive integers between a and b , inclusive . if q contains 13 multiples of 14 , how many multiples of 7 are there in q ?
Options: a ) 23 , b ) 24 , c ) 25 , d ) 26 , e ) 27
Rationale: halfway between the multiples of 14 , there will be another multiple of 7 . the total number of multiples of 7 is 13 + 12 = 25 . the answer is c .
Answer: c
Python program:
a = 13 * 2
b = a - 1
Problem: the population of a bacteria colony doubles every day . if it was started 6 days ago with 2 bacteria and each bacteria lives for 12 days , how large is the colony today ?
Options: a ) 512 , b ) 768 , c ) 1024 , d ) 2048 , e ) 128
Rationale: "2 ^ 6 ( 2 ) = 2 ^ 7 = 128 the answer is e ."
Answer: e
Python program:
a = 6 + 1 
b = 2 ** a
c = b - 1
Problem: in an election between two candidates , one got 55 % of the total valid votes , 20 % of the votes were invalid . if the total number of votes was 7500 , the number of valid votes that the other candidate got , was :
Options: a ) 2800 , b ) 2700 , c ) 2900 , d ) 2200 , e ) 2300
Rationale: "b number of valid votes = 80 % of 7500 = 6000 . valid votes polled by other candidate = 45 % of 6000 = ( 45 / 100 x 6000 ) = 2700 ."
Answer: b
Python program:
a = 20 / 100
b = 1 - a
c = 55 / 100
d = 1 - c
e = b * d
f = e * 7500
Problem: the credit card and a global payment processing companies have been suffering losses for some time now . a well known company recently announced its quarterly results . according to the results , the revenue fell to $ 48.0 billion from $ 85.0 billion , a year ago . by what percent did the revenue fall ?
Options: a ) 20.8 , b ) 30.4 , c ) 43.5 , d ) 32.5 , e ) 33.8
Rationale: $ 85 - $ 48 = 37 $ ( 37 / 85 ) * 100 = 43.5 % answer : c
Answer: c
Python program:
a = 85 - 48
b = a / 85
c = b * 100
Problem: 10 ^ 23 - 7 is divided by 6 , remainder is ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: anything power by 10 we got 10 and some zeros after that . ( i . e , 1000000000000000 . . . . ) on that , we minus 7 means , we must get last two digits is 93 . and 93 is divided by 6 , we get reminder 3 . answer : a
Answer: a
Python program:
a = 23 - 10
b = a - 6
c = b - 4
Problem: in an examination , a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer . if he attempts all 60 questions and secures 110 marks , the no of questions he attempts correctly is :
Options: a ) 34 , b ) 38 , c ) 40 , d ) 42 , e ) 44
Rationale: "explanation : let the number of correct answers be x . number of incorrect answers = ( 60 – x ) . 4 x – ( 60 – x ) = 110 = > 5 x = 170 = > x = 34 answer : a"
Answer: a
Python program:
a = 110 + 60 
b = 4 + 1 
c = a / b
Problem: the average speed of a car decreased by 3 miles per hour every successive 8 - minutes interval . if the car traveled 3.6 miles in the sixth 8 - minute interval , what was the average speed of the car , in miles per hour , in the first 8 minute interval ?
Options: a ) 30 , b ) 34 , c ) 38 , d ) 42 , e ) 46
Rationale: "( 3.6 miles / 8 minutes ) * 60 minutes / hour = 27 mph let x be the original speed . x - 5 ( 3 ) = 27 x = 42 mph the answer is d ."
Answer: d
Python program:
a = 8 / const_60
b = 3 / 6
c = b + 3 
d = c + 3 
e = d + 3 
f = e + 3
Problem: in an office , 20 percent of the workers have at least 5 years of service , and a total of 16 workers have at least 10 years of service . if 90 percent of the workers have fewer than 10 years of service , how many of the workers have at least 5 but fewer than 10 years of service ?
Options: a ) 32 , b ) 64 , c ) 50 , d ) 144 , e ) 160
Rationale: "( 10 / 100 ) workers = 16 = > number of workers = 160 ( 20 / 100 ) * workers = x + 16 = > x = 32 answer a"
Answer: a
Python program:
a = 10 / 100
b = 16 / a
c = b * 90
d = c / 100
e = 10 / 100
f = 16 / e
g = 1 / 2
h = f * g
i = d - h
j = 2 * 4
k = i / j
Problem: when a student joe , weighing 45 kg , joins a group of students whose average weight is 30 kg , the average weight goes up by 1 kg . subsequently , if two students , excluding joe , leave the group the average weight comes back to 30 kg . what is the difference between the average weight of the two students who left and the weight of joe ?
Options: a ) 7.5 kg , b ) 11 kg , c ) 30 kg , d ) 36.5 kg , e ) 71 kg
Rationale: "after two persons leave the group the average remains the same . that means the weight of the two persons = 45 + 30 = 75 so , the average the two persons = 37.5 that gives the answer 45 - 37.5 = 7.5 answer a"
Answer: a
Python program:
a = 30 + 1 
b = 45 - a
c = 30 * b
d = c + 45 
e = 30 + 1 
f = 45 - e
g = f - 1
h = g * 30
i = d - h
j = i / 2
k = 45 - j
Problem: what is the probability of getting a sum 9 from two throws of dice
Options: a ) 1 / 3 , b ) 1 / 9 , c ) 1 / 12 , d ) 2 / 9 , e ) none of these
Rationale: "explanation : total number of cases = 6 * 6 = 36 favoured cases = [ ( 3,6 ) , ( 4,5 ) , ( 6,3 ) , ( 5,4 ) ] = 4 so probability = 4 / 36 = 1 / 9 answer : b"
Answer: b
Python program:
a = 3 + 3 
b = math.comb(a, 3)
c = 2 / b
Problem: if pintu is coded as 79523 in a certain code language , how would you code buntu in the same language ?
Options: a ) 13426 , b ) 23523 , c ) 13436 , d ) 14263 , e ) 15263
Rationale: "1 2 3 4 5 6 7 8 9 a b c d e f g h i j k l m n o p q r s t u v w x y z sooo . . . buntu is 23523 . . . answer : b"
Answer: b
Python program:
a = 3 + 3 
b = 79523 / a
Problem: if neha is 10 both sonali and priyanka is 15 both sadaf and tanu is 10 . how much is prinka by the same system ?
Options: a ) 8 , b ) 11 , c ) 10 , d ) 15 , e ) 6
Rationale: c prinka is 10 , in a system that awards five for each vowel .
Answer: c
Python program:
a = 15 - 10
b = a * 2
Problem: if ( a + b ) = 14 , ( b + c ) = 9 and ( c + d ) = 3 , what is the value of ( a + d ) ?
Options: a ) 16 . , b ) 8 . , c ) 7 . , d ) 2 . , e ) - 2 .
Rationale: "given a + b = 14 = > a = 14 - b - - > eq 1 b + c = 9 c + d = 3 = > d = 3 - c - - > eq 2 then eqs 1 + 2 = > a + d = 14 - b + 3 - c = > 17 - ( b + c ) = > 17 - 9 = 8 . option b . . ."
Answer: b
Python program:
a = 14 + 3 
b = a - 9
Problem: during a sale , the price of a pair of shoes is marked down 13 % from the regular price . after the sale ends , the price goes back to the original price . what is the percent of increase to the nearest percent from the sale price back to the regular price for the shoes ?
Options: a ) 9 % , b ) 10 % , c ) 11 % , d ) 15 % , e ) 90 %
Rationale: "assume the price = 100 price during sale = 87 price after sale = 100 percent increase = 13 / 87 * 100 = 15 % approx . correct option : d"
Answer: d
Python program:
a = 13 * 100
b = 100 - 13
c = a / b
Problem: machine a can process 6000 envelopes in 3 hours . machines b and c working together but independently can process the same number of envelopes in 2.5 hours . if machines a and c working together but independently process 3000 envelopes in 1 hour , then how many hours would it take machine b to process 4200 envelopes .
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 60 / 7
Rationale: "you can either take the amount of work done as the same as karishma has done or take the work done by each in the same time . i will do the latter 1 . work done in 1 hr by a is 2000 envelopes 2 . work done in 1 hr by a and c is 3000 envelopes 3 . so work done in 1 hr by c is 1000 envelopes 4 . work done in 1 hr by b and c is 2400 envelopes 5 . so work done in 1 hr by b is 1400 envelopes 6 . so to process 4200 envelopes b will take 4200 / 1400 hrs = 3 hrs so the answer is choice b"
Answer: b
Python program:
a = 6000 / 2
b = 3000 / 1
c = 6000 / 3
d = b - c
e = a - d
f = 4200 / e
Problem: the average weight of 8 persons increases by 4.5 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?
Options: a ) 75 kg , b ) 65 kg , c ) 55 kg , d ) 85 kg , e ) 101 kg
Rationale: "total weight increased = ( 8 x 4.5 ) kg = 36 kg . weight of new person = ( 65 + 36 ) kg = 101 kg . answer : e"
Answer: e
Python program:
a = 8 * 4
b = 65 + a
Problem: if the average ( arithmetic mean ) of a and b is 45 and the average of b and c is 60 , what is the value of c â ˆ ’ a ?
Options: a ) 25 , b ) 30 , c ) 90 , d ) 140 , e ) it can not be determined from the information given
Rationale: "the arithmetic mean of a and b = ( a + b ) / 2 = 45 - - a + b = 90 - - 1 similarly for b + c = 120 - - 2 subtracting 1 from 2 we have c - a = 30 ; answer : b"
Answer: b
Python program:
a = 60 * 2
b = 45 * 2
c = a - b
Problem: the lcm and hcf of two numbers are 100000 and 10000 respectively . find the larger of the two numbers if their sum is 110000 .
Options: a ) 100000 , b ) 46 , c ) 577 , d ) 577 , e ) 767
Rationale: "there are 2 approaches in solving this . methode 1 . hcf * lcm = the actual number . 100000 * 10000 = 1000000000 so the answer which we are looking for has to be a factor of 1000000000 . so among the options shortlist the answers by eliminating those numbers which is not divisible by 1000000000 . and then take the highest number as the answer as the question asks abt the highest number . answer is a"
Answer: a
Python program:
a = 100000 * 10000
b = a / 110000
Problem: when positive integer x is divided by positive integer y , the result is 59.32 . what is the sum r of all possible 2 - digit remainders for x / y ?
Options: a ) 560 , b ) 616 , c ) 672 , d ) 728 , e ) 784
Rationale: "ans b 616 . . . remainders = . 32 = 32 / 100 = 8 / 25 = 16 / 50 and so on . . so two digit remainders are 16 + 24 + 32 + . . . . + 96 . . r = 8 ( 2 + 3 + 4 . . . . + 12 ) = 616 . b"
Answer: b
Python program:
a = math.floor(2)
b = 2 - a
c = 59 / 32
Problem: a certain family has 3 sons : richard is 6 years older than david , and david is 8 years older than scott . if in 8 years , richard will be twice as old as scott , then how old was david 5 years ago ?
Options: a ) 9 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "let ' s say age of richard isr age of david isd age of scott iss now richard is 6 years older than david , i . e . r = d + 6 david is 8 years older than scott i . e . d = s + 8 if in 8 years , richard will be twice as old as scott i . e . r + 8 = 2 x ( s + 8 ) i . e . r + 8 = 2 s + 16 i . e . r = 2 s + 8 but r = d + 6 = ( s + 8 ) + 6 = s + 14 therefore , 2 s + 8 = s + 14 i . e . s = 6 i . e . r = 20 i . e . d = 14 now , how old was david 5 years ago ? i . e . d - 5 = 14 - 5 = 9 years answer : option a"
Answer: a
Python program:
a = 6 + 8 
b = a - 5
Problem: car dealership x , the total profit from sales increased by 15 percent over the previous years , while the number of cars sold decreased by 15 percent over the previous years . approximately what was the average percent increase in profit per car over the previous year .
Options: a ) 18 % , b ) 20 % , c ) 22 % , d ) 35.29 % , e ) 55 %
Rationale: "let profit be x and cars sold be y originally profit / car = x / y now it is 1.15 x / 0.85 y = 115 / 85 ( x / y ) increase in profit per car = ( ( 30 / 85 ) ( x / y ) ) / ( x / y ) * 100 = 35.29 % answer = d"
Answer: d
Python program:
a = 100 + 15 
b = 10 - 3
c = a / b
d = 100 / 10
e = c - d
f = 100 / 10
g = e / f
h = g * 100
Problem: jill has 42 gallons of water stored in quart , half - gallon , and one gallon jars . she has equal numbers of each size jar holding the liquid . what is the total number of water filled jars ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 72 , e ) 14
Rationale: let the number of each size of jar = wthen 1 / 4 w + 1 / 2 w + w = 42 1 3 / 4 w = 42 w = 24 the total number of jars = 3 w = 72 answer : d
Answer: d
Python program:
a = 1 / 2
b = const_0_25 + a 
c = 1 + b 
d = 42 / c
e = d * 3
Problem: a sum of money becomes 7 / 6 of itself in 4 years at a certain rate of simple interest . the rate per annum is ?
Options: a ) 25 / 6 , b ) 5 5 / 7 , c ) 5 5 / 2 , d ) 5 5 / 8 , e ) 5 5 / 1
Rationale: let sum = x . then , amount = 7 x / 6 s . i . = 7 x / 6 - x = x / 6 ; time = 4 years . rate = ( 100 * x ) / ( x * 6 * 4 ) = 25 / 6 % . answer : a
Answer: a
Python program:
a = 7 / 6
b = a - 1
c = b / 4
d = c * 100
Problem: of the 3 - digit integers greater than 700 , how many have distinct digits ?
Options: a ) 216 , b ) 82 , c ) 80 , d ) 45 , e ) 36
Rationale: three digit number can have only following 3 patterns : a . all digits are distinct ; b . two digits are alike and third is different ; c . all three digits are alike . we need to calculate b . b = total - a - c total numbers from 700 to 999 = 299 ( 3 - digit numbers greater than 700 ) ; a . all digits are distinct = 3 * 9 * 8 = 216 answer : a
Answer: a
Python program:
a = 10 - 1
b = 3 * a
c = 10 - 2
d = b * c
Problem: a can finish a work in 9 days and b can do the same work in 15 days . b worked for 10 days and left the job . in how many days , a alone can finish the remaining work ?
Options: a ) 3 , b ) 5 1 / 2 , c ) 6 , d ) 8 , e ) none of these
Rationale: "b ' s 10 day ' s work = ( 1 / 15 * 10 ) = 2 / 3 remaining work = ( 1 - 2 / 3 ) = 1 / 3 now , 1 / 18 work is done by a in 1 day 1 / 3 work is done by a in ( 9 * 1 / 3 ) = 3 days . correct option : a"
Answer: a
Python program:
a = 1 / 15
b = a * 10
c = b * 9
d = c / 2
Problem: a wire can be bent in the form of a circle of radius 56 cm . if it is bent in the form of a square , then its area will be
Options: a ) 7744 , b ) 8844 , c ) 5544 , d ) 4444 , e ) 3444
Rationale: "length of wire = 2 pier = 2 * ( 22 / 7 ) * 56 = 352 cm side of the square = 352 / 4 = 88 cm area of the square = 88 * 88 = 7744 sq cm answer : a"
Answer: a
Python program:
a = circumface / (
b = a ** 4
Problem: if 40 % of a number is equal to two - third of another number , what is the ratio of first number to the second number ?
Options: a ) 2 : 5 , b ) 1 : 4 , c ) 3 : 7 , d ) 5 : 3 , e ) 2 : 3
Rationale: "let 40 % of a = 2 / 3 b then 40 a / 100 = 2 b / 3 2 a / 5 = 2 b / 3 a / b = 5 / 3 a : b = 5 : 3 answer is d"
Answer: d
Python program:
a = 1 / 4
b = 40 / 100
c = a / b
Problem: i bought two books ; for rs . 480 . i sold one at a loss of 15 % and other at a loss of 25 % and then i found each book was sold at the same price . find the cost of the book sold at a lower loss ?
Options: a ) a ) 657 , b ) b ) 280 , c ) c ) 225 , d ) d ) 289 , e ) e ) 427
Rationale: "x * ( 85 / 100 ) = ( 480 - x ) 75 / 100 x = 225 answer : c"
Answer: c
Python program:
a = 100 + 25 
b = 480 * a
c = 100 - 15
d = 100 + 25 
e = c + d 
f = b / e
Problem: what is the tens digit of 7 ^ 1213 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "7 ^ 1 = 7 7 ^ 2 = 49 7 ^ 3 = 343 7 ^ 4 = 2401 7 ^ 5 = 16807 7 ^ 6 = 117649 we should see this as pattern recognition . we have a cycle of 4 . ( we can multiply the last 2 digits only as we care about ten ' s digit ) 0 , 4 , 4 , 0 . 1213 = 4 * 304 + 1 the ten ' s digit will be 0 . answer a"
Answer: a
Python program:
a = 4 + 1 
b = 7 ** reminder
c = reminder / (
d = math.floor(c, 100)
Problem: if 5 workers collect 48 kg of cotton in 4 days , how many kg of cotton will 9 workers collect in 2 days ?
Options: a ) 47.6 kg , b ) 52.6 kg , c ) 59.6 kg , d ) 56.6 kg , e ) 57.6 kg
Rationale: "( 3 * 5 ) / 48 = ( 9 * 2 ) / x x = 57.6 kg answer : e"
Answer: e
Python program:
a = 48 / 5
b = a / 4
c = b * 9
d = c * 2
Problem: in the third grade of windblown school there are 78 students , one third of them failed the math test and 1 / 6 failed that literature test . at least how many students failed both tests ?
Options: a ) 0 . , b ) 6 . , c ) 8 . , d ) 10 . , e ) 12 .
Rationale: total = 78 failed in math = 78 / 3 = 26 failed in literature = 78 / 6 = 13 the least failed in both can be 0 while max can be 13 answer a
Answer: a
Python program:
a = 78 / 3
b = 78 / 6
c = min(a)
Problem: david has $ 2,400 at the beginning of his trip , after spending money , he still has exactly $ 800 less than he spent on the trip . how much money does john still have ?
Options: a ) $ 200 , b ) $ 400 , c ) $ 600 , d ) $ 800 , e ) $ 1,200
Rationale: "suppose total money spent = x not spend ( money he still has ) = x - 800 x + x - 800 = 2400 x = 1600 money not spend = 1600 - 800 = 800 answer : d"
Answer: d
Python program:
a = 100 * 10
b = a + 800 
c = b + 800 
d = c / 2
e = d - 800
Problem: a money lender finds that due to a fall in the annual rate of interest from 8 % to 7 3 / 5 % his yearly income diminishes by rs . 61.50 . his capital is
Options: a ) 153.75 , b ) 37.78 , c ) 246.0 , d ) 27.88 , e ) 127.71
Rationale: "explanation : capital = rs . x , then 2 / 5 x = 153.75 answer : a ) rs . 153.75"
Answer: a
Python program:
a = 4 / 5
b = 61 / 50
Problem: if 2994 ã · 14.5 = 173 , then 29.94 ã · 1.45 = ?
Options: a ) 17.1 , b ) 17.3 , c ) 17.5 , d ) 17.7 , e ) 17.2
Rationale: "29.94 / 1.45 = 299.4 / 14.5 = ( 2994 / 14.5 ) x 1 / 10 ) [ here , substitute 173 in the place of 2994 / 14.5 ] = 173 / 10 = 17.3 answer is b ."
Answer: b
Python program:
a = 14 / 5
b = 173 / a
Problem: the ages of 2 persons differ by 16 years . if 6 years ago the elder one be 3 times as old as the younger one , find the present age of younger person .
Options: a ) 10 , b ) 14 , c ) 20 , d ) 15 , e ) 32
Rationale: "age of the younger person = x age of the elder person = x + 16 3 ( x - 6 ) = x + 16 - 6 x = 14 answer is b"
Answer: b
Python program:
a = 2 * 16
b = 6 - 1
c = a / b
d = c + 6 
e = d - 2
Problem: three numbers are in the ratio 4 : 5 : 6 and their average is 39 . the largest number is :
Options: a ) 28 , b ) 32 , c ) 36 , d ) 42 , e ) 46.8
Rationale: "explanation : let the numbers be 4 x , 5 x and 6 x . therefore , ( 4 x + 5 x + 6 x ) / 3 = 39 15 x = 117 x = 7.8 largest number = 6 x = 46.8 . answer e"
Answer: e
Python program:
a = 4 * 6
b = a * 100
c = 5 * 6
d = b + c
Problem: in the first 10 overs of a cricket game , the run rate was only 3.2 . what should be the rate in the remaining 40 overs to reach the target of 262 runs ?
Options: a ) 6.25 , b ) 6.22 , c ) 6.29 , d ) 5.75 , e ) 6.13
Rationale: "required run rate = [ 262 - ( 3.2 * 10 ) ] / 40 = 230 / 40 = 5.75 answer : d"
Answer: d
Python program:
a = 10 * 3
b = 262 - a
c = b / 40
Problem: two pipes can fill a tank in 18 minutes and 60 minutes . an outlet pipe can empty the tank in 45 minutes . if all the pipes are opened when the tank is empty , then how many minutes will it take to fill the tank ?
Options: a ) 1 / 15 , b ) 1 / 16 , c ) 1 / 20 , d ) 1 / 10 , e ) 1 / 12
Rationale: "part of the filled by all the three pipes in one minute = 1 / 18 + 1 / 60 - 1 / 45 = 1 / 20 so , the tank becomes full in 20 minutes . answer : c"
Answer: c
Python program:
a = 1 / 18
b = 1 / 60
c = a + b 
d = 1 / 45
e = c - d
Problem: in a certain animal population , for each of the first 3 months of life , the probability that an animal will die during that month is 1 / 10 . for a group of 400 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ?
Options: a ) 240 , b ) 246 , c ) 252 , d ) 292 , e ) 298
Rationale: "number of newborns that can die in first month = 1 / 10 * 400 = 40 survived = 360 number of newborns that can die in second month = 1 / 10 * 360 = 36 survived = 324 number of newborns that can die in third month = 1 / 10 * 324 = 32 survived = 292 answer : d"
Answer: d
Python program:
a = 1 / 10
b = 1 - a
c = 400 * b
d = 1 / 10
e = 1 - d
f = c * e
g = 1 / 10
h = 1 - g
i = f * h
Problem: the length of the rectangular field is double its width . inside the field there is square shaped pond 8 m long . if the area of the pond is 1 / 50 of the area of the field . what is the length of the field ?
Options: a ) 73 , b ) 32 , c ) 34 , d ) 43 , e ) 80
Rationale: "explanation : a / 50 = 8 * 8 = > a = 8 * 8 * 50 x * 2 x = 8 * 8 * 50 x = 40 = > 2 x = 80 answer : option e"
Answer: e
Python program:
a = square_area * (
b = a / 50
c = 1/(2)
d = math.sqrt(b)
Problem: a fill pipe can fill 2 / 3 of cistern in 40 minutes in how many minutes , it can fill full of the cistern ?
Options: a ) 60 min , b ) 36 min , c ) 25 min , d ) 30 min , e ) 50 min
Rationale: 2 / 3 of the cistern can fill in 40 min 3 / 3 of the cistern can fill in = 40 * 3 / 2 * 3 / 3 = 60 min answer is a
Answer: a
Python program:
a = 2 / 3
b = 40 / a
Problem: a “ sophie germain ” prime is any positive prime number p for which 2 p + 1 is also prime . the product of all the possible units digits of sophie germain primes greater than 4 is
Options: a ) 3 , b ) 7 , c ) 189 , d ) 227 , e ) 234
Rationale: "in that case , the sophie prime numbers greater than 5 are 7 , 11,23 , 47,59 , . . which yields units digit as 1 , 3,7 and 9 product would be 1 x 3 x 7 x 9 = 189 answer should be c ."
Answer: c
Python program:
a = 4 - 1
b = 2 + 1 
c = a + b 
d = 2 + 1 
e = c + d 
f = e - 10
g = 4 - 1
h = 2 + 1 
i = g + h 
j = 2 * i
k = j + 1 
l = k - 10
m = f * l
n = 2 + 1 
o = m * n
p = 4 - 1
q = 2 + 1 
r = p + q 
s = 2 + 1 
t = r + s 
u = 2 + 1 
v = t + u 
w = 2 * v
x = w + 1 
y = 2 * 10
z = x - y
A = o * z
Problem: x starts a business with rs . 45000 . y joins in the business after 8 months with rs . 30000 . what will be the ratio in which they should share the profit at the end of the year ?
Options: a ) 1 : 2 , b ) 9 : 2 , c ) 1 : 3 , d ) 3 : 1 , e ) 1 : 1
Rationale: "explanation : ratio in which they should share the profit = ratio of the investments multiplied by the time period = 45000 ã — 12 : 30000 ã — 4 = 45 ã — 12 : 30 ã — 4 = 3 ã — 12 : 2 ã — 4 = 9 : 2 answer : option b"
Answer: b
Python program:
a = 45000 * 12
b = 4 + 3 
c = 30000 * b
d = a / c
Problem: what number has a 5 : 1 ratio to the number 12 ?
Options: a ) 22 , b ) 50 , c ) 88 , d ) 52 , e ) 60
Rationale: "5 : 1 = x : 12 x = 60 answer : e"
Answer: e
Python program:
a = 12 * 5