euclaise/mathqa_programs huggingface dataset:
Problem: the average mark of the students of a class in a particular exam is 80 . if 5 students whose average mark in that exam is 40 are excluded , the average mark of the remaining will be 90 . find the number of students who wrote the exam .
Options: a ) 87 , b ) 27 , c ) 25 , d ) 26 , e ) 24
Rationale: "let the number of students who wrote the exam be x . total marks of students = 80 x . total marks of ( x - 5 ) students = 90 ( x - 5 ) 80 x - ( 5 * 40 ) = 90 ( x - 5 ) 250 = 10 x = > x = 25 answer : c"
Answer: c
Python program:
a = 90 * 5
b = 5 * 40
c = a - b
d = 90 - 80
e = c / d
Problem: when x is multiplied by 3 , the result is 16 more than the result of subtracting x from 36 . what is the value of x ?
Options: a ) - 4 , b ) - 2 , c ) 11 , d ) 13 , e ) 22
Rationale: "the equation that can be formed is : 3 x - 16 = 36 - x or , 4 x = 52 or , x = 13 . answer : d"
Answer: d
Python program:
a = 36 + 16 
b = 3 + 1 
c = a / b
Problem: a goods train leaves a station at a certain time and at a fixed speed . after 6 hours , an express train leaves the same station and moves in the same direction at a uniform speed of 90 kmph . this train catches up the goods train in 4 hours . find the speed of the goods train .
Options: a ) 36 kmph , b ) 40 kmph , c ) 30 kmph , d ) 42 kmph , e ) none of these
Rationale: let the speed of the goods train be x kmph . distance covered by goods train in 10 hours = distance covered by express train in 4 hours . ∴ 10 x = 4 × 90 or x = 36 . so , speed of goods train = 36 kmph . answer a
Answer: a
Python program:
a = 4 * 90
b = 6 + 4 
c = a / b
Problem: if 3 people can do 3 times of a particular work in 3 days , then how many days would it take 4 people to do 4 times of that particular work ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 7
Rationale: "3 people can do the work one time in one day . 1 person can do 1 / 3 of the work in one day . 4 people can do 4 / 3 of the work in one day . 4 people can do 4 times the work in 3 days . the answer is c ."
Answer: c
Python program:
a = 4 / 4
b = 3 * a
Problem: 5 ! / ( 5 - 3 ) ! = ?
Options: a ) 36 , b ) 46 , c ) 56 , d ) 59 , e ) 60
Rationale: 5 ! / ( 5 - 3 ) ! = 5 ! / 2 ! = 5 * 4 * 3 = 60 . hence , the correct answer is e .
Answer: e
Python program:
a = math.factorial(5)
b = 5 - 3
c = math.factorial(b)
d = a / c
Problem: the manager of a produce market purchased a quantity of tomatoes for $ 0.80 per pound . due to improper handling , 10 percent of the tomatoes , by weight , were ruined and discarded . at what price per pound should the manager sell the remaining tomatoes if she wishes to make a profit on the sale of the tomatoes equal to 12 percent of the cost of the tomatoes .
Options: a ) $ 0.94 , b ) $ 0.96 , c ) $ 0.99 , d ) $ 1.00 , e ) $ 1.20
Rationale: assume the manager bought 100 tomatoes . cost price = 80 given : 10 % are damaged - - > available tomatoes to sell = 90 90 * x - 80 = 0.12 * 80 90 x - 80 = 9.6 90 x = 89.6 x = 89.6 / 90 = 0.995 x is slightly under 0.9955 = 0.99 answer : c
Answer: c
Python program:
a = 12 / 100
b = 1 + a 
c = 100 - 10
d = c / 100
e = 0 / 8
f = b * e
Problem: what is the remainder when 4 ^ 8707 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "4 ^ 0 = 1 4 ^ 1 = 4 4 ^ 2 = 16 4 ^ 3 = 64 4 ^ 4 = 256 4 ^ 5 = . . . . . 4 4 ^ 6 = . . . . . . . 6 and so on in a distinct last - digit pattern of 4,6 , 4,6 . . . after ignoring the first last - digit of 1 8707 / 2 = 4353 ( with a remainder of 1 ) so the last number is a 4 . alternatively , 8707 is an odd number and hence the last digit is a 4 when 4 ^ 8707 is divided by 5 the remainder is 4 , ans = e"
Answer: e
Python program:
a = 5 / 2
b = 4 * 4
c = a - b
Problem: if 5 % more is gained by selling an article for rs . 220 than by selling it for rs . 160 , the cost of the article is ?
Options: a ) 127 , b ) 1200 , c ) 1600 , d ) 1400 , e ) 1202
Rationale: "let c . p . be rs . x . then , 5 % of x = 220 - 160 = 60 x / 20 = 60 = > x = 1200 answer : b"
Answer: b
Python program:
a = 220 - 160
b = 5 / 100
c = a / b
Problem: how many integers between 100 and 170 , inclusive , can not be evenly divided by 3 nor 5 ?
Options: a ) 36 , b ) 38 , c ) 40 , d ) 42 , e ) 44
Rationale: "the total numbers between 100 and 170 , inclusive , is 71 . 3 * 34 = 102 and 3 * 56 = 168 so the number of multiples of 3 is 23 . 5 * 20 = 100 and 5 * 34 = 170 so the number of multiples of 5 is 15 . however , the multiples of 15 have been counted twice . 15 * 7 = 105 and 15 * 11 = 165 so the number of multiples of 15 is 5 . thus the total number is 71 - 23 - 15 + 5 = 38 . the answer is b ."
Answer: b
Python program:
a = 2 * 100
b = 3 + 4 
c = b * 10
d = a + c 
e = d + 2 
f = 170 - e
Problem: two persons a and b can complete a piece of work in 20 days and 40 days respectively . if they work together , what part of the work will be completed in 5 days ?
Options: a ) 1 / 8 , b ) 1 / 3 , c ) 3 / 6 , d ) 3 / 8 , e ) 5 / 3
Rationale: "a ' s one day ' s work = 1 / 20 b ' s one day ' s work = 1 / 40 ( a + b ) ' s one day ' s work = 1 / 20 + 1 / 40 = 3 / 40 the part of the work completed in 5 days = 5 ( 3 / 40 ) = 3 / 8 . answer : d"
Answer: d
Python program:
a = 1 / 20
b = 1 / 40
c = a + b 
d = 5 * c
Problem: there are x persons and y chocolates . if each person is given 1 chocolate then 1 chocolate is left , if each person is given 2 chocolates then 1 person will be left . so how many persons and chocolates are there ? ?
Options: a ) 32 , b ) 33 , c ) 34 , d ) 45 , e ) 44
Rationale: x person , y chocolates 1 st equation = = > ( y - 1 ) / x = 1 2 nd equation = = > y / ( x - 1 ) = 2 solving we get x = 3 , y = 4 answer : c
Answer: c
Python program:
a = 12 * 3
b = a - 2
Problem: working alone at their respective constant rates , a can complete a task in ‘ a ’ days and b in ‘ b ’ days . they take turns in doing the task with each working 3 days at a time . if a starts they finish the task in exactly 9 days . if b starts , they take a day more . how long does it take to complete the task if they both work together ?
Options: a ) 8 , b ) 6 , c ) 4 , d ) 5 , e ) 9 / 2
Rationale: "work done by ab in a day = xy respectively . when a starts : no . of days when a works = 6 no . of days when b works = 3 → 6 x + 3 y = 1 when b starts : no . of days when a works = 4 no . of days when a works = 5 → 5 x + 4 y = 1 solving the above two equations for xy x = 1 / 9 y = 1 / 9 → total work done by ab in a day = 1 / 9 + 1 / 9 = 2 / 9 → no . of days to complete the work when both work together = 9 / 2 ; answer : e"
Answer: e
Python program:
a = 9 - 1
b = 1/(a)
c = 9 + 2 
d = 1/(c)
e = b + d 
f = 1/(e)
Problem: find out the square of a number which when doubled exceeds its one seventh by 13 ?
Options: a ) 16 , b ) 49 , c ) 19 , d ) 26 , e ) 17
Rationale: "a let the number be p , then the square will be p ^ 2 according to question : 2 p = ( p / 7 ) + 13 = > 14 p = p + 91 = > p = 7 p ^ 2 = 7 ^ 2 = 49 . answer : b"
Answer: b
Python program:
a = 4 + 1 
b = 1 / a
c = 2 - b
d = 13 / c
e = d ** 2
Problem: a type of extra - large suv averages 12.2 miles per gallon ( mpg ) on the highway , but only 7.6 mpg in the city . what is the maximum distance , in miles , that this suv could be driven on 20 gallons of gasoline ?
Options: a ) 190 , b ) 284.6 , c ) 300 , d ) 244 , e ) 312
Rationale: "so 12.2 * 20 = 244 . . imo option d is correct answer . ."
Answer: d
Python program:
a = 12 * 2
Problem: an engineering student has to secure 36 % marks to pass . he gets 130 marks and fails by 14 marks . the maximum number of marks obtained by him is ?
Options: a ) 337 , b ) 400 , c ) 298 , d ) 2798 , e ) 271
Rationale: 130 14 - - - - - - - 361 - - - - - - 144 100 % - - - - - - ? = > 400 answer : b
Answer: b
Python program:
a = 130 + 14 
b = a * 100
c = b / 36
Problem: united telephone charges a base rate of $ 9.00 for service , plus an additional charge of $ 0.25 per minute . atlantic call charges a base rate of $ 12.00 for service , plus an additional charge of $ 0.20 per minute . for what number of minutes would the bills for each telephone company be the same ?
Options: a ) 2 minutes , b ) 10 minutes , c ) 20 minutes , d ) 40 minutes , e ) 60 minutes
Rationale: lets take number of minutesx . given that , 9 + 0.25 x = 12 + 0.2 x - > 0.05 x = 2 - > x = 60 minutes ans e
Answer: e
Python program:
a = 12 - 9
b = 0 - 25
c = a / b
Problem: the cost of carpeting a room 18 m long with a carpet 75 cm wide at 45 paise per meter is rs . 81 . the breadth of the room is :
Options: a ) 7 m , b ) 7.5 m , c ) 5.5 m , d ) 6.5 m , e ) 8.5 m
Rationale: "length of the carpet = total cost / rate / m = 8100 / 45 = 180 m area of the carpet = 180 * 75 / 100 = 135 m 2 breadth of the room = ( area / length ) = 135 / 18 = 7.5 m answer : b"
Answer: b
Python program:
a = 81 / 45
b = 75 / 100
c = a * b
d = c / 18
Problem: a swimmer can swim in still water at 4 km / h . if the speed of the water current is 2 km / h , how many hours will the swimmer take to swim against the current for 7 km ?
Options: a ) 3.0 , b ) 3.25 , c ) 3.5 , d ) 3.75 , e ) 4.0
Rationale: "the swimmer can swim against the current at a speed of 4 - 2 = 2 km / h . the time it will take is 7 / 2 = 3.5 hours . the answer is c ."
Answer: c
Python program:
a = 4 - 2
b = 7 / a
Problem: ratio between 2 numbers is 5 : 7 and their product is 560 . what is the difference between 2 numbers ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 2
Rationale: "explanation : x / y = 5 / 7 x × y = 560 ⇒ x = 560 / y substituting this value in first equation , we get 560 / yy = 57560 / yy = 57 ⇒ 560 y 2 = 57560 y 2 = 57 ⇒ y = 28 x = 20 so difference between the numbers could be x – y = – 8 y – x = 8 answer : c"
Answer: c
Python program:
a = 2 + 5 
b = 7 / a
c = 3 * 0
Problem: the edges of three metal cubes are 1 cm , 2 cm , and 3 cm respectively . a new cube is made by melting these three cubes together . what is the edge of the new cube ( in centimeters ) ?
Options: a ) 3.3 , b ) 3.5 , c ) 3.7 , d ) 3.9 , e ) 4.1
Rationale: "the total volume is 1 ^ 3 + 2 ^ 3 + 3 ^ 3 = 36 the edge of the new cube is the cube root of 36 which is about 3.3 cm . the answer is a ."
Answer: a
Python program:
a = 3 ** 2
b = 2 ** 2
c = 1 + b 
d = a + c 
e = d ** const_0_33
Problem: a scale 6 ft . 8 inches long is divided into 2 equal parts . find the length of each part .
Options: a ) 20 inches , b ) 77 inches , c ) 66 inches , d ) 97 inches , e ) 40 inches
Rationale: explanation : total length of scale in inches = ( 6 * 12 ) + 8 = 80 inches length of each of the 2 parts = 80 / 2 = 40 inches answer : e
Answer: e
Python program:
a = 6 * 12
b = a + 8 
c = b / 2
Problem: right now , al and eliot have bank accounts , and al has more money than eliot . the difference between their two accounts is 1 / 11 of the sum of their two accounts . if al ’ s account were to increase by 10 % and eliot ’ s account were to increase by 20 % , then al would have exactly $ 22 more than eliot in his account . how much money does eliot have in his account right now ?
Options: a ) $ 110 , b ) $ 120 , c ) $ 183.3 , d ) $ 220 , e ) $ 260
Rationale: "lets assume al have amount a in his bank account and eliot ' s bank account got e amount . we can form an equation from the first condition . a - e = 1 / 11 * ( a + e ) = = > 10 a = 12 e - - - - - - - - - - - - ( 1 ) second condition gives two different amounts , al ' s amount = 1.1 a and eliot ' s amount = 1.2 e 1.1 a = 22 + 1.2 e = = > 11 a = 220 + 12 e - - - - - - - ( 2 ) substituting ( 1 ) in ( 2 ) : 11 a = 220 + 10 a = = > a = 220 ; e = 183.3 c"
Answer: c
Python program:
a = 22 * 100
b = 11 + 1 
c = b * 10
d = 100 + 20 
e = c - d
f = a / e
Problem: if 11 oranges bought 10 r and 10 oranges sold 11 r . what is the profit
Options: a ) 11 % , b ) 20 % , c ) 22 % , d ) 21 % , e ) 23 %
Rationale: suppose he bought 110 apples . cp = rs 100 sp = rs 121 % profit = 100 * ( 121 - 100 ) / 100 = 21 % answer : d
Answer: d
Python program:
a = 11 / 10
b = 10 / 11
c = a - b
d = 10 / 11
e = c / d
f = e * 100
Problem: the speed at which a man can row a boat in still water is 15 km / hr . if he rows downstream , where the speed of current is 3 km / hr , how many seconds will he take to cover 110 meters ?
Options: a ) 18 , b ) 20 , c ) 22 , d ) 24 , e ) 28
Rationale: "the speed of the boat downstream = 15 + 3 = 18 km / hr 18 km / hr * 5 / 18 = 5 m / s the time taken to cover 110 meters = 110 / 5 = 22 seconds . the answer is b ."
Answer: b
Python program:
a = 15 + 3 
b = a * const_0_2778
c = 110 / b
Problem: find the simple interest on rs . 567 for 7 months at 9 paisa per month ?
Options: a ) s . 357.21 , b ) s . 322.12 , c ) s . 400 , d ) s . 278.9 , e ) s . 300
Rationale: "explanation : i = ( 567 * 7 * 9 ) / 100 = 357.21 answer : option a"
Answer: a
Python program:
a = 7 / 100
b = 567 * a
Problem: the least number which when divided by 4 , 6 , 7 and 8 leaves a remainder 6 , but when divided by 9 leaves no remainder , is
Options: a ) 340 , b ) 342 , c ) 523 , d ) 363 , e ) none of these
Rationale: "explanation : l . c . m of 4 , 6 , 7 , 8 = 168 therefore required number is of the form 168 k + 6 . least value of k for which ( 168 k + 6 ) is divisible by 9 is k = 2 therefore required number = ( 168 x 2 + 6 ) = 342 . answer : b"
Answer: b
Python program:
a = math.lcm(4, 6)
b = math.lcm(a, 7)
c = math.lcm(b, 8)
d = c * 2
Problem: if 0.6 : 1.4 : : 2 : 4 : x , then x = ?
Options: a ) 56 , b ) 5.6 , c ) 0.56 , d ) 0.056 , e ) none of these
Rationale: "explanation : 0.6 × x = 2.4 × 1.4 x = ( 2.4 × 1.4 ) / 0.6 = 24 / 10 × 17 / 10 × 1 / ( 6 / 10 ) 24 / 10 × 14 / 10 × 10 / 6 2 / 5 × 14 = 28 / 5 = 5.6 answer : option b"
Answer: b
Python program:
a = 1 * 4
b = a + 1 
c = b / 2
Problem: the tax on a commodity is diminished by 10 % and its consumption increases by 10 % . find the effects on revenue ?
Options: a ) 1 % decrease , b ) 2 % increase , c ) 3 % decrease , d ) 4 % decrease , e ) none of these
Rationale: "since tax consumption = revenue . therefore , net % change in revenue = ( x + y + xy / 100 ) % = [ - 10 + 10 + ( - 10 x 10 ) / 100 ] % or - 1 % . therefore , revenue decreased by 1 % . answer : a"
Answer: a
Python program:
a = 10 / 100
b = 1 + a 
c = 10 / 100
d = 1 - c
e = b * d
f = e * 100
g = 100 - f
Problem: at 15 : 00 there were 20 students in the computer lab . at 15 : 03 and every three minutes after that , 4 students entered the lab . if at 15 : 10 and every ten minutes after that 8 students left the lab , how many students were in the computer lab at 15 : 44 ?
Options: a ) 7 , b ) 14 , c ) 25 , d ) 27 , e ) 30
Rationale: "initial no of students + 3 * ( 1 + no of possible 3 minute intervals between 15 : 03 and 15 : 44 ) - 8 * ( 1 + no of possible 10 minute intervals between 15 : 10 and 15 : 44 ) 20 + 3 * 14 - 8 * 4 = 27 d"
Answer: d
Python program:
a = 44 / 3
b = math.floor(a)
c = b * 3
d = c + 20 
e = 44 / 8
f = math.floor(e)
g = f * 8
h = d - g
i = h + 3
Problem: ' a ' and ' b ' are positive integers such that their lcm is 20 and their hcf is 1 . what is the difference between the maximum and minimum possible values of ' a + b ' ?
Options: a ) 0 , b ) 12 , c ) 13 , d ) 9 , e ) 11
Rationale: a = 4 , b = 5 as they have to co - primes ( hcf being 1 and lcm = 20 ) so a + b = 9 is their max and min value hence difference = 0 answer - a
Answer: a
Python program:
a = 20 / 4
b = a + 4 
c = 20 / 4
d = c + 4 
e = b - d
Problem: if a , b and c together can finish a piece of work in 4 days . a alone in 6 days and b in 18 days , then c alone can do it in ?
Options: a ) 1 , b ) 7 , c ) 8 , d ) 9 , e ) 36
Rationale: "c = 1 / 4 - 1 / 6 – 1 / 18 = 1 / 36 = > 36 days ' answer : e"
Answer: e
Python program:
a = 1 / 6
b = const_0_25 - a
c = 1 / 18
d = b - c
e = 1 / d
Problem: wo passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 21 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ?
Options: a ) 227 , b ) 444 , c ) 277 , d ) 298 , e ) 212
Rationale: 1 h - - - - - 5 ? - - - - - - 60 12 h rs = 16 + 21 = 37 t = 12 d = 37 * 12 = 444 answer : b
Answer: b
Python program:
a = 21 - 16
b = 60 / a
c = 16 + 21 
d = b * c
Problem: the salary of a typist was at first raised by 10 % and then the same was reduced by 5 % . if he presently draws rs . 3135 . what was his original salary ?
Options: a ) 2277 , b ) 2999 , c ) 1000 , d ) 3000 , e ) 1971
Rationale: "x * ( 110 / 100 ) * ( 95 / 100 ) = 3135 x * ( 11 / 10 ) * ( 1 / 100 ) = 33 x = 3000 answer : d"
Answer: d
Python program:
a = 10 / 100
b = 1 + a 
c = 5 / 100
d = 1 - c
e = b * d
f = 3135 / e
Problem: a train speeds past a pole in 15 sec and a platform 130 m long in 25 sec , its length is ?
Options: a ) 195 , b ) 150 , c ) 160 , d ) 170 , e ) 180
Rationale: "let the length of the train be x m and its speed be y m / sec . then , x / y = 15 = > y = x / 15 ( x + 130 ) / 25 = x / 15 = > x = 195 m . answer : option a"
Answer: a
Python program:
a = 2 - 1
b = 130 * a
Problem: city a and city b are 140 miles apart . train c departs city a , heading towards city b , at 4 : 00 and travels at 40 miles per hour . train d departs city b , heading towards city a , at 4 : 35 and travels at 20 miles per hour . the trains travel on parallel tracks . at what time do the two trains meet ?
Options: a ) 5 : 00 , b ) 5 : 30 , c ) 6 : 00 , d ) 6 : 35 , e ) 7 : 00
Rationale: "train c has traveled 20 mi in the half hour before train d has started its journey . 140 - 20 = 120 40 + 20 = 60 mph 120 mi / 60 mph = 2 hrs 4 : 35 pm + 2 hrs = 6 : 35 pm answer : d . 6 : 35"
Answer: d
Python program:
a = 4 + 2 
b = a / 35
Problem: if - 11 a and - 8 b are negative integers , then ( - 11 a ) * ( - 8 b ) + ab is
Options: a ) 88 ab , b ) - 89 ab , c ) 89 ab , d ) - 88 a , e ) - 88 b
Rationale: answer : c
Answer: c
Python program:
a = 11 * 8
b = a + 1
Problem: what is the thousandths digit in the decimal equivalent of 43 / 5000 ?
Options: a ) 0 , b ) 1 , c ) 3 , d ) 5 , e ) 8
Rationale: "43 / 5000 = 43 / ( 5 * 10 ^ 3 ) = ( 43 / 5 ) * 10 ^ - 3 = 8.6 * 10 ^ - 3 = . 0086 thousandths digit = 8 answer e"
Answer: e
Python program:
a = 43 / 5000
b = 100 * a
c = math.floor(b)
Problem: what is the difference between the largest number and the least number written with the digits 5 , 3 , 1 , 4 ?
Options: a ) 6084 , b ) 3788 , c ) 4086 , d ) 2721 , e ) 1812
Rationale: explanation : 1345 5431 - - - - - - - - - - - - 4086 answer : c
Answer: c
Python program:
a = 5 * 100
b = a * 10
c = 4 * 100
d = b + c 
e = 3 * 10
f = d + e 
g = f + 1 
h = 3 * 100
i = 1000 + h 
j = 4 * 10
k = i + j 
l = k + 5 
m = g - l
Problem: if ( a – b ) is 9 more than ( c + d ) and ( a + b ) is 3 less than ( c – d ) , then ( a – c ) is :
Options: a ) 6 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: ( a – b ) – ( c + d ) = 9 and ( c – d ) – ( a + b ) = 3 = > ( a – c ) – ( b + d ) = 9 and ( c – a ) – ( b + d ) = 3 = > ( b + d ) = ( a – c ) – 9 and ( b + d ) = ( c – a ) – 3 = > ( a – c ) – 9 = ( c – a ) – 3 = > 2 ( a – c ) = 6 = > ( a – c ) = 3 answer : c
Answer: c
Python program:
a = 9 / 3
Problem: the population of a town increased from 1 , 75,000 to 2 , 10,000 in a decade . the average percent increase of population per year is
Options: a ) 2 % , b ) 5 % , c ) 6 % , d ) 8.75 % , e ) none
Rationale: "solution increase in 10 years = ( 210000 - 175000 ) = 35000 . increase % = ( 35000 / 175000 ã — 100 ) % = 20 % . required average = ( 20 / 10 ) % = 2 % . answer a"
Answer: a
Python program:
a = 10 * 1000
b = a * 10
c = b - 1000
d = c - 1000
e = 2 + 3 
f = e * 100
g = d - f
h = 3 + 4 
i = h * 10
j = 2 + 3 
k = i + j 
l = k * 1000
m = g / l
n = m - 1
o = n / 10
p = o * 100
q = p + 4
Problem: there are 408 boys and 240 girls in a school which are to be divided into equal sections of either boys or girls alone . find the total number of sections thus formed .
Options: a ) 27 , b ) 32 , c ) 35 , d ) 30 , e ) 45
Rationale: "explanation : hcf ( 408 , 240 ) = 24 the number of boys or girls that can be placed in a section = 24 . thus the total number of sections is given by 408 / 24 + 240 / 24 = 17 + 10 = 27 answer : a"
Answer: a
Python program:
a = 408 + 240 
b = 2 * 2
c = b * 2
d = c * 3
e = a / d
Problem: an alloy weighing 20 ounces is 70 percent gold . how many ounces of pure gold must be added to create an alloy that is 90 percent gold ?
Options: a ) 6 , b ) 9 , c ) 12 , d ) 76 , e ) 48
Rationale: "in 24 ounces , gold is 20 * ( 70 / 100 ) = 14 ounces . now we add x ounces of pure gold to make it 90 % gold . so 14 + x = ( 24 + x ) * 90 / 100 = > x = 76 . answer is d ."
Answer: d
Python program:
a = 90 / 100
b = a * 20
c = 70 / 100
d = b / c
Problem: the cost of the paint is rs . 20 per kg . if 1 kg of paint covers 15 sq . ft , how much will it cost to paint outside of a cube having 5 feet each side
Options: a ) rs . 200
b ) rs . 672
c ) rs . 546
d ) rs . 876
e ) none of these
Rationale: explanation : surface area of a cube = 6 x 5 ^ 2 = 150 sq . ft quantity of paint required = ( 150 / 15 ) = 10 kg cost of painting = 20 x 10 = rs . 200 answer : a
Answer: a
Python program:
a = surface_cube / (
b = a * 15
Problem: what is the difference between the largest number and the least number written with the digits 9 , 3 , 5 , 7 ?
Options: a ) 6084 , b ) 3788 , c ) 2077 , d ) 2721 , e ) 6174
Rationale: "explanation : 3579 9753 - - - - - - - - - - - - 6174 answer : e"
Answer: e
Python program:
a = 9 * 100
b = a * 10
c = 7 * 100
d = b + c 
e = 3 * 10
f = d + e 
g = f + 5 
h = 3 * 100
i = 1000 + h 
j = 7 * 10
k = i + j 
l = k + 9 
m = g - l
Problem: a bag contains 4 red , 3 blue and 2 green balls . if 2 ballsare picked at random , what is the probability that both are red ?
Options: a ) 1 / 13 , b ) 2 / 23 , c ) 1 / 6 , d ) 4 / 27 , e ) 3 / 23
Rationale: "p ( both are red ) , = 4 c 29 c 2 = 4 c 29 c 2 = 6 / 36 = 1 / 6 c"
Answer: c
Python program:
a = math.comb(4, 2)
b = 4 + 3 
c = b + 2 
d = math.comb(c, 2)
e = a / d
Problem: what is the value of 8 1 / 3 % of 600 + 37 ½ of 400
Options: a ) 100 , b ) 300 , c ) 150 , d ) 200 , e ) 250
Rationale: "25 * 600 / 300 + 75 * 400 / 200 = 50 + 150 = 200 answer : d"
Answer: d
Python program:
a = 8 ** 1
b = 3 ** 600
c = a - b
d = c / 1000
e = d / 1000
f = e * 8
g = 8 ** 1
h = 3 ** 600
i = g - h
j = i / 1000
k = j / 1000
l = f - k
Problem: there is a 30 % chance jen will visit chile this year , while there is a 50 % chance that she will visit madagascar this year . what is the probability that jen will visit either chile or madagascar this year , but not both ?
Options: a ) 25.0 % , b ) 37.5 % , c ) 50.0 % , d ) 62.5 % , e ) 75 %
Rationale: p ( chile and not madagascar ) = 0.3 * 0.5 = 0.15 p ( madagascar and not chile ) = 0.5 * 0.7 = 0.35 total probability = 0.15 + 0.35 = 0.5 = 50 % the answer is c .
Answer: c
Python program:
a = 2 * 5
b = a ** 2
c = b - 30
d = 2 * 5
e = d ** 2
f = c / e
g = 2 * 5
h = g ** 2
i = 50 / h
j = f * i
k = 2 * 5
l = k ** 2
m = 30 / l
n = 2 * 5
o = n ** 2
p = 50 / o
q = m * p
r = j + q 
s = 2 * 5
t = s ** 2
u = r * t
Problem: how much 45 % of 60 is greater than 35 % of 40 ?
Options: a ) 18 , b ) 13 , c ) 15 , d ) 17 , e ) 71
Rationale: "( 45 / 100 ) * 60 – ( 35 / 100 ) * 40 27 - 14 = 13 answer : b"
Answer: b
Python program:
a = 45 * 60
b = a / 100
c = 35 * 40
d = c / 100
e = b - d
Problem: three numbers are in the ratio of 2 : 3 : 4 and their l . c . m . is 180 . what is their h . c . f . ?
Options: a ) 15 , b ) 20 , c ) 40 , d ) 60 , e ) 70
Rationale: "let the numbers be 2 x , 3 x , and 4 x . lcm of 2 x , 3 x and 4 x is 12 x . 12 x = 180 x = 15 hcf of 2 x , 3 x and 4 x = x = 15 the answer is a ."
Answer: a
Python program:
a = 2 * 4
Problem: the length of minute hand of a clock is 5.4 cm . what is the area covered by this in 5 minutes
Options: a ) 15.27 , b ) 16.27 , c ) 17.27 , d ) 7.27 , e ) 7.63
Rationale: "area of circle is pi * r ^ 2 but in 5 minutes area covered is ( 5 / 60 ) * 360 = 30 degree so formula is pi * r ^ 2 * ( angle / 360 ) = 3.14 * ( 5.4 ^ 2 ) * ( 30 / 360 ) = 7.63 cm ^ 2 answer : e"
Answer: e
Python program:
a = 2 * 5
b = a + 2 
c = 3 + 4 
d = b / c
e = 5 * 4
f = 1 * const_60
g = 100 * const_3_6
h = f / g
i = e * h
j = d * i