euclaise/mathqa_programs huggingface dataset:
Problem: a strain of bacteria reproduces @ 25 % every 12 min . in how much time will it triple itself ? ?
Options: a ) 96 min , b ) 72 min , c ) 60 min , d ) 48 min , e ) 40 min
Rationale: the original question is : a strain of bacteria reproduces at the rate of 25 % every 12 min . in how much time will it triple itself ? 1.25 ^ x = 3 - - > x = ~ 5 - - > five 12 minute periods = 60 minutes . answer : c .
Answer: c
Python program:
a = math.log(3)
b = 25 / 100
c = 1 + b 
d = math.log(c)
e = a / d
f = e * 12
Problem: a person want to give his money of $ 1000 to his 3 children a , b , c in the ratio 6 : 4 : 5 what is the a + b share ?
Options: a ) $ 660.67 , b ) $ 646.67 , c ) $ 666.67 , d ) $ 500.56 , e ) $ 600.24
Rationale: "a ' s share = 1000 * 6 / 15 = $ 400 b ' s share = 1000 * 4 / 15 = $ 266.67 a + b = $ 666.67 answer is c"
Answer: c
Python program:
a = 6 + 3 
b = a + 5 
c = 3 / b
d = c * 1000
Problem: in a group of cows and hens , the number of legs are 10 more than twice the number of heads . the number of cows is :
Options: a ) 5 , b ) 6 , c ) 7 , d ) 10 , e ) 12
Rationale: "let no of cows be x , no of hens be y . so heads = x + y legs = 4 x + 2 y now , 4 x + 2 y = 2 ( x + y ) + 10 2 x = 10 x = 5 . answer : a"
Answer: a
Python program:
a = 10 - 4
Problem: a survey was sent to 60 customers , 7 of whom responded . then the survey was redesigned and sent to another 63 customers , 9 of whom responded . by approximately what percent did the response rate increase from the original survey to the redesigned survey ?
Options: a ) 2 % , b ) 5 % , c ) 14 % , d ) 28 % , e ) 4 %
Rationale: "case 1 : ( 7 / 60 ) = x / 100 x = 12 % case 2 : ( 9 / 63 ) = y / 100 y = 14 % so percent increase is = ( y - x ) = ( 14 - 12 ) % = 2 % answer is a"
Answer: a
Python program:
a = 9 / 63
b = 7 / 60
c = a - b
d = c * 100
e = math.floor(d)
Problem: 12 persons can complete the work in 18 days . after working for 6 days , 4 more persons added to complete the work fast . in how many days they will complete the work ?
Options: a ) 10 , b ) 15 , c ) 17 , d ) 5 , e ) 9
Rationale: "total work = 12 * 18 = 216 units . after 6 days , work finished = 6 * 12 = 72 units . remaining units = 216 - 72 = 144 units . remaining days = 144 / ( 2 + 4 ) = 9 days the option is e"
Answer: e
Python program:
a = 18 - 6
b = a * 12
c = 12 + 4 
d = b / c
Problem: if 2 / 3 of the air in a tank is removed with each stroke of a vacuum pump , how many strokes does it take before less than 1 % of the original amount of air in the tank remains ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "my approach is to find more or less good number and plug in . lets take 90 as the total volume of an air , and the question asks after how many stokes there will be less than 0,9 air in a tank , if each stroke takes 2 / 3 of an air . so after he 1 strokethe volume will be 30 ( 90 - 60 = 30 ) , and so on 2 stroke - 30 - 20 = 10 3 stroke - 10 - 6,7 = 3,3 4 stroke - 3,3 - 2,2 = 1,1 5 stroke - 1,1 - minus something that gets us less than 0,9 for sure . so the answer is : after 5 strokes there will be less than 1 % of air left in a tank . optiond ."
Answer: d
Python program:
a = 2 / 3
b = 2 / 3
c = b / 3
d = a + c 
e = 2 / 3
f = e / 3
g = f / 3
h = d + g 
i = 2 / 3
j = i / 3
k = j / 3
l = k / 3
m = h + l 
n = 2 / 3
o = n / 3
p = o / 3
q = p / 3
r = q / 3
s = m + r
Problem: mahesh can do a piece of work in 35 days . he works at it for 20 days and then rajesh finished it in 30 days . how long will y take to complete the work ?
Options: a ) 45 , b ) 25 , c ) 37 , d ) 41 , e ) 70
Rationale: "work done by mahesh in 35 days = 20 * 1 / 35 = 4 / 7 remaining work = 1 - 4 / 7 = 3 / 7 3 / 7 work is done by rajesh in 30 days whole work will be done by rajesh is 30 * 7 / 3 = 70 days answer is e"
Answer: e
Python program:
a = 1 / 35
b = 20 * a
c = 1 - b
d = c / 30
e = 1 / d
Problem: for every x , the action [ x ] is defined : [ x ] is the greatest integer less than or equal to x . what is the value of [ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.4 ] - 6.0 ?
Options: a ) 12.6 . , b ) 14.4 . , c ) 15.8 . , d ) 16.2 . , e ) 16.4 .
Rationale: "[ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.4 ] - 6.0 = 6 * 0 + 2 * 7.2 + 8 - 6.0 = 0 + 14.4 + 2 16.4 answer e"
Answer: e
Python program:
a = 2 * 7
b = 4 / 10
c = 8 - 4
d = a + c 
e = d - 6
Problem: a parking garage rents parking spaces for $ 10 per week or $ 42 per month . how much does a person save in a year by renting by the month rather than by the week ?
Options: a ) $ 14 , b ) $ 16 , c ) $ 22 , d ) $ 24 , e ) $ 26
Rationale: "10 $ per week ! an year has 52 weeks . annual charges per year = 52 * 10 = 520 $ 30 $ per month ! an year has 12 months . annual charges per year = 12 * 42 = 504 $ 520 - 504 = 16 ans b"
Answer: b
Python program:
a = 3 + 2 
b = 10 * a
c = b + 2 
d = c * 10
e = 42 * 12
f = d - e
Problem: what is the least number which when divided by 8 , 12 , 15 and 20 leaves in each case a remainder of 5
Options: a ) 110 , b ) 125 , c ) 75 , d ) 170 , e ) 195
Rationale: "lcm of 8 , 12 , 15 and 20 = 120 required number = 120 + 5 = 125 answer : option b"
Answer: b
Python program:
a = math.lcm(8, 12)
b = math.lcm(15, 20)
c = math.lcm(a, b)
d = c + 5
Problem: if xy = 4 , x / y = 81 , for positive numbers x and y , y = ?
Options: a ) 1 / 2 , b ) 2 , c ) 2 / 9 , d ) 3 , e ) 1 / 6
Rationale: "very easy question . 2 variables and 2 easy equations . xy = 4 - - - > x = 4 / y - ( i ) x / y = 81 - - - > replacing ( i ) here - - - > 4 / ( y ^ 2 ) = 81 - - - > y ^ 2 = 4 / 81 - - - > y = 2 / 9 or - 2 / 9 the question states that x and y are positive integers . therefore , y = 2 / 9 is the answer . answer c ."
Answer: c
Python program:
a = 4 / 81
b = math.sqrt(a)
Problem: a fellow borrowed a certain sum of money at 6 % per annum at simple interest and in 6 years the interest amounted to rs . 672 less than the sum lent . what was the sum lent ?
Options: a ) 1050 , b ) 1220 , c ) 1250 , d ) 1060 , e ) 1110
Rationale: "p - 672 = ( p * 6 * 6 ) / 100 p = 1050 answer : a"
Answer: a
Python program:
a = 6 * 6
b = a / 100
c = 1 - b
d = 672 / c
Problem: the 7 th grade french and spanish classes each have 21 students in them , and there are 6 students in the 7 th grade taking both languages . if everyone in the 7 th grade is in at least one of the two language classes , how many students are taking just one of the two classes ?
Options: a ) 24 , b ) 28 , c ) 30 , d ) 32 , e ) 34
Rationale: french class + spanish class = 42 students . six students are in both classes so they were counted twice . the number of students taking just one class is 42 - 2 ( 6 ) = 30 . the answer is c .
Answer: c
Python program:
a = 21 - 6
b = 21 - 6
c = a + b
Problem: a company that ships boxes to a total of 14 distribution centers uses color coding to identify each center . if either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors , what is the minimum number of colors needed for the coding ? ( assume that the order of the colors in a pair does not matter )
Options: a ) 7 , b ) 8 , c ) 5 , d ) 9 , e ) 6
Rationale: "back - solving is the best way to solve this problem . you basically need 14 combinations ( including single colors ) if we start from option 1 - > 1 = > 4 c 2 + 4 = 10 ( not enough ) 2 = > 5 c 2 + 5 = 15 ( enough ) since the minimum number is asked . it should be 5 . answer - c"
Answer: c
Python program:
a = 14 / 2
b = a - 1
c = math.factorial(b)
d = math.factorial(3)
e = math.factorial(2)
f = d * e
g = c / f
h = 14 / 2
i = h - 1
j = g - i
Problem: a , b , c hired a car for rs . 520 and used it for 7,8 and 11 hours respectively . hire charges paid by b were :
Options: a ) 160 , b ) 180 , c ) 220 , d ) 225 , e ) none
Rationale: sol . a : b : c = 7 : 8 : 11 . hire charges paid by b = rs . [ 520 * 8 / 26 ] = rs . 160 answer a
Answer: a
Python program:
a = 4 * 2
b = 4 + 3 
c = 4 * 2
d = b + c 
e = d + 11 
f = a / e
g = 520 * f
Problem: maximun number of identical pieces ( of same size ) of a cake by making only 3 cuts ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 5
Rationale: since cake is a 3 d object , it will have length , breadth , height . . . first cut across length now we will get 2 pieces then cut across breadth we will get 4 parts in total now . . . now cut across height , finally we will get 8 parts . . . answer : c
Answer: c
Python program:
a = 3 ** 3
b = 1 + 4 
c = b * 3
d = a + c 
e = 3 * 2
f = d + e 
g = 3 * 2
h = 1/(g)
i = f * h
Problem: how many prime numbers exist in 67 x 353 x 1110 ?
Options: a ) 30 prime number , b ) 29 prime number , c ) 27 prime number , d ) 31 prime number , e ) none of these
Rationale: "solution : = ( 2 x 3 ) 7 x ( 5 x 7 ) 3 x 1110 = 27 x 37 x 53 x 73 x 1110 thus , there are ( 7 + 7 + 3 + 3 + 10 ) = 30 prime number answer : a"
Answer: a
Python program:
a = 4 * 67
Problem: a car travels at a speed of 12 miles per hour . how far will it travel in 5 hours ?
Options: a ) 50 miles , b ) 60 miles , c ) 72 miles , d ) 22 miles , e ) 62 miles
Rationale: "during each hour , the car travels 65 miles . for 5 hours it will travel 12 + 12 + 12 + 12 + 12 = 5 * 12 = 60 miles correct answer b"
Answer: b
Python program:
a = 12 * 5
Problem: a hostel had provisions for 250 men for 36 days . if 50 men left the hostel , how long will the food last at the same rate ?
Options: a ) 30 , b ) 45 , c ) 50 , d ) 60 , e ) 65
Rationale: "a hostel had provisions for 250 men for 36 days if 50 men leaves the hostel , remaining men = 250 - 50 = 200 we need to find out how long the food will last for these 200 men . let the required number of days = x days more men , less days ( indirect proportion ) ( men ) 250 : 200 : : x : 36 250 × 36 = 200 x 5 × 36 = 4 x x = 5 × 9 = 45 answer b"
Answer: b
Python program:
a = 250 * 36
b = 250 - 50
c = a / b
Problem: 3 , 4 , 6 , 10 , 18 , ( . . . )
Options: a ) 22 , b ) 34 , c ) 27 , d ) 32 , e ) 25
Rationale: "explanation : 3 3 × 2 - 2 = 4 4 × 2 - 2 = 6 6 × 2 - 2 = 10 10 × 2 - 2 = 18 18 × 2 - 2 = 34 answer : option b"
Answer: b
Python program:
a = negate - (
Problem: the average of runs of a cricket player of 10 innings was 15 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?
Options: a ) 87 , b ) 16 , c ) 10 , d ) 76 , e ) 59
Rationale: average after 11 innings = 19 required number of runs = ( 19 * 11 ) - ( 15 * 10 ) = 209 - 150 = 59 . answer : e
Answer: e
Python program:
a = 10 + 1 
b = 4 + 15 
c = a * b
d = 10 * 15
e = c - d
Problem: 16 men can complete a piece of work in 25 days . in how many days can 15 men complete that piece of work ?
Options: a ) 26.7 days , b ) 77 days , c ) 20 days , d ) 88 days , e ) 44 days
Rationale: "16 * 25 = 15 * x = > x = 26.7 days answer : a"
Answer: a
Python program:
a = 25 * 16
b = a / 15
Problem: a bus trip of 280 miles would have taken 1 hour less if the average speed v for the trip had been greater by 5 miles per hour . what was the average speed v , in miles per hour , for the trip ?
Options: a ) 35 , b ) 40 , c ) 45 , d ) 50 , e ) 55
Rationale: "the time is the distance / speed . the time difference is 1 hour . 280 / v - 280 / ( v + 5 ) = 1 280 ( v + 5 ) - 280 v = ( v ) ( v + 5 ) 1400 = ( v ) ( v + 5 ) 35 * 40 = ( v ) ( v + 5 ) v = 35 mph the answer is a ."
Answer: a
Python program:
a = 280 * 5
b = a * 4
c = 5 ** 2
d = b + c 
e = math.sqrt(d)
f = e - 5
g = f / 2
Problem: the total age of a and b is 15 years more than the total age of b and c . c is how many years younger than a ?
Options: a ) 12 , b ) 15 , c ) c is elder than a , d ) data inadequate , e ) none
Rationale: "solution [ ( a + b ) - ( b + c ) ] = 15 â € ¹ = â € º a - c = 15 . answer b"
Answer: b
Python program:
a = 15 * 1
Problem: if the diagonal of a rectangle is 17 cm long and its perimeter is 46 cm , find the area of the rectangle .
Options: a ) 127 cm ^ 2
b ) 125 cm ^ 2
c ) 120 cm ^ 2
d ) 102 cm ^ 2
e ) none of them
Rationale: let length = x and breadth = y . then , 2 ( x + y ) = 46 or x + y = 23 and x ^ 2 + y ^ 2 = ( 17 ) ^ 2 = 289 . now , ( x + y ) ^ 2 = ( 23 ) ^ 2 < = > ( x ^ 2 + y ^ 2 ) + 2 xy = 529 < = > 289 + 2 xy = 529 = xy = 120 area = xy = 120 cm ^ 2 answer is c .
Answer: c
Python program:
a = 46 / 2
b = a ** 2
c = 17 ** 2
d = b - c
e = d / 2
Problem: the toll for crossing a certain bridge is $ 0.75 each crossing . drivers who frequently use the bridge may instead purchase a sticker each month for $ 11.00 and then pay only $ 0.30 each crossing during that month . if a particular driver will cross the bridge twice on each of x days next month and will not cross the bridge on any other day , what is the least value of x for which this driver can save money by using the sticker ?
Options: a ) 14 , b ) 15 , c ) 16 , d ) 28 , e ) 29
Rationale: option # 1 : $ 0.75 / crossing . . . . cross twice a day = $ 1.5 / day option # 2 : $ 0.30 / crossing . . . . cross twice a day = $ 0.6 / day + $ 13 one time charge . if we go down the list of possible answers , you can quickly see that 14 days will not be worth purchasing the sticker . 1.5 x 14 ( 21 ) is cheaper than 0.6 x 14 + 13 ( 21.4 ) . . . it ' s pretty close so let ' s see if one more day will make it worth it . . . if we raise the number of days to 15 , the sticker option looks like a better deal . . . 1.5 x 15 ( 22.5 ) vs 0.6 x 15 + 13 ( 22 ) . answer : e
Answer: e
Python program:
a = 0 - 75
b = a * 2
c = 11 / b
d = c * 2
e = d / 10
f = e * 2
g = 0 - 75
h = g * 2
i = 11 / h
j = i * 2
k = f + j
Problem: mother , her daughter and her grand child weighs 160 kg . daughter and her daughter ( child ) weighs 60 kg . child is 1 / 5 th of her grand mother . what is the age of the daughter ?
Options: a ) 46 , b ) 47 , c ) 48 , d ) 49 , e ) 40
Rationale: "mother + daughter + child = 160 kg daughter + child = 60 kg mother = 160 - 60 = 100 kg child = 1 / 5 th of mother = ( 1 / 5 ) * 100 = 20 kg so now daughter = 120 - ( mother + child ) = 160 - ( 100 + 20 ) = 40 kg answer : e"
Answer: e
Python program:
a = 160 - 60
b = a / 5
c = 60 - b
Problem: a batsman makes a score of 100 runs in the 17 th inning and thus increases his averages by 5 . what is his average after 17 th inning ?
Options: a ) 39 , b ) 35 , c ) 20 , d ) 40.5 , e ) 41.5
Rationale: "let the average after 16 th inning = x then total run after 16 th inning = 16 x then total run after 17 th inning = 16 x + 100 then average run after 17 th inning = ( 16 x + 100 ) / 17 ( 16 x + 100 ) / 17 = x + 5 = > 16 x + 100 = 17 x + 85 = > x = 15 x = 15 ; average after 17 th inning = 15 + 5 = 20 answer : c"
Answer: c
Python program:
a = 17 * 5
b = 100 - a
c = b + 5
Problem: a fair coin is tossed 5 times . what is the probability of getting more heads than tails in 5 tosses ?
Options: a ) 1 / 2 , b ) 63 / 128 , c ) 4 / 7 , d ) 61 / 256 , e ) 63 / 64
Rationale: "on each toss , the probability of getting a head is 1 / 2 and the probability of getting a tail is 1 / 2 . there is no way to get the same number of heads and tails on an odd number of tosses . there will either be more heads or more tails . then there must be more heads on half of the possible outcomes and more tails on half of the possible outcomes . p ( more heads ) = 1 / 2 the answer is a ."
Answer: a
Python program:
a = math.comb(5, 2)
b = math.comb(5, 3)
c = a + b 
d = math.comb(5, 4)
e = c + d 
f = math.comb(5, 5)
g = e + f 
h = 2 ** 5
i = g / h
Problem: the difference between the squares of two consecutive numbers is 35 . the numbers are
Options: a ) 14,15 , b ) 15,16 , c ) 17,18 , d ) 18,19 , e ) none
Rationale: "explanation : let the numbers be a and ( a + 1 ) ( a + 1 ) 2 − a 2 = 35 ⇒ a 2 + 2 a + 1 − a 2 = 35 ⇒ 2 a = 34 ⇒ 2 a = 34 or a = 17 the numbers are 17 & 18 . correct option : c"
Answer: c
Python program:
a = 35 + 1 
b = a / 2
Problem: john want to buy a $ 100 trouser at the store , but he think it ’ s too expensive . finally , it goes on sale for $ 60 . what is the percent decrease ?
Options: a ) 20 % , b ) 30 % , c ) 40 % , d ) 70 % , e ) 80 %
Rationale: the is always the difference between our starting and ending points . in this case , it ’ s 100 – 60 = 40 . the “ original ” is our starting point ; in this case , it ’ s 100 . ( 40 / 100 ) * 100 = ( 0.4 ) * 100 = 40 % . c
Answer: c
Python program:
a = 100 - 60
Problem: if rs . 561 be divided among a , b , c in such a way that a gets 2 / 3 of what b gets and b gets 1 / 4 of what c gets , then their shares are respectively ?
Options: a ) s . 300 , b ) s . 360 , c ) s . 396 , d ) s . 368 , e ) s . 323
Rationale: "( a = 2 / 3 b and b = 1 / 4 c ) = a / b = 2 / 3 and b / c = 1 / 4 a : b = 2 : 3 and b : c = 1 : 4 = 3 : 12 a : b : c = 2 : 3 : 12 a ; s share = 561 * 2 / 17 = rs . 66 b ' s share = 561 * 3 / 17 = rs . 99 c ' s share = 561 * 12 / 17 = rs . 396 . answer : c"
Answer: c
Python program:
a = 2 / 3
b = 1 / 4
c = a * b
d = 1 / 4
e = c + d 
f = e + 1 
g = 561 / f
Problem: a certain car can travel 56 kilometers on a liter of fuel . if the fuel tank ’ s contents decrease by 3.9 gallons over a period of 5.7 hours as the car moves at a constant speed , how fast is the car moving , in miles per hour ? ( 1 gallon = 3.8 liters ; 1 mile = 1.6 kilometers )
Options: a ) 52 , b ) 65 , c ) 78 , d ) 91 , e ) 104
Rationale: fuel used 3.9 gallons ; convert to liters - - > 3.9 x 3.8 liters time = 5.7 hours 1 mile = 1.6 kilometers ; convert to miles - - > 1 km = 1 / 1.6 mile speed ( km / hour ) = d / t = 56 ( km * ) x 3.9 x 3.8 / 5.7 replace ( km * ) to miles ; multiply by 1 / 1.6 mile speed ( miles / hour ) = 56 x 3.9 x 3.8 / 5.7 x 1.6 = 78 miles / hour ans : d ps : i felt the factors were easy to cancel out , so did n ' t require much rounding off = 56 x 3.9 x 3.8 / 5.7 x 1.6 = 91 d
Answer: d
Python program:
a = 56 * 3
b = a / 1
c = b * 3
d = c / 5
Problem: if the length of the longest chord of a certain circle is 14 , what is the radius of that certain circle ?
Options: a ) 2.5 , b ) 5 , c ) 10 , d ) 7 , e ) 9
Rationale: "longest chord of a circle is the diameter of the circle diameter = 2 * radius if diameter of the circle is given as 14 = 2 * 7 so radius of the circle = 7 correct answer - d"
Answer: d
Python program:
a = 14 / 2
Problem: at a certain organisation , the number of male members went up by 13 % in the year 2001 from year 2000 , and the number of females members went down by 6 % in the same time period . if the total membership at the organisation went up by 1.2 % from the year 2000 to 2001 , what was the ratio of male members to female members in the year 2000 ?
Options: a ) 1 : 2 , b ) 1 : 3 , c ) 2 : 3 , d ) 3 : 5 , e ) 2 : 1
Rationale: men increase by 13 % = = > 1.13 m = males in 2001 women decrease by 6 % = = > 0.94 f = women in 2001 total employees increase by 1.2 % = = > 1.012 * ( m + f ) = total number of employees in 2001 obviously ( males in 2001 ) + ( females in 2001 ) = total number of employees in 2001 1.13 m + 0.94 f = 1.012 * ( m + f ) 1.13 m + 0.94 f = 1.012 m + 1.012 f 1.13 m - 1.012 m = 1.012 f - 0.94 f 0.108 m = 0.072 f m / f = ( 0.072 ) / ( 0.118 ) = 72 / 118 = 3 / 5 answer = ( d )
Answer: d
Python program:
a = 1 / 2
b = 1 + a 
c = b * 1000
d = 6 / 100
e = 1 - d
f = e * 1000
g = c - f
h = 13 / 100
i = 1 + h 
j = i * 1000
k = 1 / 2
l = 1 + k 
m = l * 1000
n = j - m
o = g / n
Problem: in a certain pond , 40 fish were caught , tagged , and returned to the pond . a few days later , 50 fish were caught again , of which 2 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what is the approximate number of fish in the pond ?
Options: a ) 400 , b ) 625 , c ) 1,250 , d ) 2,500 , e ) 1,000
Rationale: "this is a rather straight forward ratio problem . 1 . 40 fish tagged 2 . 2 out of the 50 fish caught were tagged thus 2 / 50 2 / 50 = 40 / x thus , x = 1000 think of the analogy : 2 fish is to 50 fish as 50 fish is to . . . ? you ' ve tagged 50 fish and you need to find what that comprises as a percentage of the total fish population - we have that information with the ratio of the second catch . e"
Answer: e
Python program:
a = 2 / 50
b = 40 / a
Problem: set a of 8 positive integers may have the same element and have 35 . and set b of 8 positive integers must have different elements and have 35 . when m and n are the greatest possible differences between 35 and other elements ’ sums in set a and set b , respectively , m - n = ?
Options: a ) 20 , b ) 26 , c ) 23 , d ) 25 , e ) 21
Rationale: this is maximum - minimum . hence , 35 - ( 1 + 1 + 1 + 1 + 1 + 1 + 1 ) = 28 and 35 - ( 1 + 2 + 3 + 4 + 5 + 6 + 7 ) = 7 . so , 28 - 7 = 21 . the correct answer is e .
Answer: e
Python program:
a = 8 + 2 
b = a + 8 
c = 35 - b
Problem: a vessel of capacity 50 litres is fully filled with pure milk . nine litres of milk is removed from the vessel and replaced with water . nine litres of the solution thus formed is removed and replaced with water . find the quantity of pure milk in the final milk solution ?
Options: a ) 23.89 , b ) 72.9 , c ) 33.62 , d ) 78.3 , e ) 79.3
Rationale: "explanation : let the initial quantity of milk in vessel be t litres . let us say y litres of the mixture is taken out and replaced by water for n times , alternatively . quantity of milk finally in the vessel is then given by [ ( t - y ) / t ] ^ n * t for the given problem , t = 50 , y = 9 and n = 2 . hence , quantity of milk finally in the vessel = [ ( 50 - 9 ) / 50 ] ^ 2 ( 50 ) = 33.62 litres . answer : option c"
Answer: c
Python program:
a = 3 * 3
b = 50 - a
c = 3 * 3
d = 50 - c
e = d / 50
f = 3 * 3
g = e * f
h = b - g
Problem: on a saturday night , each of the rooms at a certain motel was rented for either $ 40 or $ 60 . if 10 of the rooms that were rented for $ 60 had instead been rented for $ 40 , then the total rent the motel charged for that night would have been reduced by 20 percent . what was the total rent the motel actually charged for that night ?
Options: a ) $ 600 , b ) $ 800 , c ) $ 1,000 , d ) $ 1,600 , e ) $ 2,400
Rationale: "let total rent the motel charge for all rooms = x if 10 rooms that were rented for 60 $ had instead been rented for 40 $ , then total difference in prices = 20 $ * 10 = 200 $ total rent the motel charged would have been reduced by 20 % . 2 x = 200 = > x = 1000 answer c"
Answer: c
Python program:
a = 60 - 40
b = 10 * a
c = 20 / 100
d = b / c
Problem: total of the ages of a , b ahd c at present is 90 years . 10 years ago , the ratio of their ages was 1 : 2 : 3 . what is the age of b at present
Options: a ) 25 , b ) 30 , c ) 45 , d ) 60 , e ) 65
Rationale: explanation : let their ages 10 years ago is x , 2 x and 3 x years . 10 + 2 x + 10 + 3 x + 10 = 90 hence x = 10 b � s present age = ( 2 x + 10 ) = 30 years answer : option b
Answer: b
Python program:
a = 10 + 10 
b = a + 10 
c = 90 - b
d = 3 + 2 
e = d + 1 
f = c / e
g = f * 2
h = 10 + 10 
i = h + 10 
j = 90 - i
k = 3 + 2 
l = k + 1 
m = j / l
n = g + m
Problem: ( ( - 1.9 ) ( 0.6 ) – ( 2.6 ) ( 1.2 ) ) / 8.0 = ?
Options: a ) - 0.53 , b ) 1.0 , c ) 1.07 , d ) 1.71 , e ) 2.71
Rationale: "dove straight into calculation ( ( - 1.9 ) ( 0.6 ) – ( 2.6 ) ( 1.2 ) ) / 7.0 = - 0.53 answer a"
Answer: a
Python program:
a = 1 * 9
b = negate - (
c = 2 * 6
d = b / c
Problem: two pipes a and b can separately fill a tank in 12 and 20 minutes respectively . a third pipe c can drain off 45 liters of water per minute . if all the pipes are opened , the tank can be filled in 15 minutes . what is the capacity of the tank ?
Options: a ) 542 , b ) 540 , c ) 675 , d ) 829 , e ) 279
Rationale: 1 / 12 + 1 / 20 - 1 / x = 1 / 15 x = 15 15 * 45 = 675 answer : c
Answer: c
Python program:
a = 1 / 12
b = 1 / 20
c = a + b 
d = 1 / 45
e = c + d 
f = 1 / 15
g = e - f
h = 1/(g)
i = h * 3
j = i * 20