euclaise/mathqa_programs huggingface dataset:
Problem: apple costs l rupees per kilogram for first 30 kgs and q rupees per kilogram for each additional kilogram . if the price of 33 kilograms is 333 and for 36 kgs of apples is 366 then the cost of first 15 kgs of apples is
Options: a ) 3.69 , b ) 3.66 , c ) 3.6 , d ) 150 , e ) 3.61
Rationale: "ans : by framing equations we get 30 l + 3 q = 333 30 l + 6 q = 366 eliminate q by multiplying the first equation by 2 and subtracting second equation from the first 60 l + 6 q = 666 30 l + 6 q = 366 30 l = 300 = > l = 10 then we get l = 10 cost of 15 kgs of apples = 15 x 10 = 150 answer : d"
Answer: d
Python program:
a = 33 - 30
b = 366 - 333
c = 36 - 33
d = b / c
e = a * d
f = 333 - e
g = f / 30
h = g * 15
Problem: the sub - duplicate ratio of 16 : 36 is
Options: a ) 4 : 6 , b ) 1 : 2 , c ) 1 : 3 , d ) 1 : 4 , e ) 2 : 3
Rationale: "root ( 16 ) : root ( 36 ) = 4 : 6 answer : a"
Answer: a
Python program:
a = math.sqrt(16)
b = math.sqrt(36)
c = a / b
Problem: there are 2 red chips and 4 blue ones . when arranged in a row , they form a certain color pattern , for example rbrrb . how many color patterns ?
Options: a ) a ) 10 , b ) b ) 12 , c ) c ) 50 , d ) d ) 60 , e ) e ) 100
Rationale: "using anagram method : 6 _ 5 _ 4 _ 3 _ 2 _ 1 r _ r _ b _ b _ b _ b so . . 6 ! / number of repeated letters ( 2 ! ) ( 4 ! ) = 10 ans : e"
Answer: e
Python program:
a = math.factorial(2)
b = math.factorial(4)
c = a * b
Problem: a can give b 70 meters start and c 200 meters start in a kilometer race . how much start can b give c in a kilometer race ?
Options: a ) 139.78 , b ) 139.13 , c ) 139.22 , d ) 111.0 , e ) 111.12
Rationale: "a runs 1000 m while b runs 930 m and c runs 800 m . the number of meters that c runs when b runs 1000 m , = ( 1000 * 800 ) / 930 = 860.21 m . b can give c = 1000 - 860.21 = 139.78 m . answer : a"
Answer: a
Python program:
a = 100 * 10
b = 100 * 10
c = 100 * 10
d = c - 200
e = b * d
f = 100 * 10
g = f - 70
h = e / g
i = a - h
Problem: a car drives 40 miles on local roads at 20 mph , and 180 miles on the highway at 60 mph , what is the average speed of the entire trip ?
Options: a ) 36 mph , b ) 40 mph , c ) 44 mph , d ) 52 mph , e ) 58 mph
Rationale: "explanations 1 ) in phase # 1 of the trip , the car traveled 40 mi at 20 mph . that time of this phase was : time = distance / rate = ( 40 mi ) / ( 20 mph ) = 2 hr in phase # 2 of the trip , the car traveled 180 mi at 60 mph . that time of this phase was : time = distance / rate = ( 180 mi ) / ( 60 mph ) = 3 hr the total distance of the trip = 40 mi + 180 mi = 220 mi the total time of the trip = 2 hr + 3 hr = 5 hr the average speed of trip is given by speed = distance / time = ( 220 mi ) / ( 5 hr ) = 44 mph answer : c ."
Answer: c
Python program:
a = 40 + 180 
b = 40 / 20
c = 180 / 60
d = b + c 
e = a / d
Problem: a man sold 18 toys for rs . 16800 , gaining thereby the cost price of 3 toy find the cost price of a toy
Options: a ) rs . 600 , b ) rs . 800 , c ) rs . 500 , d ) rs . 900 , e ) rs . 970
Rationale: "let the cost of one toy = x . then , cost of 18 toys = 18 x . gain = 3 x . sp of 18 toys = rs . 16800 . gain = sp – cp 3 x = 16800 – 18 x 21 x = 16800 x = rs . 800 . answer : b"
Answer: b
Python program:
a = 18 + 3 
b = 16800 / a
Problem: in the coordinate plane , points ( x , 1 ) and ( 10 , y ) are on line k . if line k passes through the origin and has slope 1 / 4 , then x + y =
Options: a ) 6.5 , b ) 7 , c ) 8 , d ) 11 , e ) 12
Rationale: "line k passes through the origin and has slope 1 / 4 means that its equation is y = 1 / 4 * x . thus : ( x , 1 ) = ( 4 , 1 ) and ( 10 , y ) = ( 10 , 2.5 ) - - > x + y = 4 + 2.5 = 6.5 answer : a ."
Answer: a
Python program:
a = 10 * 4
b = 1 / 4
c = a * b
Problem: a doctor prescribed 20 cubic centimeters of a certain drug to a patient whose body weight was 120 pounds . if the typical dosage is 2 cubic centimeters per 15 pounds of the body weight , by what percent was the prescribed dosage greater than the typical dosage ?
Options: a ) 25 % , b ) 9 % , c ) 11 % , d ) 12.5 % , e ) 14.8 %
Rationale: "typical dosage per 15 pound of the body weight = 2 c . c typical dosage per 120 pound of the body weight = 2 * ( 120 / 15 ) = 2 * 8 = 16 c . c dosage prescribed by doctor for 120 pound patient = 20 c . c % prescribed dosage greater than the typical dosage = ( 20 - 16 / 16 ) * 100 % = ( 2 / 16 ) * 100 % = 25 % answer a"
Answer: a
Python program:
a = 2 / 15
b = a * 120
c = b - 20
d = 2 / 15
e = d * 120
f = c / e
g = f * 100
Problem: the ratio between the present age of p and q is 6 : 7 . if q is 4 years old then p , what will be the ratio of the ages of p and q after 4 year ?
Options: a ) 3 : 4 , b ) 3 : 5 , c ) 7 : 8 , d ) 4 : 3 , e ) none of these
Rationale: "solution let p ' s age and q ' s age be 6 x years and 7 x years respectively . then , 7 x - 6 x = 4 ⇔ x = 4 . ∴ required ratio = ( 6 x + 4 ) : ( 7 x + 4 ) = 28 : 32 = 7 : 8 . answer c"
Answer: c
Python program:
a = 6 * 4
b = 7 - 6
c = a / b
d = 4 + c 
e = 4 + d 
f = 6 * 4
g = 7 - 6
h = f / g
i = 4 + h 
j = e / i
Problem: 3 people have $ 28 , $ 72 , and $ 98 , respectively . if they pool their money then redistribute it among them , what is the maximum value for the median amount of money ?
Options: a ) $ 72 , b ) $ 85 , c ) $ 99 , d ) $ 101 , e ) $ 202
Rationale: solution - total money distributed is $ 198 . in order to maximize median , one person has to accept $ 0 and remaining two people share $ 99 each . hence median is $ 99 . ans c
Answer: c
Python program:
a = 28 + 72 
b = a + 98 
c = b / 2
Problem: if a is an integer greater than 2 but less than 11 and b is an integer greater than 11 but less than 21 , what is the range of a / b ?
Options: a ) 52 / 45 , b ) 23 / 47 , c ) 60 / 41 , d ) 51 / 42 , e ) 41 / 60
Rationale: "the way to approach this problem is 2 < a < 11 and 11 < b < 21 minimum possible value of a is 3 and maximum is 10 minimum possible value of b is 12 and maximum is 20 range = max a / min b - min a / max b ( highest - lowest ) 10 / 12 - 3 / 20 = 41 / 60 hence e"
Answer: e
Python program:
a = 11 - 1
b = 11 + 1 
c = a / b
d = 2 + 1 
e = 21 - 1
f = d / e
g = c - f
Problem: at what price must an article costing rs . 100 be marked in order that after deducting 5 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 131.58 , b ) 62.0 , c ) 62.6 , d ) 62.1 , e ) 62.2
Rationale: "cp = 100 sp = 100 * ( 125 / 100 ) = 125 mp * ( 95 / 100 ) = 125 mp = 131.58 answer : a"
Answer: a
Python program:
a = 100 * 25
b = a / 100
c = 100 + b 
d = c * 100
e = 100 - 5
f = d / e
Problem: how long does a train 110 m long running at a speed of 72 kmph take to cross a bridge 132 m in length ?
Options: a ) 9.8 sec , b ) 12.1 sec , c ) 12.42 sec , d ) 14.3 sec , e ) 24.3 sec
Rationale: "72 km / hr = 72 * 5 / 18 m / sec = 20 m / sec time = d / s = 110 + 132 / 20 = 242 / 20 = 12.1 sec answer : b"
Answer: b
Python program:
a = 110 + 132 
b = 72 * const_0_2778
c = a / b
Problem: a train 110 meters long is running with a speed of 60 kmph . in what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ?
Options: a ) 7 sec , b ) 6 sec , c ) 8 sec , d ) 4 sec , e ) 2 sec
Rationale: "speed of train relative to man = ( 60 + 6 ) km / hr = 66 km / hr [ 66 * 5 / 18 ] m / sec = [ 55 / 3 ] m / sec . time taken to pass the man = [ 110 * 3 / 55 ] sec = 6 sec answer : b"
Answer: b
Python program:
a = 110 / 1000
b = 60 + 6 
c = a / b
d = 3600 * c
Problem: a person can swim in still water at 4 km / h . if the speed of water 2 km / h , how many hours will the man take to swim back against the current for 6 km ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 67 , e ) 7
Rationale: "m = 4 s = 2 us = 4 - 2 = 2 d = 6 t = 6 / 2 = 3 answer : a"
Answer: a
Python program:
a = 4 - 2
b = 6 / a
Problem: in an election , candidate x got 75 % of the total valid votes . if 15 % of the total votes were declared invalid and the total numbers of votes is 560000 , find the number of valid vote polled in favour of candidate ?
Options: a ) 280000 , b ) 300000 , c ) 355000 , d ) 356000 , e ) 357000
Rationale: total number of invalid votes = 15 % of 560000 = 15 / 100 × 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 – 84000 = 476000 percentage of votes polled in favour of candidate x = 75 % therefore , the number of valid votes polled in favour of candidate x = 75 % of 476000 = 75 / 100 × 476000 = 35700000 / 100 = 357000 e )
Answer: e
Python program:
a = 100 - 15
b = a * 75
c = 560000 / 100
d = c / 100
e = b * d
Problem: the average of first 15 natural numbers is ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "sum of 15 natural no . = 240 / 2 = 120 average = 120 / 15 = 8 answer : b"
Answer: b
Python program:
a = 15 + 1
Problem: at 6 ′ o a clock ticks 6 times . the time between first and last ticks is 35 seconds . how long does it tick at 12 ′ o clock
Options: a ) 77 , b ) 76 , c ) 28 , d ) 66 , e ) 11
Rationale: "explanation : for ticking 6 times , there are 5 intervals . each interval has time duration of 35 / 5 = 7 secs at 12 o ' clock , there are 11 intervals , so total time for 11 intervals = 11 × 7 = 77 secs . answer : a"
Answer: a
Python program:
a = 6 - 1
b = 35 / a
c = 12 - 1
d = b * c
Problem: a no . when divided by the sum of 555 and 445 gives 2 times their difference as quotient & 20 as remainder . find the no . is ?
Options: a ) 122456 , b ) 220020 , c ) 220022 , d ) 235467 , e ) 220026
Rationale: "( 555 + 445 ) * 2 * 110 + 20 = 220000 + 20 = 220020 b"
Answer: b
Python program:
a = 555 + 445 
b = a * 2
c = 555 - 445
d = b * c
e = d + 20
Problem: a case contains c cartons . each carton contains b boxes , and each box contains 300 paper clips . how many paper clips are contained in 2 cases ?
Options: a ) 300 bc , b ) 300 b / c , c ) 600 bc , d ) 600 b / c , e ) 600 / bc
Rationale: "2 cases * c cartons / case * b boxes / carton * 300 clips / box = 600 bc paper clips the answer is c ."
Answer: c
Python program:
a = 2 * 300
Problem: solve the equation for x : 2 x - 21 + 3 x = 4 + 9 - x
Options: a ) 4 , b ) 5 , c ) 5.6 , d ) 9.2 , e ) 3.1
Rationale: "c 5.6 5 x + x = 13 + 21 6 x = 34 = > x = 5.6"
Answer: c
Python program:
a = 21 + 4 
b = 2 + 2 
c = a / b
Problem: how many positive integers less than 5,000 are evenly divisible by neither 15 nor 20 ?
Options: a ) 4,514 , b ) 4,477 , c ) 4,521 , d ) 4,428 , e ) 4,349
Rationale: "integers less than 5000 divisible by 15 5000 / 15 = 333 . something , so 333 integers less than 5000 divisible by 20 5000 / 20 = 238 . # # , so 238 we have double counted some , so take lcm of 15 and 20 = 105 and divide by 5000 , we get 47 . so all numbers divisible by 15 and 20 = 333 + 238 - 47 = 524 now subtract that from 4999 . 4999 - 524 = 4477 answer b ."
Answer: b
Python program:
a = 4 + 15 
b = a - 1
c = math.factorial(b)
d = math.factorial(15)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: the cost price of an article is 70 % of the marked price . calculate the gain percent after allowing a discount of 10 % .
Options: a ) 13.6 % , b ) 28.6 % , c ) 35.6 % , d ) 42.3 % , e ) none
Rationale: "sol . let marked price = rs . 100 . then , c . p . = rs . 70 . s . p = rs . 90 . â ˆ ´ gain % = [ 20 / 70 * 100 ] % = 28.6 % . answer b"
Answer: b
Python program:
a = 100 - 10
b = a / 70
c = b - 1
d = c * 100
Problem: lola rolls a die 3 times . what is the probability that she gets a 4 on the last one of the 3 rolls ?
Options: a ) 215 / 216 , b ) 216 , c ) 1 / 216 , d ) none , e ) 2
Rationale: the die has 6 sides and it was rolle 3 times , then 6 * 6 * 6 = 216 the number of ways to get 4 is 1 then 1 / 216 the probability would be 1 - 1 / 216 = 215 / 216 answer a
Answer: a
Python program:
a = 1 / 6
b = 1 / 6
c = a * b
d = 4 + 1 
e = d / 6
f = c * e
g = 1 - f
Problem: the contents of a certain box consist of 48 apples and 30 kiwis . how many kiwis must be added to the box so that exactly 30 % of the pieces of fruit in the box will be apples ?
Options: a ) 90 , b ) 72 , c ) 82 , d ) 54 , e ) 65
Rationale: "apple = ( apple + kiwi + x ) * 0.3 48 = ( 30 + 48 + x ) * 0.3 x = 82 answer : c"
Answer: c
Python program:
a = 48 + 30 
b = 30 / 100
c = 48 / b
d = a - c
Problem: a group of people participate in some curriculum , 35 of them practice yoga , 20 study cooking , 15 study weaving , 7 of them study cooking only , 5 of them study both the cooking and yoga , 3 of them participate all curriculums . how many people study both cooking and weaving ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "both cooking and weaving = 20 - ( 7 + 5 + 3 ) = 5 so , the correct answer is e ."
Answer: e
Python program:
a = 20 - 5
b = a - 3
c = b - 7
Problem: a can finish a work in 48 days , b in 9 days and c in 2 days , b and c start the work but are forced to leave after 3 days . the remaining work was done by a in ?
Options: a ) 10 days , b ) 12 days , c ) 6 days , d ) 20 days , e ) 8 days
Rationale: "b + c 1 day work = 1 / 9 + 1 / 12 = 7 / 36 work done by b and c in 3 days = 7 / 36 * 3 = 7 / 12 remaining work = 1 - 7 / 12 = 5 / 12 1 / 48 work is done by a in 1 day 5 / 12 work is done by a in 48 * 5 / 12 = 20 days answer is d"
Answer: d
Python program:
a = 1 / 9
b = 1 / 2
c = a + b 
d = 1 / c
e = d * 3
Problem: in a certain animal shelter , the ratio of the number of catsto the number of dogs is 15 to 7 . if 16 additional dogs were to be taken in by the shelter , the ratio of the number of cats to the number of dogs would be 15 to 11 . how many cats are in the shelter ?
Options: a ) 15 , b ) 25 , c ) 30 , d ) 45 , e ) 60
Rationale: "this ratio question can be solved in a couple of different ways . here ' s an algebraic approach . . . we ' re told that the ratio of the number of cats to the number of dogs is 15 : 7 . we ' re then told that 16 more dogs are added to this group and the ratio becomes 15 : 11 . we ' re asked for the number of cats . algebraically , since the number of cats is a multiple of 15 and the number of dogs is a multiple of 7 , we can write this initial relationship as . . . 15 x / 7 x when we add the 16 cats and factor in the ' ending ratio ' , we have an equation . . . . 15 x / ( 7 x + 16 ) = 15 / 11 here we have 1 variable and 1 equation , so we can solve for x . . . . ( 15 x ) ( 11 ) = ( 7 x + 16 ) ( 15 ) ( x ) ( 11 ) = ( 7 x + 16 ) ( 1 ) 11 x = 7 x + 16 4 x = 16 x = 4 with this x , we can figure out the initial number of dogs and cats . . . initial dogs = 15 x = 15 ( 4 ) = 60 final answer : d"
Answer: d
Python program:
a = 11 - 7
b = 16 / a
c = 15 * b
Problem: for the positive integers x , x + 2 , x + 4 , x + 7 , and x + 32 , the mean is how much greater than the median ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 4 , e ) 5
Rationale: "mean = ( x + x + 2 + x + 4 + x + 7 + x + 32 ) / 5 = ( 5 x + 45 ) / 5 = x + 9 median = x + 4 thus mean - median = x + 9 - ( x + 4 ) = 5 answer = e"
Answer: e
Python program:
a = 2 + 4 
b = a + 7 
c = b + 32 
d = 4 + 1 
e = c / d
f = e - 4
Problem: the ratio of the volumes of two cubes is 27 : 64 . what is the ratio of their total surface areas ?
Options: a ) 18 : 21
b ) 81 : 13
c ) 8 : 15
d ) 16 : 21
e ) 1 : 13
Rationale: ratio of the sides = ³ √ 27 : ³ √ 64 = 3 : 4 ratio of surface areas = 32 : 42 = 16 : 21 answer : d
Answer: d
Python program:
a = 27 / 64
b = 1 / 3
c = a ** b
Problem: a driver would have reduced the time it took to drive from home to the store by 1 / 3 if the average speed had been increased by 18 miles per hour . what was the actual average speed , in miles per hour , when the driver drove from home to the store ?
Options: a ) 36 , b ) 40 , c ) 44 , d ) 48 , e ) 52
Rationale: "let r be the original speed and let t be the original time . since the distance remains the same ( we ' re just changing the rate and time ) , any increase in rate or time is met with a decrease in the other term . decreasing the time by 1 / 3 would give us : d = ( r ) ( t ) = ( 2 t / 3 ) ( x * r ) x = 3 / 2 since ( 2 t / 3 ) ( 3 r / 2 ) = ( r ) ( t ) = d 3 r / 2 = r + 18 r / 2 = 18 r = 36 the answer is a ."
Answer: a
Python program:
a = 1 / 3
b = 1 - a
c = b * 18
d = 1 / 3
e = 1 - d
f = 1 - e
g = c / f
Problem: what is the probability q of randomly selecting an arrangement of the letters of the wordmediterraneanin which the first letter is e and the last letter is r ?
Options: a ) 1 / 13 , b ) 1 / 20 , c ) 1 / 26 , d ) 1 / 50 , e ) 1 / 100
Rationale: why do you calculate the total combinations and everything , it is much easier to calculate as follows : 3 / 13 * 1 * 1 * 1 * 1 . . . . . * 2 / 12 = 6 / 156 = 1 / 26 this is because 3 / 13 = probability that first letter will be e and 2 / 12 = probability that thefirstletter will be r . between everything else cuts down to 1 * 1 * 1 . . . e . g . probability q of the second letter is 11 / 11 = 1 , > we do not care what ' s in between . c
Answer: c
Python program:
a = 3 * 4
b = a - 1
c = math.factorial(b)
d = math.factorial(2)
e = d ** 3
f = c / e
g = 3 * 4
h = g - 1
i = h + 2 
j = math.factorial(i)
k = math.factorial(3)
l = math.factorial(2)
m = l ** 3
n = k * m
o = j / n
p = f / o
Problem: the speed of a train is 90 kmph . what is the distance covered by it in 20 minutes ?
Options: a ) 15 , b ) 66 , c ) 77 , d ) 30 , e ) 42
Rationale: "90 * 20 / 60 = 30 kmph answer : d"
Answer: d
Python program:
a = 20 / const_60
b = a * 90
Problem: a man can row downstream at the rate of 45 kmph and upstream at 23 kmph . find the man ’ s rate in still water and rate of current ?
Options: a ) 8.5 , b ) 10.0 , c ) 12.5 , d ) 11.0 , e ) 8.25
Rationale: rate of still water = 1 / 2 ( down stream + upstream ) = 1 / 2 ( 45 + 23 ) = 34 kmph rate of current = 1 / 2 ( down stream - upstream ) = 1 / 2 ( 45 - 23 ) = 1 / 2 ( 22 ) = 11 kmph answer is d .
Answer: d
Python program:
a = 45 - 23
b = a / 2
Problem: how many numbers from 9 to 79 are exactly divisible by 11 ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 11 , e ) 12
Rationale: "9 / 11 = 0 and 79 / 11 = 7 = = > 7 - 0 = 7 numbers answer : b"
Answer: b
Python program:
a = 79 / 11
b = math.floor(a)
c = b * 11
d = 9 / 11
e = math.floor(d)
f = e + 1 
g = f * 11
h = c - g
i = h / 11
j = i + 1
Problem: the speed of a car is 20 km in the first hour and 60 km in the second hour . what is the average speed of the car ?
Options: a ) 79 kmph , b ) 40 kmph , c ) 34 kmph , d ) 23 kmph , e ) 14 kmph
Rationale: "s = ( 20 + 60 ) / 2 = 40 kmph answer : b"
Answer: b
Python program:
a = 20 + 60 
b = a / 2
Problem: what least number should be added to 1053 , so that the sum is completely divisible by 23
Options: a ) a ) 4 , b ) b ) 1 , c ) c ) 2 , d ) d ) 3 , e ) e ) 5
Rationale: "explanation : ( 1053 / 23 ) gives remainder 18 18 + 5 = 23 , so we need to add 5 answer : option e"
Answer: e
Python program:
a = 23 - reminder
Problem: the average weight of 6 person ' s increases by 2.5 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 ) 76 kg , b ) 80 kg , c ) 85 kg , d ) data inadequate , e ) none of these
Rationale: "explanation : total weight increased = ( 6 x 2.5 ) kg = 15 kg . weight of new person = ( 65 + 15 ) kg = 80 kg . answer : b"
Answer: b
Python program:
a = 6 * 2
b = a + 65
Problem: which greatest possible length can be used to measure exactly 10 meter 40 cm , 14 meter 10 cm and 7 meter 90 cm
Options: a ) 45 cm , b ) 25 cm , c ) 24 cm , d ) 15 cm , e ) 10 cm
Rationale: "explanation : convert first all terms into cm . i . e . 1040 cm , 1410 cm , 790 cm . now whenever we need to calculate this type of question , we need to find the hcf . hcf of above terms is 10 . option e"
Answer: e
Python program:
a = 10 * 100
b = a + 40 
c = 14 * 100
d = c + 10 
e = b / d
f = math.floor(e)
Problem: a shopkeeper sells 200 metres of cloth for rs . 12000 at a loss of rs . 6 per metre . find his cost price for one metre of cloth ?
Options: a ) s . 59 , b ) s . 58 , c ) s . 09 , d ) s . 50 , e ) s . 66
Rationale: "sp per metre = 12000 / 200 = rs . 60 loss per metre = rs . 6 cp per metre = 60 + 6 = rs . 66 answer : e"
Answer: e
Python program:
a = 12000 / 200
b = a + 6
Problem: in what ratio must rice at $ 9.30 / kg be mixed with rice at $ 10.80 / kg so that the mixture is worth $ 10 / kg ?
Options: a ) 1 : 3 , b ) 9 : 4 , c ) 8 : 7 , d ) 11 : 9 , e ) 11 : 7
Rationale: 9.30 x + 10.80 y = 10 ( x + y ) . 80 y = . 70 x x / y = 8 / 7 c is the answer
Answer: c
Python program:
a = 10 - 8
b = 10 - 9
c = a / b
Problem: a can contains a mixture of liquids a and b is the ratio 7 : 5 . when 9 litres of mixture are drawn off and the can is filled with b , the ratio of a and b becomes 7 : 9 . how many liter q of liquid a was contained by the can initially ?
Options: a ) 10 , b ) 20 , c ) 21 , d ) 25 , e ) 27
Rationale: "as a : b : : 7 : 5 - - - > only option c is a multiple of 7 and hence it is a good place to start . also a : b : : 7 : 5 means that , a = ( 712 ) * total and b = ( 5 / 12 ) * total if a = 21 , b = 15 - - - > remove 9 litres - - - > you remove ( 7 / 12 ) * 9 of a - - - > a remaining = 21 - ( 7 / 12 ) * 9 = 63 / 4 similarly , for b , you remove ( 5 / 12 ) * 9 - - - > b remaining = 15 - ( 5 / 12 ) * 9 = 45 / 4 and then add 9 more litres of b - - - > 9 + 45 / 4 = 81 / 4 thus a / b ( final ratio ) = ( 45 / 4 ) / ( 81 / 4 ) = 7 : 9 , the same as the final ratio mentioned in the question . hence c is the correct answer . a / b = 7 / 9 = ( 7 x - ( 7 / 12 ) * 9 ) / ( 5 x - ( 5 / 12 ) * 9 + 9 ) , where 7 x and 5 x are initial quantities of a and b respectively . thus , 7 / 9 = ( 7 x - ( 7 / 12 ) * 9 ) / ( 5 x - ( 5 / 12 ) * 9 + 9 ) - - - > giving you x = 3 . thus a ( original ) q = 7 * 3 = 21 . c"
Answer: c
Python program:
a = 7 + 9 
b = 7 + 5 
c = 5 / b
d = c * 9
e = 9 - d
f = a * e
g = 9 * 7
h = 7 * 5
i = g - h
j = f / i
k = 7 * j
Problem: a sum of money at simple interest amounts to rs . 855 in 3 years and to rs . 854 in 4 years . the sum is :
Options: a ) s . 650 , b ) s . 690 , c ) s . 738 , d ) s . 700 , e ) s . 718
Rationale: "s . i . for 1 year = rs . ( 854 - 815 ) = rs . 39 . s . i . for 3 years = rs . ( 39 x 3 ) = rs . 117 . principal = rs . ( 855 - 117 ) = rs . 738 . answer : option c"
Answer: c
Python program:
a = 854 - 855
b = a * 3
c = b / 4
d = 855 - c
Problem: a salesperson received a commission of 3 percent of the sale price for each of the first 100 machines that she sold and 4 percent of the sale price for each machine that she sold after the first 100 . if the sale price of each machine was $ 10,000 and the salesperson received a $ 42,000 commission , how many machines did she sell ?
Options: a ) 90 , b ) 103 , c ) 130 , d ) 115 , e ) 120
Rationale: first 100 machines = 3 % commission = 0.03 * 100 * 10000 = 30000 commission from sale of next machines = 42000 - 30000 = 12000 so 30 more machines . . total = 130 machines imo c . . .
Answer: c
Python program:
a = 4 + 3 
b = 3 * 2
c = a * b
d = c * 100
e = 4 + 1 
f = e * 2
g = d * f
h = 100 * 100
i = 3 / 100
j = h * i
k = j * 100
l = g - k
m = 100 * 100
n = 4 / 100
o = m * n
p = l / o
q = 100 + p
Problem: in a class of students , 1 / 2 of the number of girls is equal to 1 / 6 of the total number of students . what is the ratio of boys to girls in the class ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 2 / 1 , d ) 3 / 2 , e ) 4 / 3
Rationale: "( 1 / 2 ) g = ( 1 / 6 ) ( b + g ) 6 g = 2 b + 2 g 4 g = 2 b b / g = 2 / 1 . the answer is c ."
Answer: c
Python program:
a = 1 / 2
b = 1 / 6
c = a - b
d = 1 / 6
e = c / d
Problem: if x is less than y by 45 % then y exceed x by :
Options: a ) 33.33 % , b ) 25 % , c ) 81.81 % , d ) 66.66 % , e ) none of these
Rationale: "using formula ( x / ( 100 - x ) * 100 ) where x is percentage decrease ( here it is 25 % ) = > 45 / ( 100 - 45 ) * 100 = 81.81 % answer : c"
Answer: c
Python program:
a = 100 - 45
b = 100 / a
c = b - 1
d = c * 100
Problem: if the least common multiple of two prime numbers x and y is 77 , where x > y , then the value of 2 x + y is
Options: a ) 11 , b ) 17 , c ) 21 , d ) 29 , e ) 33
Rationale: "lcm ( x , y ) = 77 and both x an y are prime . the only values of x and y can be 11 and 7 ( x = 11 and y = 7 ) 2 x + y = 2 * 11 + 7 = 29 correct option : d"
Answer: d
Python program:
a = 77 / 2
b = a * 2
c = b + 2