euclaise/mathqa_programs huggingface dataset:
Problem: the area of one square is x ^ 2 + 10 x + 25 and the area of another square is 4 x ^ 2 − 12 x + 9 . if the sum of the perimeters of both squares is 64 , what is the value of x ?
Options: a ) 0 , b ) 2 , c ) 4.8 , d ) 4.67 , e ) 10
Rationale: "spotting the pattern of equations both are in form of ( x + c ) ^ 2 so a 1 = ( x + 5 ) ^ 2 a 2 = ( 2 x - 3 ) ^ 2 l 1 = x + 5 l 2 = 2 x - 3 p 1 = 4 ( x + 5 ) p 2 = 4 ( 2 x - 3 ) p 1 + p 2 = 64 4 ( x + 5 ) + 4 ( 2 x - 3 ) = 64 . . . . . . . . . . . . > x = 4.8 answer : c"
Answer: c
Python program:
a = 10 / 2
b = 4 * a
c = b - 10
d = 64 - c
e = d / 10
Problem: how long does a train 100 m long traveling at 72 kmph takes to cross a tunnel of 1400 m in length ?
Options: a ) 70 sec , b ) 60 sec , c ) 82 sec , d ) 75 sec , e ) 62 sec
Rationale: d = 1400 + 100 = 1500 m s = 72 * 5 / 18 = 20 t = 1500 * 1 / 20 = 75 sec answer : d
Answer: d
Python program:
a = 100 + 1400 
b = 72 * const_0_2778
c = a / b
Problem: a person walks from one end to the other of a 60 - meter long moving walkway at a constant rate in 30 seconds , assisted by the walkway . when this person reaches the end , they reverse direction and continue walking with the same speed , but this time it takes 120 seconds because the person is traveling against the direction of the moving walkway . if the walkway were to stop moving , how many seconds would it take this person to walk from one end of the walkway to the other ?
Options: a ) 48 , b ) 60 , c ) 72 , d ) 84 , e ) 96
Rationale: "let v be the speed of the person and let x be the speed of the walkway . 30 ( v + x ) = 60 then 120 ( v + x ) = 240 120 ( v - x ) = 60 when we add the two equations : 240 v = 300 v = 5 / 4 time = 60 / ( 5 / 4 ) = 48 seconds the answer is a ."
Answer: a
Python program:
a = 60 / 30
b = 60 / 120
c = a + b 
d = c / 2
e = 60 / d
Problem: mike took a taxi to the airport and paid $ 2.50 to start plus $ 0.25 per mile . annie took a different route to the airport and paid $ 2.50 plus $ 5.00 in bridge toll fees plus $ 0.25 per mile . if each was charged exactly the same amount , and annie ' s ride was 22 miles , how many miles was mike ' s ride ?
Options: a ) 30 , b ) 36 , c ) 42 , d ) 48 , e ) 54
Rationale: "the cost of annie ' s ride was 2.5 + 5 + ( 0.25 * 22 ) = $ 13 let x be the distance of mike ' s ride . the cost of mike ' s ride is 2.5 + ( 0.25 * x ) = 13 0.25 * x = 10.5 x = 42 miles the answer is c ."
Answer: c
Python program:
a = 2 + 50 
b = 0 * 25
c = a + b 
d = c - 2
e = d / 0
Problem: what is the dividend from tony ' s stock , if he invested rs . 3200 at 85 to obtain an income of rs . 250 .
Options: a ) 4 , b ) 7.6 , c ) 6.6 , d ) 7.6 , e ) 9.6
Rationale: by investing rs . 3200 , income = rs . 250 by investing rs . 85 , income = 250 ã — 85 / 3200 = 6.6 ie , dividend = 6.6 % answer is c .
Answer: c
Python program:
a = 250 * 85
b = a / 3200
Problem: a is twice as good a workman as b and together they finish a piece of work in 14 days . the number of days taken by a alone to finish the work is :
Options: a ) 11 , b ) 21 , c ) 28 , d ) 42 , e ) none of these
Rationale: "( a ' s 1 day ' s work ) : ( b ' s 1 day ' s work ) = 2 : 1 ( a + b ) ' s 1 day ' s work = 1 / 14 divide 1 / 14 in the ratio 2 : 1 a ' s 1 day ' s work = ( 1 / 14 x 2 / 3 ) = 1 / 21 hence , a alone can finish the work in 21 days . correct option : b"
Answer: b
Python program:
a = 1 + 2 
b = a * 14
Problem: a test has 160 questions . each question has 5 options , but only 1 option is correct . if test - takers mark the correct option , they are awarded 1 point . however , if an answer is incorrectly marked , the test - taker loses 0.25 points . no points are awarded or deducted if a question is not attempted . a certain group of test - takers attempted different numbers of questions , but each test - taker still received the same net score of 40 . what is the maximum possible number of such test - takers ?
Options: a ) 23 , b ) 25 , c ) 27 , d ) 29 , e ) 31
Rationale: a correct answers get you 1 point , an incorrect answer gets you minus 1 / 4 point and a skipped question gets you 0 points . since there are 200 total questions , there are a variety of ways to get a total of 40 points . let c be the number of correct answers and let i be the number of incorrect answers . to get 40 points , a test taker must have at least 40 correct answers . then c = > 40 . for every correct question above 40 , the test taker has 4 incorrect answers . then , the i = 4 * ( c - 40 ) . also , i + c < = 160 . thus 5 c < = 320 and so c < = 64 . then 40 < = c < = 64 and c can have 25 possible values . the answer is b .
Answer: b
Python program:
a = 160 - 40
b = a / 5
c = b + 1 
d = c + 1
Problem: a glucose solution contains 15 grams of glucose per 100 cubic centimeters of solution . if 65 cubic centimeters of the solution were poured into an empty container , how many grams of glucose would be in the container ?
Options: a ) 7.50
b ) 8.75
c ) 7.75
d ) 9.50
e ) 9.75
Rationale: we are given that a glucose solution contains 15 grams of glucose per 100 cubic centimeters of solution . since we are dealing with a solution , we know that the grams of glucose is proportional to the number of cubic centimeters of solution . thus , to determine how many grams of glucose would be in the container when we have 45 cubic centimeters of solution , we can set up a proportion . we can say : “ 15 grams of glucose is to 100 cubic centimeters of solution as x grams of glucose is to 65 cubic centimeters of solution . ” let ’ s now set up the proportion and solve for x . 15 / 100 = x / 65 when we cross multiply we obtain : ( 15 ) ( 65 ) = 100 x 975 = 100 x 9.75 = x there are 9.75 grams of glucose in the solution in the container . the answer is e .
Answer: e
Python program:
a = 15 / 100
b = 65 * a
Problem: the price of a coat in a certain store is $ 500 . if the price of the coat is to be reduced by $ 150 , by what percent is the price to be reduced ?
Options: a ) 10 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 30 %
Rationale: "price of a coat in a certain store = $ 500 the price of the coat is to be reduced by $ 150 % change = ( final value - initial value ) * 100 / initial value % reduction = ( reduction in price ) * 100 / initial value i . e . % reduction = ( 150 ) * 100 / 500 = 30 % answer : option e"
Answer: e
Python program:
a = 150 / 500
b = a * 100
Problem: if a man lost 4 % by selling oranges at the rate of 60 a rupee at how many a rupee must he sell them to gain 44 % ?
Options: a ) 11 , b ) 28 , c ) 39 , d ) 40 , e ) 43
Rationale: "96 % - - - - 60 144 % - - - - ? 96 / 144 * 60 = 40 answer : d"
Answer: d
Python program:
a = 100 - 4
b = a * 60
c = 100 + 44 
d = b / c
Problem: a man can row 9 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and back . what is the total distance traveled by the man ?
Options: a ) 6.24 km , b ) 6 km , c ) 8.84 km , d ) 5.66 km , e ) 10 km
Rationale: "m = 9 s = 1.2 ds = 10.2 us = 7.8 x / 10.2 + x / 7.8 = 1 x = 4.42 d = 4.42 * 2 = 8.84 answer : c"
Answer: c
Python program:
a = 9 + 1 
b = 9 - 1
c = a * b
d = 9 + 1 
e = 9 - 1
f = d + e 
g = c / f
h = g * 2
Problem: a train speeds past a pole in 15 sec and a platform 100 m long in 25 sec , its length is ?
Options: a ) 158 m , b ) 150 m , c ) 110 m , d ) 130 m , e ) 157 m
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 + 100 ) / 25 = x / 15 = > x = 150 m . answer : b"
Answer: b
Python program:
a = 2 - 1
b = 100 * a
Problem: two trains 300 m and 450 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
Options: a ) 10.6 , b ) 27 , c ) 10.4 , d ) 10.8 , e ) 10.1
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 300 + 450 = 750 m . required time = 700 * 9 / 250 = 27 sec . answer : b"
Answer: b
Python program:
a = 300 + 450 
b = 60 + 40 
c = b * const_0_2778
d = a / c
Problem: a shopkeeper buys mangoes at the rate of 6 a rupee and sells them at 3 a rupee . find his net profit or loss percent ?
Options: a ) 33 4 / 3 % , b ) 33 1 / 7 % , c ) 50 % , d ) 32 1 / 3 % , e ) 60 %
Rationale: the total number of mangoes bought by the shopkeeper be 18 . if he buys 6 a rupee , his cp = 3 he selling at 3 a rupee , his sp = 6 profit = sp - cp = 6 - 3 = 3 profit percent = 3 / 6 * 100 = 50 % answer : c
Answer: c
Python program:
a = 3 * 100
b = a / 6
Problem: what percent of 180 is 45 ?
Options: a ) 0.25 % , b ) 4 % , c ) 25 % , d ) 40 % , e ) 250 %
Rationale: "here ' s an algebraic approach . let p = the required percent . this means p / 100 = the percent as a fraction . so , ` ` what percent of 180 is 45 ? ' ' becomes ` ` ( p / 100 ) of 180 = 45 or : ( p / 100 ) ( 180 ) = 45 divide both sides by 180 to get : p / 100 = 45 / 180 simplify right side : p / 100 = 1 / 4 multiply both sides by 100 to get : p = 25 answer : c"
Answer: c
Python program:
a = 180 / 45
b = a * 100
Problem: if 20 men can build a wall 112 metres long in 6 days , what length of a similar wall can be built by 15 men in 3 days ?
Options: a ) 65 mtr . , b ) 52 mtr , c ) 70 mtr . , d ) 78 mtr . , e ) 42 mtr .
Rationale: "20 men is 6 days can build 112 metres 15 men in 3 days can build = 112 * ( 15 / 20 ) x ( 3 / 6 ) = 42 meters answer : e ."
Answer: e
Python program:
a = 15 * 3
b = 20 * 6
c = a / b
d = 112 * c
Problem: b completes a work in 3 days . a alone can do it in 10 days . if both work together , the work can be completed in how many days ?
Options: a ) 2.31 days , b ) 4.31 days , c ) 5.31 days , d ) 6.31 days , e ) 7.31 days
Rationale: 1 / 3 + 1 / 10 = 13 / 30 30 / 13 = 2.31 days answer : a
Answer: a
Python program:
a = 10 * 3
b = 3 + 10 
c = a / b
Problem: a and b started a business in partnership investing rs . 20,000 and rs . 15,000 respectively . after 6 months , c joined them with rs . 20,000 . whatwill be b ' s share in total profit of rs . 20,000 earned at the end of 2 years from the startingof the business ?
Options: a ) s . 5,000 , b ) s . 5,500 , c ) s . 5,700 , d ) s . 6,000 , e ) s . 7,500
Rationale: a : b : c = ( 20,000 x 24 ) : ( 15,000 x 24 ) : ( 20,000 x 18 ) = 4 : 3 : 3 . b ' s share = rs . 20000 x 3 / 10 = rs . 6,000 . d
Answer: d
Python program:
a = 4 + 1 
b = a * 4
c = 3 * 4
d = 2 * c
e = b * d
Problem: nick took a bus from home to market , that travels at 80 kmph . while walking back at 8 kmph , halfway through , he suddenly realized he was getting late and he cycled back the remaining distance in 60 kmph . find the average speed .
Options: a ) 49.5 kmph , b ) 49.0 kmph , c ) 48.5 kmph , d ) 48.0 kmph , e ) none of these
Rationale: let the distance be 2 x ( one way ) time taken by bus = 2 x / 80 , by walking = x / 8 , by cycling = x / 60 hours : . average speed = total distance / total time = 8 x / x / 40 + x / 8 + x / 60 = 8 * 60 / 1.5 + 7.5 + 1 = 12.0 answer : d
Answer: d
Python program:
a = 1/(60)
b = a / 2
c = 1/(80)
d = b + c 
e = 1/(d)
Problem: a boat having a length 6 m and breadth 3 m is floating on a lake . the boat sinks by 1 cm when a man gets on it . the mass of the man is :
Options: a ) 100 kg , b ) 120 kg , c ) 89 kg , d ) 180 kg , e ) 110 kg
Rationale: "volume of water displaced = ( 6 x 3 x 0.01 ) m 3 = 0.18 m 3 . mass of man = volume of water displaced x density of water = ( 0.18 x 1000 ) kg = 180 kg . answer : d"
Answer: d
Python program:
a = 6 * 3
b = 1 / 100
c = a * b
d = c * 1000
Problem: a computer is programmed to multiply consecutive even integers 2 * 4 * 6 * 8 * … * n until the product is divisible by 1551 , what is the value of n ?
Options: a ) 22 , b ) 38 , c ) 62 , d ) 94 , e ) 672
Rationale: "factorise 1551 . . 3 * 11 * 47 . . so n has to be a multiple of largest prime number , 61 . . so n = 2 * 47 = 94 . . ans : d"
Answer: d
Python program:
a = 10 + 1 
b = 1551 / a
c = b / 3
d = 2 * c
Problem: 0.999999 + 0.111111 = ?
Options: a ) 1 , b ) 1.0001 , c ) 1.0021 , d ) 1.111 , e ) 1.11111
Rationale: "0.999999 + 0.111111 = 0.999999 + 0.11111 + 0.000001 = ( 0.999999 + 0.000001 ) + 0.11111 = 1 + 0.11111 = 1.11111 e"
Answer: e
Python program:
a = 0 / 999999
b = a * 100
Problem: if the cost price of 10 articles is same as the selling price of 25 articles . find the gain or loss percentage ?
Options: a ) 30 % gain , b ) 30 % loss , c ) 40 % gain , d ) 60 % loss , e ) 50 % loss
Rationale: "explanation : 10 cp = 25 sp cost price cp = 25 selling price sp = 10 formula = ( sp - cp ) / cp * 100 = ( 10 - 25 ) / 25 * 100 = 60 % loss answer : option d"
Answer: d
Python program:
a = 100 * 25
b = a / 10
c = 100 - b
d = 100 * 25
e = d / 10
f = c / e
g = 100 * f
Problem: julie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest . after two years she earned $ 112 and $ 120 from the simple interest account and the compound interest account respectively . if the interest rates for both accounts were the same , what was the amount of julie ' s initial savings ?
Options: a ) 600 , b ) 784 , c ) 1080 , d ) 1200 , e ) 1440
Rationale: $ 112 for 2 years = $ 56 per year . extra $ 8 yearned with the compound interest is the percent yearned on percent . so , $ 8 is yearned on $ 56 , which means that the interest = 7 % . this on the other hand means that half of the savings = 56 * 7 = $ 392 . twice of that = $ 784 . answer : b .
Answer: b
Python program:
a = 120 - 112
b = 2 * a
c = b / 112
d = 112 / c
Problem: if 70 % of ( x - y ) = 30 % of ( x + y ) then what percent of x is y ?
Options: a ) 2.5 % , b ) 40 % , c ) 5 % , d ) 15 % , e ) 25 %
Rationale: "70 % of ( x - y ) = 30 % of ( x + y ) ( 70 / 100 ) ( x - y ) = ( 30 / 100 ) ( x + y ) 7 ( x - y ) = 3 ( x + y ) 4 x = 10 y x = 5 / 2 y therefore required percentage = ( ( y / x ) x 100 ) % = ( ( y / ( 5 / 2 ) y ) x 100 ) = 40 % answer is b ."
Answer: b
Python program:
a = 70 - 30
b = 70 + 30 
c = a / b
d = c * 100
Problem: a man spends 1 / 3 rd of his salary on food . he spends 1 / 4 th on rent and 1 / 5 th on cloths . if he is left with 1760 , then who much salary does he earn .
Options: a ) 8120 , b ) 8123 , c ) 8222 , d ) 8322 , e ) 8422
Rationale: "let salary be x total spent = ( x / 3 + x / 4 + x / 5 ) = ( 47 / 60 ) * x left = ( x - 47 x / 60 ) = ( 13 / 60 ) * x given , ( 13 / 60 ) * x = 1760 x = ( 1760 * 60 ) / 13 = 8123.077 = 8123 ( approax ) answer : b"
Answer: b
Python program:
a = 1 / 3
b = 1 / 4
c = a + b 
d = 1 / 5
e = c + d 
f = 1 - e
g = 1760 / f
Problem: what is the least value of x , so that 2 x 5476 is divisible by 9
Options: a ) 7 , b ) 8 , c ) 9 , d ) 3 , e ) 2
Rationale: "explanation : the sum of the digits of the number is divisible by 9 . then the number is divisible by 9 . 2 + x + 5 + 4 + 7 + 6 = 24 + x least value of x may be ' 3 ' , so that the total 24 + 3 = 27 is divisible by 9 . answer : option d"
Answer: d
Python program:
a = math.lcm(2, 5476)
b = a / 5476
c = b / 4
d = c / 4
Problem: the length of the ribbon was originally 55 cm . it was reduced in the ratio 11 : 7 . what is its length now ?
Options: a ) 6 cm , b ) 12 cm , c ) 35 cm , d ) 44 cm , e ) none of these
Rationale: explanation : length of ribbon originally = 55 cm let the original length be 11 x and reduced length be 7 x . but 11 x = 55 cm x = 55 / 11 cm = 5 cm therefore , reduced length = 7 x cm = 7 5 cm = 35 cm answer : c
Answer: c
Python program:
a = 7 / 11
b = 55 * a
Problem: at 12.00 hours , j starts to walk from his house at 6 kmph . at 13.30 , p follows him from j ' s house on his bicycle at 8 kmph . when will j be 3 km behind p ?
Options: a ) 19.39 , b ) 19.3 , c ) 19.32 , d ) 19.33 , e ) 19.36
Rationale: by the time p starts j is 1.5 hr x 6 = 9 km away from his house . j is 3 km behind when p is 3 km ahead of him . ie . , p has to cover 12 km . so he takes 12 / ( 8 - 6 ) = 6 hrs after 13.30 . so the required time is 19.30 hrs answer : b
Answer: b
Python program:
a = 3 / 2
b = 6 * a
c = b + 3 
d = 8 - 6
e = c / d
f = 13 + 3
Problem: how many seconds will a 800 m long train take to cross a man walking with a speed of 5 km / hr in the direction of the moving train if the speed of the train is 65 km / hr ?
Options: a ) 30 , b ) 50 , c ) 66 , d ) 44 , e ) 48
Rationale: "speed of train relative to man = 65 - 5 = 60 km / hr . = 60 * 5 / 18 = 50 / 3 m / sec . time taken to pass the man = 800 * 3 / 50 = 48 sec . answer : e"
Answer: e
Python program:
a = 65 - 5
b = a * const_0_2778
c = 800 / b
Problem: the sum of five consecutive even numbers is 500 . find the middle number of the five ?
Options: a ) 140 , b ) 66 , c ) 100 , d ) 99 , e ) 120
Rationale: "middle number = 500 / 5 = 100 ans c"
Answer: c
Python program:
a = 500 - 10
b = a - 2
c = b / 4
d = c + 2 
e = d + 2 
f = e ** 2
g = 500 - 10
h = g - 2
i = h / 4
j = i + 2 
k = j + 2 
l = k + 2 
m = l ** 2
n = f + m 
o = 500 - 10
p = o - 2
q = p / 4
r = q ** 2
s = 500 - 10
t = s - 2
u = t / 4
v = u + 2 
w = v ** 2
x = r + w 
y = n + x
Problem: a and b together can do a piece of work in 6 days and a alone can do it in 14 days . in how many days can b alone can do it ?
Options: a ) 12 days , b ) 15 days , c ) 21 / 2 days , d ) 21 days , e ) 22 days
Rationale: "explanation : a and b can do work 1 / 6 in 1 day a alone can do 1 / 14 work in 1 day b alone can do ( 1 / 6 - 1 / 14 ) = 2 / 21 work in 1 day = > complete work can be done in 21 / 2 days by b answer : option c"
Answer: c
Python program:
a = 1/(6)
b = 1/(14)
c = a - b
d = 1/(c)
Problem: triathlete dan runs along a 2 - mile stretch of river and then swims back along the same route . if dan runs at a rate of 8 miles per hour and swims at a rate of 6 miles per hour , what is his average rate for the entire trip in miles per minute ?
Options: a ) 1 / 9 , b ) 2 / 15 , c ) 3 / 15 , d ) 1 / 4 , e ) 3 / 8
Rationale: "dan travels 4 miles round trip . running part : ( 2 / 8 = 1 / 4 * 60 = 15 minutes ) swimming part : ( 2 / 6 = 1 / 3 * 60 = 20 minutes ) 4 miles in ( 15 + 20 ) minutes 4 / 35 = 1 / 9 mile per minute answer : 1 / 9 mile per minute"
Answer: a
Python program:
a = 2 + 2 
b = 2 / 6
c = b * const_60
d = 2 / 8
e = d * const_60
f = c + e 
g = a / f
Problem: a man engaged a servant on the condition that he would pay him rs . 600 and a uniform after one year service . he served only for 9 months and received uniform and rs . 400 , find the price of the uniform ?
Options: a ) s . 80 , b ) s . 85 , c ) s . 90 , d ) s . 100 , e ) s . 200
Rationale: 9 / 12 = 3 / 4 * 600 = 450 400 - - - - - - - - - - - - - 50 1 / 4 - - - - - - - - 50 1 - - - - - - - - - ? = > rs . 200 answer : e
Answer: e
Python program:
a = 9 * 600
b = 3 * 4
c = b * 400
d = a - c
e = 3 * 4
f = e * 1
g = d / f
h = g * 4
Problem: find the value of y from ( 12 ) ^ 1 x 6 ^ 4 ÷ 432 = y ?
Options: a ) 2134 , b ) 2234 , c ) 2540 , d ) 2560 , e ) 36
Rationale: "36 e"
Answer: e
Python program:
a = 12 ** 1
b = 6 ** 4
c = a * b
d = c / 432
Problem: find the least number which when divided by 20 , 25,35 and 40 leaves remainders 14 , 19,29 and 34 respectively .
Options: a ) 1394 , b ) 1294 , c ) 1194 , d ) 1094 , e ) none of them
Rationale: "here , ( 20 - 14 ) = 6 , ( 25 – 19 ) = 6 , ( 35 - 29 ) = 6 and ( 40 - 34 ) = 6 . therefore , required number = ( l . c . m . of 20,25 , 35,40 ) – 6 = 1394 . answer is a ."
Answer: a
Python program:
a = math.lcm(20, 25)
b = 40 + a
Problem: if 1 / 8 of a pencil is black , 1 / 2 of the remaining is white and the remaining 3 1 / 2 cm is blue , find the total length of the pencil .
Options: a ) 12 , b ) 9 , c ) 8 , d ) 6 , e ) 5
Rationale: let the total length of the pencil be x cm . black part is 1 / 8 of the length so x / 8 . so the remaining part is x - x / 8 = = > 8 x / 8 - x / 8 = = > 7 x / 8 cm . white part = 1 / 2 * 7 x / 8 = 7 x / 16 cm . so the remaining part is 7 x / 8 - 7 x / 16 = = > 14 x / 16 - 7 x / 16 = 7 x / 16 which is equal to 3 1 / 2 . 7 x / 16 = 7 / 2 cross multiply and we get x = 16 / 2 = 8 cm . so the total length of the pencil is 8 cm . the correct answer is option c ) 8 .
Answer: c
Python program:
a = 8 * 1
Problem: marcella has 25 pairs of shoes . if she loses 9 individual shoes , what is the greatest number of matching pairs she could have left ?
Options: a ) 21 , b ) 20 , c ) 19 , d ) 16 , e ) 15
Rationale: "greatest number of paired shoes means greatest number of lost pairs 9 shoes have 4 pairs and 1 extra shoes of a pair . so a otal of 5 pairs she loses leftover pair = 20 answer : b"
Answer: b
Python program:
a = 9 / 2
b = math.floor(a)
c = b + 1 
d = 25 - c
Problem: the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 180 resolutions ?
Options: a ) 724 m , b ) 704 m , c ) 287 m , d ) 278 m , e ) 253.4 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 180 resolutions . = 180 * 2 * 22 / 7 * 22.4 = 25344 cm = 253.4 m answer : e"
Answer: e
Python program:
a = 3 + 4 
b = a * 3
c = b + 1 
d = 3 + 4 
e = c / d
f = e * 22
g = f * 2
h = g * 180
i = h / 100
Problem: if a motorist had driven 1 hour longer on a certain day and at an average rate of 5 miles per hour faster , he would have covered 80 more miles than he actually did . how many more miles would he have covered than he actually did if he had driven 2 hours longer and at an average rate of 10 miles per hour faster on that day ?
Options: a ) 100 , b ) 120 , c ) 140 , d ) 150 , e ) 160
Rationale: "case 1 : let rate = r , time = t , and distance = d so d = rt case 2 : ( d + 80 ) = ( r + 5 ) ( t + 1 ) case 3 : ( d + x ) = ( r + 10 ) ( t + 2 ) x = 160 ans e"
Answer: e
Python program:
a = 80 - 5
b = a * 2
c = 2 * 10
d = b + c
Problem: a reduction of 20 % in the price of oil enables a house wife to obtain 10 kgs more for rs . 1500 , what is the reduced price for kg ?
Options: a ) rs . 20 , b ) rs . 25 , c ) rs . 30 , d ) rs . 35 , e ) rs . 40
Rationale: "explanation : 1500 * ( 20 / 100 ) = 300 - - - - 10 ? - - - - 1 = > rs . 30 answer : c"
Answer: c
Python program:
a = 1500 * 20
b = a / 100
c = b / 10
Problem: a train passes a station platform in 36 sec and a man standing on the platform in 20 sec . if the speed of the train is 99 km / hr . what is the length of the platform ?
Options: a ) 440 , b ) 488 , c ) 477 , d ) 426 , e ) 422
Rationale: "speed = 99 * 5 / 18 = 27.5 m / sec . length of the train = 27.5 * 20 = 550 m . let the length of the platform be x m . then , ( x + 550 ) / 36 = 27.5 = > x = 440 m . answer : a"
Answer: a
Python program:
a = 99 * const_0_2778
b = 20 * a
Problem: 100 white and black tiles will be used to form a 20 x 20 square pattern . if there must be at least one black tile in every row and at least one white tile in every column , what is the maximum difference between the number of black and white tiles that can be used ?
Options: a ) 75 , b ) 70 , c ) 85 , d ) 90 , e ) 95
Rationale: "answer = b please refer diagram below 90 - 20 = 70"
Answer: b
Python program:
a = 100 - 20
Problem: two numbers a and b are such that the sum of 6 % of a and 4 % of b is two - third of the sum of 6 % of a and 8 % of b . find the ratio of a : b .
Options: a ) 2 : 3 , b ) 1 : 2 , c ) 4 : 3 , d ) 1 : 1 , e ) 3 : 2
Rationale: "explanation : 6 % of a + 4 % of b = 2 / 3 ( 6 % of a + 8 % of b ) 6 a / 100 + 4 b / 100 = 2 / 3 ( 6 a / 100 + 8 b / 100 ) ⇒ 6 a + 4 b = 2 / 3 ( 6 a + 8 b ) ⇒ 18 a + 12 b = 12 a + 16 b ⇒ 6 a = 4 b ⇒ ab = 4 / 6 = 2 / 3 ⇒ a : b = 2 : 3 answer : option a"
Answer: a
Python program:
a = 8 / 100
b = a * 4
c = b / 3
d = 2 / 0
e = c - d
f = 6 / 100
g = 6 / 100
h = g * 2
i = h / 3
j = f - i
k = e / j
Problem: if you add all the numbers on your mobile phone except 9 , what is the answer ?
Options: a ) 45 , b ) 28 , c ) 65 , d ) 36 , e ) 42
Rationale: "we have to add 0 to 8 to find the answer . therefore 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36 answer is d"
Answer: d
Python program:
a = 10 - 1
b = 1 + a 
c = b / 2
d = 10 - 1
e = c * d