euclaise/mathqa_programs huggingface dataset:
Problem: a meal cost $ 37.50 and there was no tax . if the tip was more than 10 pc but less than 15 pc of the price , then the total amount paid should be :
Options: a ) 41 - 43 , b ) 39 - 41 , c ) 38 - 40 , d ) 37 - 39 , e ) 36 - 37
Rationale: "10 % ( 37.5 ) = 3.75 15 % ( 37.5 ) = 5.625 total amount could have been 37.5 + 3.75 and 37.5 + 5.625 = > could have been between 41.25 and 43.125 = > approximately between 41 and 43 answer is a ."
Answer: a
Python program:
a = 15 / 100
b = 37 * 50
c = b + 37
Problem: find the slope of the line perpendicular to the line y = ( 1 / 4 ) x - 7
Options: a ) 1 , b ) 2 , c ) - 4 , d ) 4 , e ) 5
Rationale: "two lines are perpendicular if the product of their slopes is equal to - 1 . the slope of the given line is equal to 1 / 4 . if m is the slope of the line perpendicular to the given line , then m × ( 1 / 4 ) = - 1 solve for m m = - 4 correct answer c ) - 4"
Answer: c
Python program:
a = 1 / 4
Problem: a person can row at 9 kmph and still water . he takes 7 1 / 2 hours to row from a to b and back . what is the distance between a and b if the speed of the stream is 1 kmph ?
Options: a ) 60 km , b ) 87 km , c ) 33 km , d ) 67 km , e ) 20 km
Rationale: "let the distance between a and b be x km . total time = x / ( 9 + 1 ) + x / ( 9 - 1 ) = 7.5 = > x / 10 + x / 8 = 15 / 2 = > ( 4 x + 5 x ) / 40 = 15 / 2 = > x = 33 km . answer : c"
Answer: c
Python program:
a = 9 - 1
b = 9 + 1 
c = a * b
d = c * 7
e = 9 + 1 
f = 9 - 1
g = e + f 
h = d / g
Problem: walking with 4 / 5 of my usual speed , i miss the bus by 4 minutes . what is my usual time ?
Options: a ) 16 min , b ) 26 min , c ) 34 min , d ) 20 min , e ) 12 min
Rationale: "speed ratio = 1 : 4 / 5 = 5 : 4 time ratio = 4 : 5 1 - - - - - - - - 4 4 - - - - - - - - - ? è 16 answer : a"
Answer: a
Python program:
a = 5 / 4
b = 4 / a
c = b * 5
Problem: find the principal which yields a simple interest of rs . 20 and compound interest of rs . 22 in two years , at the same percent rate per annum ?
Options: a ) s . 520 , b ) s . 480 , c ) s . 420 , d ) s . 100 , e ) s . 200
Rationale: explanation : si in 2 years = rs . 20 , si in 1 year = rs . 10 ci in 2 years = rs . 22 % rate per annum = [ ( ci – si ) / ( si in 1 year ) ] * 100 = [ ( 22 – 20 ) / 20 ] * 100 = 10 % p . a . let the principal be rs . x time = t = 2 years % rate = 10 % p . a . si = ( prt / 100 ) 20 = ( x * 10 * 2 ) / 100 x = rs . 100 answer : d
Answer: d
Python program:
a = 22 - 20
b = a * 100
c = b / 2
Problem: if x / ( 11 p ) is an odd prime number , where x is a positive integer and p is a prime number , what is the least value of x ?
Options: a ) 22 , b ) 33 , c ) 44 , d ) 66 , e ) 99
Rationale: x / ( 11 p ) = odd prime number x = odd prime number * 11 p least value of x = lowest odd prime number * 11 * lowest value of p = 3 * 11 * 2 = 66 answer d
Answer: d
Python program:
a = 3 * 11
b = a * 2
Problem: 9 persons went to a hotel for taking their meals . 8 of them spent rs . 12 each on their meals and the ninth spent rs . 8 more than the average expenditure of all the 9 . what was the total money spent by them .
Options: a ) rs . 115 , b ) rs . 116 , c ) rs . 117 , d ) rs . 118 , e ) none
Rationale: solution : let the average expenditure of all the nine be x . then , 12 × 8 + ( x + 8 ) = 9 x . therefore , x = 13 . total money spent , = 9 x = rs . ( 9 × 13 ) = rs . 117 answer : option c
Answer: c
Python program:
a = 12 + 9 
b = 8 * 12
c = a + b
Problem: a cube of edge 6 cm is cut into cubes each of edge 1 cm . the ratio of the total surface area of one of the small cubes to that of the large cube is equal to :
Options: a ) 1 : 25 , b ) 1 : 36 , c ) 1 : 52 , d ) 1 : 522 , e ) none
Rationale: "sol . required ratio = 6 * 1 * 1 / 6 * 6 * 6 = 1 / 36 = 1 : 36 . answer b"
Answer: b
Python program:
a = 4 / 100
Problem: the difference between a two - digit number and the number obtained by interchanging the positions of its digits is 36 . what is the difference between the two digits of that number ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: "sol . let the ten ’ s digit be x and unit ’ s digit be y , then , ( 10 x + y ) - ( 10 y + x ) = 36 ⇔ 9 ( x - y ) = 36 ⇔ x - y = 4 answer a"
Answer: a
Python program:
a = 10 - 1
b = 36 / a
Problem: a snail , climbing a 66 feet high wall , climbs up 4 feet on the first day but slides down 2 feet on the second . it climbs 4 feet on the third day and slides down again 2 feet on the fourth day . if this pattern continues , how many days will it take the snail to reach the top of the wall ?
Options: a ) 42 , b ) 63 , c ) 77 , d ) 80 , e ) 91
Rationale: "total transaction in two days = 4 - 2 = 2 feet in 62 days it will climb 62 feet on the 63 rd day , the snail will climb 4 feet , thus reaching the top therefore , total no of days required = 63 b"
Answer: b
Python program:
a = 66 - 4
Problem: if 6 pr = 360 and if 6 cr = 15 , find r ?
Options: a ) 5 , b ) 6 , c ) 4 , d ) 3 , e ) 2
Rationale: solution : npr = ncr � r ! 6 pr = 15 * r ! 360 = 15 * r ! r ! = 360 / 15 = 24 r ! = 4 * 3 * 2 * 1 = > r ! = 4 ! therefore , r = 4 . answer : option c
Answer: c
Python program:
a = 360 / 15
b = a / 6
Problem: by selling 90 pens , a trader gains the cost of 15 pens . find his gain percentage ?
Options: a ) 16.66 % , b ) 17.66 % , c ) 18.66 % , d ) 19.66 % , e ) 20.66 %
Rationale: "let the cp of each pen be rs . 1 . cp of 90 pens = rs . 90 profit = cost of 15 pens = rs . 15 profit % = 15 / 90 * 100 = 16.66 % answer : a"
Answer: a
Python program:
a = 15 / 90
b = a * 100
Problem: how many paying stones , each measuring 2 m * 2 m are required to pave a rectangular court yard 30 m long and 18 m board ?
Options: a ) 99 , b ) 18 , c ) 135 , d ) 17 , e ) 12
Rationale: "30 * 18 = 2 * 2 * x = > x = 135 answer : c"
Answer: c
Python program:
a = rectangle_area / (
Problem: a jogger running at 9 km / hr along side a railway track is 250 m ahead of the engine of a 100 m long train running at 99 km / hr in the same direction . in how much time will the train pass the jogger ?
Options: a ) 14 sec , b ) 67 sec , c ) 98 sec , d ) 36 sec , e ) 23 sec
Rationale: "speed of train relative to jogger = 99 - 9 = 90 km / hr . = 90 * 5 / 18 = 25 m / sec . distance to be covered = 250 + 100 = 350 m . time taken = 350 / 25 = 14 sec . answer : a"
Answer: a
Python program:
a = 250 + 100 
b = 99 - 9
c = 10 / 2
d = 99 - 9
e = d / 2
f = c / e
g = b * f
h = a / g
Problem: a train 200 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 20 seconds . the speed of the train is ?
Options: a ) 36 , b ) 50 , c ) 88 , d ) 66 , e ) 23
Rationale: "speed of the train relative to man = ( 200 / 20 ) m / sec = 5 m / sec . [ 5 * ( 18 / 5 ) ] km / hr = 18 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 18 = = > x = 23 km / hr . answer : e"
Answer: e
Python program:
a = 5 * const_0_2778
b = a * 5
c = 200 - b
d = c / 5
e = d / const_0_2778
Problem: a pupil ' s marks were wrongly entered as 73 instead of 65 . due to the average marks for the class got increased by half . the number of pupils in the class is ?
Options: a ) 18 , b ) 82 , c ) 16 , d ) 27 , e ) 29
Rationale: "let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 x / 2 = ( 73 - 65 ) = > x / 2 = 8 = > x = 16 . answer : c"
Answer: c
Python program:
a = 73 - 65
b = a * 2
Problem: the average salary of 16 people in the shipping department at a certain firm is $ 20,000 . the salary of 5 of the employees is $ 25,000 each and the salary of 4 of the employees is $ 16,000 each . what is the average salary of the remaining employees ?
Options: a ) $ 18,714 , b ) $ 18,500 , c ) $ 18,000 , d ) $ 15,850 , e ) $ 12,300
Rationale: total salary . . . 16 * 20 k = 320 k 5 emp @ 25 k = 125 k 4 emp @ 16 k = 64 k remaing 7 emp sal = 320 k - 125 k - 64 k = 131 k average = 131 k / 7 = 18714 ans : a
Answer: a
Python program:
a = 5 * 4
b = 4 * 4
c = a * b
d = 5 * 5
e = d * 5
f = c - e
g = 4 * 16
h = f - g
i = 2 + 5 
j = h / i
Problem: a shopkeeper sold an article at $ 100 with 30 % profit . then find its cost price ?
Options: a ) $ 120 , b ) $ 100 , c ) $ 91 , d ) $ 77 , e ) $ 69
Rationale: "cost price = selling price * 100 / ( 100 + profit ) c . p . = 100 * 100 / 130 = $ 77 ( approximately ) answer is d"
Answer: d
Python program:
a = 100 + 30 
b = 100 / a
c = 100 * b
Problem: in an election between two candidates , the first candidate got 80 % of the votes and the second candidate got 480 votes . what was the total number of votes ?
Options: a ) 1600 , b ) 1800 , c ) 2000 , d ) 2200 , e ) 2400
Rationale: "let v be the total number of votes . 0.2 v = 480 v = 2400 the answer is e ."
Answer: e
Python program:
a = 480 * 100
b = 100 - 80
c = a / b
Problem: peter invested a certain sum of money in a simple interest bond whose value grew to $ 400 at the end of 4 years and to $ 500 at the end of another 2 years . what was the rate of interest in which he invested his sum ?
Options: a ) 12 % , b ) 12.5 % , c ) 67 % , d ) 25 % , e ) 33 %
Rationale: "lets assume the principal amount ( initial amount invested ) to be p rate of interest to berand time as t . we need to find r now after a time of 4 years the principal p amounts to $ 400 and after a time of 6 years ( question says after another 6 years so 4 + 2 ) p becomes $ 500 . formulating the above data amount ( a 1 ) at end of 4 years a 1 = p ( 1 + 4 r / 100 ) = 400 amount ( a 2 ) at end of 6 years a 2 = p ( 1 + 2 r / 100 ) = 500 dividing a 2 by a 1 we get ( 1 + 4 r / 100 ) / ( 1 + 2 r / 100 ) = 5 / 4 after cross multiplication we are left with 4 r = 100 which gives r = 25 % option : d"
Answer: d
Python program:
a = 500 - 400
b = a / 2
c = 500 - 400
d = c / 2
e = d * 4
f = 400 - e
g = b / f
h = g * 100
Problem: twenty - one dots are evenly spaced on the circumference of a circle . how many combinations of three dots can we make from these 21 dots that do not form an equilateral triangle ?
Options: a ) 1299
b ) 1305
c ) 1311
d ) 1317
e ) 1323
Rationale: the total number of ways we can choose three dots is 21 c 3 = 1330 . we can form seven equilateral triangles from these twenty - one dots . there are 1330 - 7 = 1323 combinations which do not form an equilateral triangle . the answer is e .
Answer: e
Python program:
a = 21 - 1
b = 21 * a
c = 21 - 1
d = c - 1
e = b * d
f = e / 3
g = f / 2
h = 3 + 4 
i = g - h
Problem: the ratio of boarders to day scholars at a school is 7 to 16 . however , after a few new students join the initial 560 boarders , the ratio changed to 1 to 2 , respectively . if no boarders became day scholars and vice versa , and no students left the school , how many boarders joined the school ?
Options: a ) 48 , b ) 64 , c ) 70 , d ) 80 , e ) 84
Rationale: let day scholars be ds and boarders be b given b / ds = 7 / 16 - - - > eq 1 initially b = 560 and x be new boarders joined then from eq 1 , we get ds = 16 / 7 * 560 = 1280 now , new ration is 560 + x / ds = 1 / 2 560 + x / 1280 = 1 / 2 = > 1120 + 2 x = 1280 = > 2 x = 160 = > x = 80 ans option d
Answer: d
Python program:
a = 560 / 7
b = a * 16
c = 1 + 2 
d = 2 / c
e = b / d
f = 560 / 7
g = f * 16
h = 560 + g 
i = e - h
Problem: when positive integer n is divided by positive integer p , the quotient is 18 , with a remainder of 6 . when n is divided by ( p + 2 ) , the quotient is 15 and the remainder is 3 . what is the value of n ?
Options: a ) 151 , b ) 331 , c ) 168 , d ) 691 , e ) 871
Rationale: n / p = 18 6 / p = 18 p + 6 n / ( p + 2 ) = 15 2 / ( p + 2 ) = 15 p + 30 + 3 solving these two equations we get p = 9 n = 168 answer is c .
Answer: c
Python program:
a = 15 * 2
b = a + 3 
c = b - 6
d = 18 - 15
e = c / d
f = 18 * e
Problem: in an examination , 25 % of total students failed in hindi , 35 % failed in english and 40 % in both . the percentage of these who passed in both the subjects is :
Options: a ) 10 % , b ) 20 % , c ) 60 % , d ) 80 % , e ) 50 %
Rationale: "pass percentage = 100 - ( 25 + 35 - 40 ) = 100 - 20 = 80 answer : d"
Answer: d
Python program:
a = 25 + 35 
b = a - 40
c = 100 - b
Problem: population of a city in 20004 was 1400000 . if in 2005 there isan increment of 15 % , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45 % , then find the population of city at the end of the year 2007
Options: a ) 354354 , b ) 545454 , c ) 465785 , d ) 456573 , e ) 2818075 / 2
Rationale: "required population = p ( 1 + r 1 / 100 ) ( 1 - r 2 / 100 ) ( 1 + r 3 / 100 ) = p ( 1 + 15 / 100 ) ( 1 - 35 / 100 ) ( 1 + 45 / 100 ) = 2818075 / 2 e"
Answer: e
Python program:
a = 15 / 100
b = 1 + a 
c = 35 / 100
d = 1 - c
e = b * d
f = 35 / 100
g = 1 + f 
h = e * g
i = 1400000 * h
Problem: the slant height of a cone is 15 cm and radius of the base is 3 cm , find the curved surface of the cone ?
Options: a ) 26 , b ) 134 , c ) 141 , d ) 190 , e ) 28
Rationale: "π * 15 * 3 = 141 answer : c"
Answer: c
Python program:
a = math.pi * 3
b = a * 15
Problem: a train 360 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 340 m long ?
Options: a ) 56 sec , b ) 42 sec , c ) 45 sec , d ) 48 sec , e ) 50 sec
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 360 + 340 = 700 m required time = 700 * 2 / 25 = 56 sec answer : a"
Answer: a
Python program:
a = 45 - 340
b = a * const_0_2778
c = 360 / b
Problem: if ( 55 ^ 55 + 55 ) is divided by 56 , then the remainder is : ?
Options: a ) 54 , b ) 55 , c ) 53 , d ) 56 , e ) 57
Rationale: solution : ( x ^ n + 1 ) is divisible by ( x + 1 ) , when n is odd . . ' . ( 55 ^ 55 + 1 ) is divisible by ( 55 + 1 ) = 56 . when ( 55 ^ 55 + 1 ) + 54 is divided by 56 , the remainder is 54 . answer a
Answer: a
Python program:
a = 55 - 56
b = 55 + a
Problem: g ( x ) is defined as the product of all even integers k such that 0 < k ≤ x . for example , g ( 14 ) = 2 × 4 × 6 × 8 × 10 × 12 × 14 . if g ( a ) is divisible by 4 ^ 11 , what is the smallest possible value for a ?
Options: a ) 22 , b ) 24 , c ) 28 , d ) 32 , e ) 44
Rationale: "g ( a ) = 4 ^ 11 = 2 ^ 22 . so we have to find a product with atleast 22 2 ' s in it . in option 1 22 the total no of 2 ' s = [ 22 / 2 ] + [ 22 / 4 ] + [ 22 / 8 ] + [ 22 / 16 ] = 11 + 5 + 2 + 1 = 19 in option 2 24 the total no of 2 ' s = [ 24 / 2 ] + [ 24 / 4 ] + [ 24 / 8 ] + [ 24 / 16 ] = 12 + 6 + 3 + 1 = 22 . hence b"
Answer: b
Python program:
a = 2 * 12
Problem: the least common multiple of positive integer m and 3 - digit integer n is 690 . if n is not divisible by 3 and m is not divisible by 2 , what is the value of n ?
Options: a ) 115 , b ) 230 , c ) 460 , d ) 575 , e ) 690
Rationale: the lcm of n and m is 690 = 2 * 3 * 5 * 23 . m is not divisible by 2 , thus 2 goes to n n is not divisible by 3 , thus 3 goes to m . from above : n must be divisible by 2 and not divisible by 3 : n = 2 * . . . in order n to be a 3 - digit number it must take all other primes too : n = 2 * 5 * 23 = 230 . answer : b .
Answer: b
Python program:
a = 690 / 3
Problem: if 5 % more is gained by selling an article for rs . 350 than by selling it for rs . 340 , the cost of the article is :
Options: a ) rs . 50 , b ) rs . 160 , c ) rs . 200 , d ) rs . 225 , e ) rs . 325
Rationale: "let c . p . be rs . x . then , 5 % of x = 350 - 340 = 10 x / 20 = 10 = > x = 200 answer : c"
Answer: c
Python program:
a = 350 - 340
b = 5 / 100
c = a / b
Problem: a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 68 percent of the distribution lies within one standard deviation d of the mean , what percent f of the distribution is less than m + d ?
Options: a ) 16 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 %
Rationale: "d the prompt says that 68 % of the population lies between m - d and m + d . thus , 32 % of the population is less than m - d or greater than m + d . since the population is symmetric , half of this 32 % is less than m - d and half is greater than m + d . thus , f = ( 68 + 16 ) % or ( 100 - 16 ) % of the population is less than m + d . d"
Answer: d
Python program:
a = 100 - 68
b = a / 2
c = 100 - b
Problem: the difference between the local value and the face value of 9 in the numeral 62975148 is
Options: a ) 899999 , b ) 899991 , c ) 899891 , d ) 899981 , e ) 899000
Rationale: "explanation : ( local value of 9 ) - ( face value of 9 ) = ( 900000 - 9 ) = 899991 b )"
Answer: b
Python program:
a = 9 * 1000
b = a - 9
Problem: a man complete a journey in 10 hours . he travels first half of the journey at the rate of 21 km / hr and second half at the rate of 24 km / hr . find the total journey in km .
Options: a ) 220 km , b ) 224 km , c ) 230 km , d ) 234 km , e ) 255 km
Rationale: "( 1 / 2 ) x / 21 + ( 1 / 2 ) x / 24 = 10 x / 21 + x / 24 = 20 15 x = 168 x 20 x = [ 168 x 20 / 15 ] = 224 km answer is b"
Answer: b
Python program:
a = 21 * 24
b = a * 10
c = 21 + 24 
d = b / c
e = 2 * d
Problem: the compound ratio of 3 : 4 , 3 : 2 and 4 : 5 ?
Options: a ) 1 : 9 , b ) 1 : 7 , c ) 1 : 2 , d ) 9 : 10 , e ) 1 : 4
Rationale: "3 / 4 * 3 / 2 * 4 / 5 = 9 / 10 = 9 : 10 answer : d"
Answer: d
Python program:
a = 3 * 3
b = 4 * 2
c = a / b
d = 3 * 4
e = 2 * 5
f = d / e
g = c / f
Problem: the true discount on a bill of rs . 2460 is rs . 360 . what is the banker ' s discount ?
Options: a ) rs . 432 , b ) rs . 422 , c ) rs . 412 , d ) rs . 442 , e ) none of these
Rationale: "explanation : f = rs . 2460 td = rs . 360 pw = f - td = 2460 - 360 = rs . 2100 true discount is the simple interest on the present value for unexpired time = > simple interest on rs . 2100 for unexpired time = rs . 360 banker ' s discount is the simple interest on the face value of the bill for unexpired time = simple interest on rs . 2460 for unexpired time = 360 / 2100 × 2460 = 0.17 × 2460 = rs . 422 answer : option b"
Answer: b
Python program:
a = 2460 - 360
b = 360 / a
c = b * 2460
Problem: a number is doubled and 5 is added . if the resultant is trebled , it becomes 111 . what is that number ?
Options: a ) 12 , b ) 29 , c ) 27 , d ) 16 , e ) 99
Rationale: "explanation : let the number be x . therefore , 3 ( 2 x + 5 ) = 111 6 x + 15 = 111 6 x = 96 x = 16 answer : d"
Answer: d
Python program:
a = 3 * 5
b = 111 - a
c = 3 * 2
d = b / c
Problem: a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets rs . 700 more than d , what is b ' s share ?
Options: a ) rs . 500 , b ) rs . 1400 , c ) rs . 2000 , d ) rs . 2500 , e ) none of the above
Rationale: "let the shares of a , b , c and d be rs . 5 x , rs . 2 x , rs . 4 x and rs . 3 x respectively . then , 4 x - 3 x = 700 x = 700 . b ' s share = rs . 2 x = rs . ( 2 x 700 ) = rs . 1400 . answer = b"
Answer: b
Python program:
a = 4 - 3
b = a * 700
c = b * 3
Problem: if the simple interest on a sum of money for 5 years at 9 % per annum is rs . 800 , what is the compound interest on the same sum at the rate and for the same time ?
Options: a ) rs . 947.55 , b ) rs . 957.55 , c ) rs . 857.55 , d ) rs . 657.55 , e ) rs . 357.55
Rationale: "sum = ( 800 * 100 ) / ( 5 * 9 ) = rs . 1 , 777.78 c . i . on rs . rs . 1 , 777.78 for 5 years at 9 % = rs . 2 , 735.33 . = rs . 2 , 735.33 - 1 , 777.78 = rs . 957.55 answer : b"
Answer: b
Python program:
a = 9 / 100
b = a * 5
c = 800 / b
d = c * 9
e = d / 100
f = 9 / 100
g = f * 5
h = 800 / g
i = e + h 
j = 9 / 100
k = j * 5
l = 800 / k
m = l * 9
n = m / 100
o = 9 / 100
p = o * 5
q = 800 / p
r = n + q 
s = r * 9
t = s / 100
u = i + t 
v = 9 / 100
w = v * 5
x = 800 / w
y = u - x
Problem: find the difference between c . i and s . i on a sum of money rs . 2000 for 2 years . at 4 % p . a
Options: a ) rs . 2.20 , b ) rs . 3.20 , c ) rs . 4.20 , d ) rs . 5.20 , e ) rs . 3.25
Rationale: p 9 r / 100 ) ^ 2 = 2000 ( 4 / 100 ) ^ 2 = rs . 3.20 answer : b
Answer: b
Python program:
a = 4 / 100
b = 1 + a 
c = 2000 * b
d = 4 / 100
e = 1 + d 
f = c * e
g = f - 2000
h = 4 / 100
i = 2000 * h
j = 2 * i
k = g - j
Problem: if 5 machines can produce 20 units in 10 hours , how long would it take 10 machines to produce 100 units ?
Options: a ) 25 , b ) 30 , c ) 35 , d ) 24 , e ) 96
Rationale: "5 machines would produce 100 units in 50 hours . increasing the amount of machines by 2 would mean dividing 50 hours by 2 . 50 / 2 = 25 answer : a"
Answer: a
Python program:
a = 10 / 10
b = a / 5
c = b * 20
d = 100 / c
Problem: a , b and c , each working alone can complete a job in 6 , 8 and 12 days respectively . if all three of them work together to complete a job and earn $ 2340 , what will be a ' s share of the earnings ?
Options: a ) $ 1100 , b ) $ 520 , c ) $ 1040 , d ) $ 1170 , e ) $ 630
Rationale: "explanatory answer a , b and c will share the amount of $ 2340 in the ratio of the amounts of work done by them . as a takes 6 days to complete the job , if a works alone , a will be able to complete 1 / 6 th of the work in a day . similarly , b will complete 1 / 8 th and c will complete 1 / 12 th of the work . so , the ratio of the work done by a : b : c when they work together will be equal to 1 / 6 : 1 / 8 : 1 / 12 multiplying the numerator of all 3 fractions by 24 , the lcm of 6 , 8 and 12 will not change the relative values of the three values . we get 24 / 6 : 24 / 8 : 24 / 12 = 4 : 3 : 2 . i . e . , the ratio in which a : b : c will share $ 2340 will be 4 : 3 : 2 . hence , a ' s share will be 4 * 2340 / 9 = 1040 correct choice is ( c )"
Answer: c
Python program:
a = 1/(8)
b = 1/(12)
c = 1/(6)
d = 1/(8)
e = c + d 
f = b + e 
g = a / f
h = 2340 * g
Problem: the area of a square field 3136 sq m , if the length of cost of drawing barbed wire 3 m around the field at the rate of rs . 1.00 per meter . two gates of 1 m width each are to be left for entrance . what is the total cost ?
Options: a ) s . 666 , b ) s . 1140 , c ) s . 999 , d ) s . 1085 , e ) s . 1020
Rationale: "a 2 = 3136 = > a = 56 56 * 4 * 3 = 672 – 6 = 666 * 1.0 = 666 answer : a"
Answer: a
Python program:
a = math.sqrt(3136)
b = a * 4
c = 2 * 1
d = b - c
e = d * 1
f = e * 3
Problem: the pinedale bus line travels at an average speed of 60 km / h , and has stops every 5 minutes along its route . yahya wants to go from his house to the pinedale mall , which is 5 stops away . how far away , in kilometers , is pinedale mall away from yahya ' s house ?
Options: a ) 25 km , b ) 30 km , c ) 40 km , d ) 50 km , e ) 60 km
Rationale: "number of stops in an hour : 60 / 5 = 12 distance between stops : 60 / 12 = 5 km distance between yahya ' s house and pinedale mall : 5 x 5 = 25 km imo , correct answer is ` ` a . ' '"
Answer: a
Python program:
a = 5 * 5
b = a / 60
c = 60 * b
Problem: a positive number x is multiplied by 10 , and this product is then divided by 3 . if the positive square root of the result of these two operations equals x , what is the value of x ?
Options: a ) 9 / 4 , b ) 3 / 2 , c ) 4 / 3 , d ) 2 / 3 , e ) 10 / 3
Rationale: "sq rt ( 10 x / 3 ) = x = > 10 x / 3 = x ^ 2 = > x = 10 / 3 ans - e"
Answer: e
Python program:
a = 10 / 3
Problem: if 90 % of a = 30 % of b and b = c % of a , then the value of c is ?
Options: a ) 900 , b ) 800 , c ) 600 , d ) 300 , e ) none
Rationale: "answer ∵ 90 a / 100 = 30 b / 100 = ( 30 / 100 ) x ac / 100 ∴ c = 100 x ( 100 / 30 ) x ( 90 / 100 ) = 300 correct option : d"
Answer: d
Python program:
a = 30 / 90
Problem: in a group of dogs and people , the number of legs was 28 more than twice the number of heads . how many dogs were there ? [ assume none of the people or dogs is missing a leg . ]
Options: a ) 4 , b ) 7 , c ) 12 , d ) 14 , e ) 28
Rationale: if there were only people , there would be exactly twice the number of legs as heads . each dog contributes two extra legs over and above this number . so 28 extra legs means 14 dogs . correct answer d
Answer: d
Python program:
a = 28 / 2