euclaise/mathqa_programs huggingface dataset:
Problem: in a lottery there are 10 prizes and 25 blanks . a lottery is drawn at random . what is the probability of getting a blank ?
Options: a ) 2 / 3 , b ) 6 / 7 , c ) 5 / 7 , d ) 8 / 7 , e ) 4 / 3
Rationale: total draws = prizes + blanks = 10 + 25 = 35 probability of getting a blank = 25 / 35 = 5 / 7 correct option is c
Answer: c
Python program:
a = 10 + 25 
b = 25 / a
Problem: what is the maximum number of pieces that a circular pizza can be cut into with 6 linear cuts ?
Options: a ) 12
b ) 13
c ) 16
d ) 20
e ) 22
Rationale: 1 cut makes 2 pieces a second cut can make 4 pieces by cutting through 2 of the pieces a third cut can make 7 pieces by cutting through 3 of the pieces a fourth cut can make 11 pieces by cutting through 4 of the pieces a fifth cut can make 16 pieces by cutting through 5 of the pieces a sixth cut can make 22 pieces by cutting through 6 of the pieces e
Answer: e
Python program:
a = 6 * 3
Problem: walking at the rate of 4 kmph a man cover certain distance in 2 hr 45 min . running at a speed of 16.5 kmph the man will cover the same distance in .
Options: a ) 12 min , b ) 25 min , c ) 40 min , d ) 48 min , e ) 52 min
Rationale: distance = speed * time 4 * 11 / 4 = 11 km new speed = 16.5 kmph therefore time = d / s = 11 / 16.5 = 40 min answer : c
Answer: c
Python program:
a = 45 / const_60
b = 2 + a 
c = 4 * b
d = c / 16
e = d * const_60
Problem: how many positive factors do 120 and 96 have in common ?
Options: a ) 8 , b ) 12 , c ) 16 , d ) 18 , e ) 24
Rationale: "the number of common factors will be same as number of factors of the highest common factor ( hcf ) hcf of 120 and 96 is 24 number of factors of 24 = 8 answer : a"
Answer: a
Python program:
a = 96 - 10
b = a / 10
Problem: if p and q are positive integers each greater than 1 , and 15 ( p + 1 ) = 29 ( q + 1 ) , what is the least possible value of p + q ?
Options: a ) 36 , b ) 42 , c ) 44 , d ) 46 , e ) none
Rationale: 17 ( p + 1 ) = 29 ( q + 1 ) - - > ( p + 1 ) / ( q + 1 ) = 29 / 17 - - > the least positive value of p + 1 is 29 , so the least value of p is 28 and the least positive value of q + 1 is 15 , so the least value of q is 14 - - > the least value of p + q is 28 + 14 = 42 . answer : b .
Answer: b
Python program:
a = 29 + 15 
b = a - 2
Problem: how many numbers from 10 to 50 are exactly divisible by 3 ?
Options: a ) 13 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: "12 , 15 , 18 , 21 , 24 , 27 , 30 , 33 , 36 , 39 , 42 , 45,48 . 13 numbers . 10 / 3 = 3 and 50 / 3 = 16 = = > 16 - 3 = 13 . therefore 13 digits a )"
Answer: a
Python program:
a = 50 / 3
b = math.floor(a)
c = b * 3
d = 10 / 3
e = math.floor(d)
f = e + 1 
g = f * 3
h = c - g
i = h / 3
j = i + 1
Problem: the percentage profit earned by selling an article for rs . 1820 is equal to the percentage loss incurred by selling the same article for rs . 1280 . at what price should the article be sold to make 25 % profit ?
Options: a ) 3000 , b ) 1230 , c ) 2000 , d ) 5600 , e ) 1937.5
Rationale: "c . p . be rs . x . then , ( 1820 - x ) / x * 100 = ( x - 1280 ) / x * 100 1820 - x = x - 1280 2 x = 3100 = > x = 1550 required s . p . = 125 % of rs . 1550 = 125 / 100 * 1550 = rs . 1937.5 . answer e"
Answer: e
Python program:
a = 100 + 25 
b = a / 100
c = 1820 + 1280 
d = c / 2
e = b * d
Problem: if the remainder is 3 when positive integer n is divided by 18 , what is the remainder when n is divided by 6 ?
Options: a ) 3 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: assume x is quotient here , n = 18 x + 3 - - - - - - - - - - ( 1 ) and n = 6 x + ? we can also write first term as n = ( 18 x + 6 ) = 6 ( 3 x + 1 ) + 3 ie 6 ( 3 x + 1 ) + 3 ie the first term is perfectly divisible by 6 . so , the remainder left is 3 . so , answer ( a ) is right choice .
Answer: a
Python program:
a = 18 / 6
Problem: how many 4 digit numbers are there , if it is known that the first digit is even , the second is odd , the third is prime , the fourth ( units digit ) is divisible by 3 , and the digit 7 can be used only once ?
Options: a ) 20 , b ) 150 , c ) 304 , d ) 310 , e ) 320
Rationale: "4 options for the first digit : 2 , 4 , 6 , 8 ; 5 options for the second digit : 1 , 3 , 5 , 7 , 9 ; 4 options for the third digit : 2 , 3 , 5 , 7 ; 4 options for the fourth digit : 0 , 3 , 6 , 9 . four digit # possible without the restriction ( about the digit 2 ) : 4 * 5 * 4 * 4 = 320 numbers with seven 7 - s , 7 x 7 x 4 * 1 * 1 * 4 = 16 . thus there are 320 - 16 = 304 such numbers . answer : c ."
Answer: c
Python program:
a = 4 + 1 
b = 4 + 1 
c = a * b
d = 4 * 4
e = c * d
f = 4 + 1 
g = 4 + 1 
h = f * g
i = h * 4
j = e - i
Problem: two kinds of vodka are mixed in the ratio 1 : 2 and 2 : 1 and they are sold fetching the profit 10 % and 20 % respectively . if the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4 / 3 and 5 / 3 times respectively , then the mixture will fetch the profit of
Options: a ) 18 % , b ) 20 % , c ) 21 % , d ) 23 % , e ) can not be determined
Rationale: "mixture 1 and 2 having individual profit % of 10 and 20 respectively . individual profits of vodka a for mixture 1 = 1 / 3 * 10 = 3.33 individual profits of vodka b for mixture 1 = 2 / 3 * 10 = 6.77 individual profits for a and b are increased 4 / 3 and 5 / 3 times . means profits of mixtures 1 and 2 will increase too . increased profits of vodka a for mixture 1 = 4 / 3 * 3.33 = 4.44 increased profits of vodka b for mixture 2 = 5 / 3 * 6.77 = 10.55 total increased profits for mixture 1 = 14.99 similarly total increased profits for mixture 2 = 24.42 using allegation formula va : vb = 1 : 1 = [ 24.42 - ( profit of mixture ) ] / [ ( profit of mixture ) - 14.99 ] hence profit of mixture = 19.705 approx = 20 % answer : b"
Answer: b
Python program:
a = 10 * 4
b = a / 2
c = 10 + 5 
d = b + c
Problem: farm tax is levied on the 40 % of the cultivated land . the tax department collected total $ 3840 through the farm tax from the village of mr . willam . mr . willam paid only $ 480 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is :
Options: a ) 31.25 % , b ) 25 % , c ) 12.5 % , d ) 0.2083 % , e ) none
Rationale: "only trick n this question is to ignore 40 % information as farm tax is levied uniformly in the village and that includes mr william ' s land . what percentage of tax mr william paid ? this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to ( 480 / 3840 ) x 100 = 12.5 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 12.5 % x ( 100 / 40 ) = 31.25 % and the answer is not there in the options . the correct answer is ( a ) ."
Answer: a
Python program:
a = 480 / 3840
b = a * 100
c = b * 100
d = c / 40
Problem: the area of a circular field is 13.86 hectares . find the cost of fencing it at the rate of rs . 4.50 per metre .
Options: a ) 2399 , b ) 3888 , c ) 2999 , d ) 5940 , e ) 2888
Rationale: "explanation : area = ( 13.86 x 10000 ) sq . m = 138600 sq . m circumference = cost of fencing = rs . ( 1320 x 4.50 ) = rs . 5940 . answer : d ) 5940"
Answer: d
Python program:
a = 13 / 86
b = math.sqrt(a)
c = b * 100
d = circumface * (
Problem: a mixture contains alcohol and water in the ratio 4 : 3 . if 6 litres of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture
Options: a ) 15 litres , b ) 10 litres , c ) 30 litres , d ) 12 litres , e ) 8 litres
Rationale: "let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 4 x / ( 3 x + 6 ) = 4 / 5 20 x = 4 ( 3 x + 6 ) 8 x = 24 x = 3 quantity of alcohol = ( 4 x 3 ) litres = 12 litres . answer is d"
Answer: d
Python program:
a = 6 * 1
Problem: if the sides of a triangle are 26 cm , 25 cm and 10 cm , what is its area ?
Options: a ) 120 , b ) 110 , c ) 130 , d ) 140 , e ) 125
Rationale: "the triangle with sides 26 cm , 25 cm and 10 cm is right angled , where the hypotenuse is 26 cm . area of the triangle = 1 / 2 * 25 * 10 = 125 cm 2 answer : option e"
Answer: e
Python program:
a = 25 * 10
b = a / 2
Problem: ( 7.5 × 7.5 + 37.5 + 2.5 × 2.5 ) is equal to :
Options: a ) 30 , b ) 60 , c ) 80 , d ) 100 , e ) none of these
Rationale: solution given expression = ( 7.5 × 7.5 + 2 × 7.5 × 2.5 + 2.5 × 2.5 ) = ( a 2 + 2 ab + b 2 ) = ( a + b ) 2 = ( 7.5 + 2.5 ) 2 = 102 = 100 . answer d
Answer: d
Python program:
a = 7 * 5
b = 2 * 5
c = a + b 
d = c + 37
Problem: a theater charges $ 12 for seats in the orchestra and $ 8 for seats in the balcony . on a certain night , a total of 350 tickets were sold for a total cost of $ 3,320 . how many more tickets were sold that night for seats in the balcony than for seats in the orchestra ?
Options: a ) 90 , b ) 110 , c ) 120 , d ) 130 , e ) 220
Rationale: "orchestra seats - a balcony seats - b a + b = 350 and 12 a + 8 b = 3320 solving equations simultaneously ( multiply equation 1 with 8 and subtract from second equation ) 4 a = 3320 - 8 * 350 = 3320 - 2800 = 520 i . e . a = 130 and b = 350 - 130 = 220 more seats in balcony than orchestra = b - a = 220 - 130 = 90 answer : option a"
Answer: a
Python program:
a = 12 * 350
b = 3 * 1000
c = 3 * 100
d = b + c 
e = 2 * 10
f = d + e 
g = a - f
h = 12 - 8
i = g / h
j = 12 * 350
k = 3 * 1000
l = 3 * 100
m = k + l 
n = 2 * 10
o = m + n 
p = j - o
q = 12 - 8
r = p / q
s = 350 - r
t = i - s
Problem: if a - b = 3 and a 2 + b 2 = 29 , find the value of ab .
Options: a ) 10 , b ) 12 , c ) 13 , d ) 15 , e ) 18
Rationale: "2 ab = ( a 2 + b 2 ) - ( a - b ) 2 = 29 - 9 = 20 ab = 10 . answer : a"
Answer: a
Python program:
a = 3 ** 2
b = 29 - a
c = b / 2
Problem: each child has 4 pencils and 13 skittles . if there are 8 children , how many pencils are there in total ?
Options: a ) 16 , b ) 12 , c ) 18 , d ) 22 , e ) 32
Rationale: 4 * 8 = 32 . answer is e .
Answer: e
Python program:
a = 4 * 8
Problem: sandy had $ 140 left after spending 30 % of the money she took for shopping . how much money did sandy take along with her ?
Options: a ) $ 180 , b ) $ 200 , c ) $ 220 , d ) $ 240 , e ) $ 260
Rationale: let the money sandy took for shopping be x . 0.7 x = 140 x = 200 the answer is b .
Answer: b
Python program:
a = 100 - 30
b = a / 100
c = 140 / b
Problem: three pipes , a , b , & c are attached to a tank . a & b can fill it in 20 & 30 minutes respectively while c can empty it in 15 minutes . if a , b & c are kept open successively for 1 minute each , how soon will the tank be filled ?
Options: a ) 2 hours , b ) 4 hours , c ) 3 hours , d ) 5 hours , e ) 6 hours
Rationale: "in three minute 1 / 20 + 1 / 30 - 1 / 15 = 1 / 60 part is filled 3 min - - - - - - - - 1 / 60 parts x min - - - - - - - - - 1 part ( full ) x = 180 min = 3 hours answer : c"
Answer: c
Python program:
a = 1 + 1 
b = a + 1
Problem: a total of $ 20,000 was invested in two certificates of deposit at simple annual interest rates of 6 percent and 8 percent , respectively . if the total interest on the two certificates was $ 1,440 at the end of one year , what fractional part of the $ 20.000 was invested at the higher rate ?
Options: a ) 3 / 8 , b ) 2 / 5 , c ) 1 / 2 , d ) 3 / 5 , e ) 3 / 4
Rationale: "let ` ` $ x ' ' be invested with the higher rate of 8 % thus , ` ` 20000 - x ' ' must have been invested with lower rate of 6 % simple interest = principal * rate * time for the amount invested at 8 % principal = x rate = 0.08 time = 1 simple interest = x * 0.08 * 1 = 0.08 x for the amount invested at 6 % principal = 20000 - x rate = 0.06 time = 1 simple interest = ( 20000 - x ) * 0.06 * 1 = 1200 - 0.06 x total interest = $ 1440 0.08 x + 1200 - 0.06 x = 1440 0.02 x = 240 x = 240 / 0.02 = 12000 fraction of x per total amount = 12000 / 20000 = 12 / 20 = 3 / 5 ans : ` ` d ' '"
Answer: d
Python program:
a = 1 + 4 
b = 2 * a
c = 100 * b
d = 4 * 100
e = c + d 
f = 1 + 4 
g = 2 * f
h = 4 * g
i = e + h 
j = i / 20
k = j / 8
l = k + 8 
m = l - 6
n = m / 20
Problem: the average of 5 quantities is 6 . the average of 3 of them is 4 . what is the average of remaining 2 numbers ?
Options: a ) 9 , b ) 10 , c ) 8 , d ) 9.5 , e ) none of these
Rationale: answer : a
Answer: a
Python program:
a = 5 * 6
b = 3 * 4
c = a - b
d = c / 2
Problem: having received his weekly allowance , john spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 0.40 at the candy store . what is john ’ s weekly allowance ?
Options: a ) $ 1.50 , b ) $ 2.00 , c ) $ 2.50 , d ) $ 3.00 , e ) $ 3.50
Rationale: "x = 3 x / 5 + 1 / 3 * 2 x / 5 + 40 4 x / 15 = 40 x = 150 = $ 1.50 the answer is a ."
Answer: a
Python program:
a = 3 / 5
b = 1 / 3
c = 3 / 5
d = 1 - c
e = b * d
f = a + e 
g = 1 - f
h = 0 / 40
Problem: how much space , in cubic units , is left vacant when maximum number of 2 x 2 x 2 cubes are fitted in a rectangular box measuring 8 x 10 x 9 ?
Options: a ) 60 , b ) 65 , c ) 70 , d ) 75 , e ) 80
Rationale: "no of cubes that can be accommodated in box = ( 8 * 10 * 9 ) / ( 2 * 2 * 2 ) 8 * 10 in numerator can be perfectly divided by 2 * 2 in denominator . side with length 9 ca n ' t be perfectly divided by 2 and hence is the limiting factor . closet multiple of 2 less that 9 is 8 . so vacant area in cube = = 10 * 8 ( 9 - 8 ) = 10 * 8 * 1 = 80 ans - e"
Answer: e
Python program:
a = 2 * 2
b = 8 - a
c = 10 * 9
d = b * c
Problem: how many 4 digit numbers are there , if it is known that the first digit is even , the second is odd , the third is prime , the fourth ( units digit ) is divisible by 3 , and the digit 3 can be used only once ?
Options: a ) 20 , b ) 150 , c ) 225 , d ) 250 , e ) 316
Rationale: "4 options for the first digit : 2 , 4 , 6 , 8 ; 5 options for the second digit : 1 , 3 , 5 , 7 , 9 ; 4 options for the third digit : 2 , 3 , 5 , 7 ; 4 options for the fourth digit : 0 , 3 , 6 , 9 . four digit # possible without the restriction ( about the digit 6 ) : 4 * 5 * 4 * 4 = 320 numbers with three 3 - s , 3 x 3 x 3 4 * 1 * 1 * 1 = 4 thus there are 320 - 4 = 316 such numbers . answer : e ."
Answer: e
Python program:
a = 4 + 1 
b = 4 + 1 
c = a * b
d = 4 * 4
e = c * d
f = 4 + 1 
g = 4 + 1 
h = f * g
i = h * 4
j = e - i
Problem: in an examination , there were 2,000 candidates , out of which 900 candidates were girls and rest were boys . if 32 % of the boys and 32 % of the girls passed , then the total percentage of failed candidates is ?
Options: a ) 35.67 % , b ) 64.75 % , c ) 68.00 % , d ) 69.57 % , e ) none of these
Rationale: "girls = 900 , boys = 1100 passed = ( 32 % of 1100 ) + ( 32 % of 900 ) = 352 + 288 = 640 failed = 2000 - 640 = 1360 failed % = [ ( 1360 / 2000 ) x 100 ] % = 68 % . answer : c"
Answer: c
Python program:
a = 100 * 10
b = 2 * a
c = 32 / 100
d = 100 * 10
e = 2 * d
f = e - 900
g = c * f
h = b - g
i = 32 / 100
j = i * 900
k = h - j
l = 100 * 10
m = 2 * l
n = k / m
o = n * 100
Problem: find ( 7 x + 5 y ) / ( x - 2 y ) if x / 2 y = 3 / 2 ?
Options: a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 29
Rationale: "x / 2 y = 3 / 2 = > x = 6 y / 2 = 3 y = > ( 7 x + 5 y ) / ( x - 2 y ) = ( ( 7 * ( 3 y ) ) + 5 y ) / ( 3 y - 2 y ) = > 26 y / y = 26 answer : c"
Answer: c
Python program:
a = 3 / 2
b = a * 2
c = b * 7
d = c + 5 
e = 3 / 2
f = e * 2
g = f - 2
h = d / g
Problem: when a student weighing 45 kgs left a class , the average weight of the remaining 59 students increased by 200 g . what is the average weight of the remaining 59 students
Options: a ) 55 , b ) 56 , c ) 57 , d ) 58 , e ) 59
Rationale: explanation : let the average weight of the 59 students be a . so the total weight of the 59 of them will be 59 * a . the questions states that when the weight of this student who left is added , the total weight of the class = 59 a + 45 when this student is also included , the average weight decreases by 0.2 kgs 59 a + 45 / 60 = a − 0.2 = > 59 a + 45 = 60 a - 12 = > 45 + 12 = 60 a - 59 a = > a = 57 answer : option c
Answer: c
Python program:
a = 59 + 1 
b = 200 / 1000
c = a * b
d = 45 + c
Problem: mike drives his new corvette from san francisco to las vegas , a journey of 640 miles . he drives the first half of the trip at an average rate of 80 miles per hour , but has to slow down for the second half of his journey . if the second half of the trip takes him 200 percent longer than the first half , what is his average rate j in miles per hour for the entire trip ?
Options: a ) 26.7 , b ) j = 30.0 , c ) j = 40.0 , d ) j = 53.3 , e ) 60.0
Rationale: veritas prepofficial solution correct answer : c using the formula : time = distance / rate , we find that mike takes 4 hours to cover the first 320 miles of his trip . since the 2 nd 320 miles take 200 % longer than the first , it takes mike 8 hours longer , or 12 hours . ( note : 200 % longer than the first half is not 200 % of the first half . ) the overall time is 4 hours + 12 hours or 16 hours . since the definition of average rate = total distance traveled / total time of travel , mike ' s average rate = 640 / 16 or 40 miles per hour . answer choice c is correct .
Answer: c
Python program:
a = 640 / 2
b = a / 80
c = b * 2
d = 640 / 2
e = d / 80
f = c + e 
g = 640 / 2
h = g / 80
i = f + h 
j = 640 / i
Problem: if f ( x ) = 12 - x ^ 2 / 2 and f ( 2 k ) = 3 k , what is one possible value for k ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: first of all , see thisgmat blog postand check the related lesson linked below for some background on function notation . we can plug anything in for x and get a result . you can find f ( 1 ) , for example , by plugging in 1 where x is , and you would get 12 - 1 / 2 = 11.5 . or we could find f ( 2 ) , which would be 12 - 4 / 2 = 10 . so the notation f ( 2 k ) means that we are going to plug a 2 k in for x everywhere in the formula for f ( x ) . that would be : f ( 2 k ) = 12 - ( 2 k ) ^ 2 / 2 = 12 - 2 k ^ 2 . remember that we have to square both the 2 and the k , to get 4 k 2 . now , this expression , the output , we will set equal to 2 k . 12 - 2 k ^ 2 = 2 k - - > k = - 4 or k = 3 . all the answers are positive , so we choose k = 3 . answer = b
Answer: b
Python program:
a = 2 ** 2
b = a / 2
c = b + 1
Problem: two numbers n and 14 have lcm = 56 and gcf = 12 . find n .
Options: a ) 48 , b ) 34 , c ) 44 , d ) 54 , e ) 64
Rationale: "the product of two integers is equal to the product of their lcm and gcf . hence . 14 × n = 56 × 12 n = 56 × 12 / 14 = 48 correct answer a"
Answer: a
Python program:
a = 56 * 12
b = a / 14
Problem: express a speed of 414 kmph in meters per second ?
Options: a ) 201 mps , b ) 114 mps , c ) 118 mps , d ) 115 mps , e ) 111 mps
Rationale: "414 * 5 / 18 = 115 mps answer : d"
Answer: d
Python program:
a = const_0_2778 * 414
Problem: two pipes p and q can fill a cistern in 10 and 15 minutes respectively . both are opened together , but at the end of 3 minutes the first is turned off . how much longer will the cistern take to fill ?
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 2 / 4 , d ) 1 / 4 , e ) 1 / 4
Rationale: "3 / 10 + x / 15 = 1 x = 10 1 / 2 answer : a"
Answer: a
Python program:
a = 1 / 10
b = 1 / 15
c = a + b 
d = c * 3
e = 1 - d
f = e * 15
Problem: the malibu country club needs to drain its pool for refinishing . the hose they use to drain it can remove 60 cubic feet of water per minute . if the pool is 80 feet wide by 150 feet long by 10 feet deep and is currently at 100 % capacity , how long will it take to drain the pool ?
Options: a ) 1400 , b ) 1600 , c ) 1800 , d ) 1500 , e ) 2000
Rationale: "volume of pool = 80 * 150 * 10 cu . ft , 100 % full = 60 * 100 * 10 * 1 cu . ft water is available to drain . draining capacity = 60 cu . ft / min therefore time taken = 80 * 150 * 10 * 1 / 60 min = 2000 min e"
Answer: e
Python program:
a = 100 / 100
b = 80 * 150
c = b * 10
d = a * c
e = d / 60
Problem: tom and john traveled in the same direction along the equal route at their constant speed rates of 15 km per hour and 10 km per hour , respectively . after 15 minutes tom passed john , tom reaches a certain gas station , how many r minutes it takes john to reach the station ?
Options: a ) 5 min , b ) 6 min , c ) 7 and 1 / 2 min , d ) 8 min , e ) 10 min
Rationale: since the question states “ after 15 minutes ” , we can say tom traveled 15 / 4 km for 15 minutes as he can travel 15 km per hour . hence , using the same logic , we can say john traveled 10 / 4 km as he travels 10 km per hour . so , john has to travel ( 15 / 4 ) - ( 10 / 4 ) km = 5 / 4 km more . since john ’ s speed is 10 km / hour , which means 1 km / 6 minutes . as he has to travel 5 / 4 km more , it is going to take him 6 ( 5 / 4 ) minutes . hence , r = 6 ( 5 / 4 ) = 15 / 2 minutes . the correct answer is c .
Answer: c
Python program:
a = 15 - 10
b = 15 / const_60
c = a * b
d = c * const_60
e = d / 10
f = e / 2
g = f - const_0_25
h = g * 10
Problem: a professional athlete was offered a 3 - year contract to play with team k that provided for an annual salary of $ 100000 in the first year , an increase in annual salary of 20 % over the previous year for the next two years , and a bonus of $ 50000 on signing . team l offered a 3 - year contract providing for an annual salary of $ 150000 in the first year , an increase in annual salary of 20 % over the previous year for the next two years , and no signing bonus . if he accepts the offer of team l and fulfills the 3 - year contract terms , the athlete will receive how much more money by choosing team l over team k ?
Options: a ) $ 132,000 , b ) $ 50,000 , c ) $ 82,500 , d ) $ 92,000 , e ) $ 100,000
Rationale: team k ' s contract = $ 100,000 + $ 100,000 * 1.2 + $ 100,000 * 1.2 * 1.2 + $ 50,000 = $ 414,000 team l ' s contract = $ 150,000 + $ 150,000 * 1.2 + $ 150,000 * 1.2 * 1.2 = $ 546,000 the difference = $ 132,000 . answer : a .
Answer: a
Python program:
a = 20 / 100
b = 1 + a 
c = 150000 * b
d = 150000 + c 
e = 20 / 100
f = 1 + e 
g = 150000 * f
h = 20 / 100
i = 1 + h 
j = g * i
k = d + j 
l = 100000 + 50000 
m = 20 / 100
n = 1 + m 
o = 100000 * n
p = l + o 
q = 20 / 100
r = 1 + q 
s = 100000 * r
t = 20 / 100
u = 1 + t 
v = s * u
w = p + v 
x = k - w
y = x / 1000
Problem: there are 19 teams in the hockey league , and each team faces all the other teams 10 times each . how many games are played in the season ?
Options: a ) 1710 , b ) 1920 , c ) 2440 , d ) 2860 , e ) 3260
Rationale: "the number of ways to choose two teams is 19 c 2 = 19 * 18 / 2 = 171 the total number of games in the season is 10 * 171 = 1710 . the answer is a ."
Answer: a
Python program:
a = 19 - 1
b = 19 * a
c = b * 10
d = c / 2
Problem: in a family 11 people eat only vegetarian , 6 people eat only non veg . , 9 people eat both veg and non veg . . how many people eat veg in the family ?
Options: a ) 20 , b ) 11 , c ) 9 , d ) 31 , e ) 21
Rationale: "total people eat veg = only veg + both veg and non veg total = 11 + 9 = 20 answer = a"
Answer: a
Python program:
a = 11 + 9
Problem: a cyclist climbs a hill with a length of 400 m with a speed of 7.2 km / h . when descending , the speed is two times greater . how much time is necessary for the cyclist to climb and descend the hill ?
Options: a ) 30 seconds , b ) 20 seconds , c ) 40 seconds , d ) 10 seconds , e ) none
Rationale: 7.2 km = 7200 m . 1 h = 3600 s . the speed will be 7200 m / 3600 s = 2 m / s . the necessary time to climb will be 20 seconds . when descending , if the speed is two times greater , the necessary time will be two times smaller , so 10 seconds . the total necessary time is 20 s + 10 s = 30 seconds . answer a
Answer: a
Python program:
a = 7 * 2
b = a / 3600
c = 400 / b
d = c / 2
e = 7 * 2
f = e / 3600
g = 400 / f
h = d + g 
i = h / 10
Problem: the radius of a semi circle is 6.8 cm then its perimeter is ?
Options: a ) 32.7 , b ) 32.4 , c ) 22.4 , d ) 34.9 , e ) 35.1
Rationale: "36 / 7 r = 6.8 = 34.9 answer : d"
Answer: d
Python program:
a = circumface / (
b = a + 2
Problem: 6.513 / 10.02 =
Options: a ) 0.35 , b ) 0.3505 , c ) 0.3509 , d ) 0.65 , e ) 0.3527
Rationale: "6.513 / 10.02 6.513 / 1002 = 6.5 move the comma two places to the left as we have 2 decimal places from the divisor : 0.65 . answer : d"
Answer: d
Python program:
a = 6 / 513
b = a * 100