euclaise/mathqa_programs huggingface dataset:
Problem: in 10 years , a will be twice as old 5 as b was 10 years ago . if a is now 7 years older than b , the present age of b is
Options: a ) 35 , b ) 37 , c ) 39 , d ) 41 , e ) 42
Rationale: explanation : let b ' s age = x years . then , as age = ( x + 7 ) years . ( x + 7 + 10 ) = 2 ( x — 10 ) hence x = 37 . present age of b = 37 years answer : option b
Answer: b
Python program:
a = 2 * 10
b = 7 + 10 
c = a + b
Problem: the distance between 2 cities a and b is 1000 km . a train starts from a at 9 a . m . and travels towards b at 100 km / hr . another starts from b at 10 a . m . and travels towards a at 150 km / hr . at what time do they meet ?
Options: a ) 11 am . , b ) 12 p . m . , c ) 3 pm . , d ) 2 p . m . , e ) 1 p . m .
Rationale: "suppose they meet x hrs after 9 a . m . distance moved by first in x hrs + distance moved by second in ( x - 1 ) hrs = 1000 100 x + 150 ( x - 1 ) = 1000 x = 4.60 = 5 hrs they meet at 9 + 5 = 2 p . m . answer is d"
Answer: d
Python program:
a = 2 + 10 
b = 9 + 10 
c = a / b
d = c + 1000
Problem: sachin is younger than rahul by 14 years . if the ratio of their ages is 7 : 9 , find the age of sachin
Options: a ) 48 , b ) 24.8 , c ) 24.21 , d ) 24.88 , e ) 49
Rationale: "explanation : if rahul age is x , then sachin age is x - 14 , so , 9 x - 126 = 7 x 2 x = 126 x = 63 so sachin age is 63 - 14 = 49 answer : e ) 49"
Answer: e
Python program:
a = 9 - 7
b = 14 / a
c = b * 7
Problem: the number x of cars sold each week varies with the price y in dollars according to the equation x = 800000 – 50 y . what would be the total weekly revenue w , in dollars , from the sale of cars priced at $ 15000 ?
Options: a ) 50000 , b ) 750000 , c ) 850000 , d ) 7 , 500000 , e ) w = 75000,000
Rationale: number of cars sold = x = 800000 - 50 y y = 15000 x = 800000 - 750000 = 50000 revenue from 50000 cars = 15000 * 50000 = 750000000 e
Answer: e
Python program:
a = 50 * 15000
b = 800000 - a
c = b * 15000
d = 1000 * 1000
e = 100 * d
f = reminder / (
Problem: two varieties of steel , a and b , have a ratio of iron to chromium as 5 : 1 and 7 : 2 , respectively . steel c is produced by mixing alloys a and b at a ratio of 3 : 2 . what is the ratio of iron to chromium in c ?
Options: a ) 17 : 73 , b ) 78 : 14 , c ) 45 : 30 , d ) 73 : 17 , e ) 4 : 9
Rationale: in 6 parts of alloy a , 5 parts are iron , and 1 part is chromium . in 9 parts of alloy b , 7 parts are iron and 2 parts are chromium . first , to compare the two alloys , get the same number of parts in total - we can use 18 . so we have : in 18 parts of alloy a , 15 parts are iron and 3 are chromium . in 18 parts of alloy b , 14 parts are iron and 4 are chromium . so combining 3 of a with 2 of b , we ' d be combining 45 and 28 parts of iron , or 73 parts of iron , with 9 and 8 of chromium , or 17 of chromium , so 73 to 17 is the answer . answer : d
Answer: d
Python program:
a = 5 / 1
b = 3 + 2 
c = 3 / b
d = a * c
e = 7 / 2
f = 3 + 2 
g = 2 / f
h = e * g
i = d / h
j = i * 2
Problem: there are 11 boys and 10 girls in a class . if three students are selected at random , in how many ways that 3 girl & 2 boys are selected ?
Options: a ) 6600 , b ) 1300 , c ) 6780 , d ) 1976 , e ) 2448
Rationale: "e = event that 3 girl and 2 boys are selected n ( e ) = we have to select 2 boys from 11 and 3 girl from 10 = 11 c 2 * 10 c 3 = 6600 ans - a"
Answer: a
Python program:
a = math.comb(11, 2)
b = math.comb(10, 3)
c = a * b
Problem: two goods trains each 400 m long are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 38.4 , b ) 32.6 , c ) 48 , d ) 27.4 , e ) 21
Rationale: "relative speed = 45 + 30 = 75 km / hr . 75 * 5 / 18 = 125 / 6 m / sec . distance covered = 400 + 400 = 800 m . required time = 800 * 6 / 125 = 38.40 sec . answer : a"
Answer: a
Python program:
a = 45 + 30
Problem: a man purchased 3 blankets @ rs . 200 each , 5 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 150 . find the unknown rate of two blankets ?
Options: a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) 500
Rationale: "10 * 150 = 1500 3 * 200 + 5 * 150 = 1350 1350 – 1050 = 300 answer : c"
Answer: c
Python program:
a = 10 * 150
b = 3 * 100
c = 5 * 150
d = b + c 
e = a - d
Problem: how many positive integers less than 5,000 are evenly divisible by neither 15 nor 22 ?
Options: a ) 4,514 , b ) 4,475 , 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 22 5000 / 22 = 238 . # # , so 238 we have double counted some , so take lcm of 15 and 22 = 105 and divide by 5000 , we get 47 . so all numbers divisible by 15 and 22 = 333 + 238 - 47 = 524 now subtract that from 4999 . 4999 - 524 = 4514 answer a ."
Answer: a
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: a man buys a cycle for rs . 1800 and sells it at a loss of 25 % . what is the selling price of the cycle ?
Options: a ) s . 1090 , b ) s . 1160 , c ) s . 1190 , d ) s . 1350 , e ) s . 1256
Rationale: "s . p . = 75 % of rs . 1800 = rs . 75 / 100 x 1800 = rs . 1350 answer : d"
Answer: d
Python program:
a = 100 - 25
b = a * 1800
c = b / 100
Problem: a man goes from a to b at a speed of 60 kmph and comes back to a at a speed of 40 kmph . find his average speed for the entire journey ?
Options: a ) 49 kmph , b ) 58 kmph , c ) 44 kmph , d ) 47 kmph , e ) 48 kmph
Rationale: "distance from a and b be ' d ' average speed = total distance / total time average speed = ( 2 d ) / [ ( d / 60 ) + ( d / 40 ] = ( 2 d ) / [ 5 d / 120 ) = > 48 kmph . answer : e"
Answer: e
Python program:
a = 60 + 40 
b = a / 2
Problem: 5358 x 54 = ?
Options: a ) 272258 , b ) 272358 , c ) 289332 , d ) 274258 , e ) 274358
Rationale: "5358 x 51 = 5358 x ( 50 + 4 ) = 5358 x 50 + 5358 x 4 = 267900 + 21432 = 289332 . c )"
Answer: c
Python program:
a = 5358 / 54
b = a * 100
Problem: a basketball is dropped from a height of 20 feet . if it bounces back up to a height that is exactly half of its previous height , and it stops bouncing after hitting the ground for the fourth time , then how many total feet will the ball have traveled after 2 full bounces .
Options: a ) 50 , b ) 55 , c ) 60 , d ) 75 , e ) 100
Rationale: initial distance = 40 feet first bounce = 20 feet up + 20 feet down = 40 feet second bouche = 10 feet up + 10 feet down = 20 feet total distance covered = 40 + 40 + 20 = 100 answer is e
Answer: e
Python program:
a = 20 / 2
b = a / 2
c = b / 2
d = c / 2
e = 20 / 2
f = 20 + e 
g = 20 / 2
h = f + g 
i = 20 / 2
j = i / 2
k = h + j 
l = 20 / 2
m = l / 2
n = k + m 
o = 20 / 2
p = o / 2
q = p / 2
r = n + q 
s = 20 / 2
t = s / 2
u = t / 2
v = r + u 
w = d + v 
x = w * 2
y = 20 / 2
z = y / 2
A = z / 2
B = x - A
C = 20 / 2
D = C / 2
E = D / 2
F = B - E
G = 20 / 2
H = G / 2
I = H / 2
J = F - I
K = 20 / 2
L = K / 2
M = L / 2
N = J - M
Problem: a 200 meter long train crosses a man standing on the platform in 9 sec . what is the speed of the train ?
Options: a ) 228 , b ) 108 , c ) 1266 , d ) 188 , e ) 80
Rationale: "s = 200 / 9 * 18 / 5 = 80 kmph answer : e"
Answer: e
Python program:
a = 200 / 9
b = a * const_3_6
Problem: find the area of a parallelogram with base 32 cm and height 14 cm ?
Options: a ) 498 cm 2 , b ) 384 cm 2 , c ) 430 cm 2 , d ) 128 cm 2 , e ) 448 cm 2
Rationale: "area of a parallelogram = base * height = 32 * 14 = 448 cm 2 answer : e"
Answer: e
Python program:
a = 32 * 14
Problem: raman mixed 44 kg of butter at rs . 150 per kg with 36 kg butter at the rate of rs . 125 per kg . at what price per kg should he sell the mixture to make a profit of 40 % in the transaction ?
Options: a ) 129.25 , b ) 287.25 , c ) 194.25 , d ) 188.25 , e ) 112.25
Rationale: "explanation : cp per kg of mixture = [ 44 ( 150 ) + 36 ( 125 ) ] / ( 44 + 36 ) = rs . 138.75 sp = cp [ ( 100 + profit % ) / 100 ] = 138.75 * [ ( 100 + 40 ) / 100 ] = rs . 194.25 answer : c"
Answer: c
Python program:
a = 44 * 150
b = 36 * 125
c = a + b 
d = 36 + 44 
e = c / d
f = 44 * 150
g = 36 * 125
h = f + g 
i = 36 + 44 
j = h / i
k = 40 / 100
l = j * k
m = e + l
Problem: the average age of 42 students in a group is 16 years . when teacher â € ™ s age is included to it , the average increases by one . what is the teacher â € ™ s age in years ?
Options: a ) 31 , b ) 56 , c ) 41 , d ) 59 , e ) none
Rationale: "sol . age of the teacher = ( 43 ã — 17 â € “ 42 ã — 16 ) years = 59 years . answer d"
Answer: d
Python program:
a = 42 + 1
Problem: the l . c . m of two numbers is 2310 and their h . c . f is 30 . if one number is 231 the other is
Options: a ) 330 , b ) 300 , c ) 270 , d ) 250 , e ) 350
Rationale: "the other number = l . c . m * h . c . f / given number = 2310 * 30 / 231 = 300 answer is b ."
Answer: b
Python program:
a = 30 * 2310
b = a / 231
Problem: hcf and lcm two numbers are 12 and 396 respectively . if one of the numbers is 24 , then the other number is ?
Options: a ) 36 , b ) 198 , c ) 132 , d ) 264 , e ) 364
Rationale: "12 * 396 = 24 * x x = 198 answer : b"
Answer: b
Python program:
a = 12 * 396
b = a / 24
Problem: company kw is being sold , and both company a and company b were considering the purchase . the price of company kw is 30 % more than company a has in assets , and this same price is also 100 % more than company b has in assets . if companies a and b were to merge and combine their assets , the price of company kw would be approximately what percent of these combined assets ?
Options: a ) 66 % , b ) 79 % , c ) 86 % , d ) 116 % , e ) 150 %
Rationale: let the price of company a ' s assets be 100 price of assets of kw is 30 % more than company a ' s assets which is 130 price of assets of kw is 100 % more than company b ' s assets which means price of company b ' s assets is half the price of kw = 65 a + b = 165 kw = 130 kw / ( a + b ) * 100 = 130 / 165 * 100 = 78.78 % or 79 % b
Answer: b
Python program:
a = 100 + 30 
b = 100 + 30 
c = b / 2
d = 100 + c 
e = a / d
f = e * 100
Problem: two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 24 kmph and 21 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ?
Options: a ) 288 , b ) 540 , c ) 877 , d ) 278 , e ) 178
Rationale: "1 h - - - - - 5 ? - - - - - - 60 12 h rs = 24 + 21 = 45 t = 12 d = 45 * 12 = 540 answer : b"
Answer: b
Python program:
a = 21 - 24
b = 60 / a
c = b * 24
d = 21 - 24
e = 60 / d
f = e * 21
g = c + f
Problem: what is the sum of the greatest common factor and the lowest common multiple of 48 and 72 ?
Options: a ) 192 , b ) 120 , c ) 168 , d ) 160 , e ) 184
Rationale: "prime factorization of the given numbers 72 = 2 ^ 3 * 3 ^ 2 48 = 2 ^ 4 * 3 greatest common factor = 2 ^ 3 * 3 = 24 lowest common multiple = 2 ^ 4 * 3 ^ 2 = 144 sum = 24 + 144 = 168 answer c"
Answer: c
Python program:
a = 48 * 72
b = a / 4
Problem: the ration of the number of boys and girls in a college is 2 : 3 . if the percentage is increase in the number of boys and girls be 10 % and 20 % respectively . what will be the new ration ?
Options: a ) 21 : 22 , b ) 13 : 17 , c ) 15 : 43 , d ) 11 : 18 , e ) 15 : 23
Rationale: "let the number of boys and girls be 2 x and 3 x their increased number is 110 % of 2 x and 120 % of 3 x 2 x * 110 / 100 and 3 x * 120 / 100 11 x / 5 and 18 x / 5 required ratio = 11 x / 5 : 18 x / 5 = 11 : 18 answer is d"
Answer: d
Python program:
a = 10 / 100
b = a + 1 
c = 2 * b
d = 20 / 100
e = d + 1 
f = 3 * e
g = c / f
Problem: how many positive integers between 1 and 100 are there such that they are multiples of 13 ?
Options: a ) 6 , b ) 5 , c ) 4 , d ) 7 , e ) 3
Rationale: "multiples of 13 = 13 , 26,39 , - - - - - 91 number of multiples of 13 = > 13 * 7 = 91 answer is d"
Answer: d
Python program:
a = 100 - 1
b = a / 13
Problem: in the xy - coordinate plane , the graph of y = - x ^ 2 + 9 intersects line l at ( p , 4 ) and ( t , - 7 ) . what is the least possible value of the slope of line l ?
Options: a ) 6 , b ) 2 , c ) - 2 , d ) - 6 , e ) - 5.5
Rationale: "we need to find out the value of p and l to get to the slope . line l and graph y intersect at point ( p , 5 ) . hence , x = p and y = 5 should sactisfy the graph . soliving 5 = - p 2 + 9 p 2 = 4 p = + or - 2 simillarly point ( t , - 7 ) should satisfy the equation . hence x = t and y = - 7 . - 7 = - t 2 + 9 t = + or - 4 considering p = - 2 and t = 4 , the least slope is ( - 7 - 4 ) / ( 4 - 2 ) = - 5.5 imo option e is correct answer ."
Answer: e
Python program:
a = 7 - 4
b = 9 + 7 
c = math.sqrt(b)
d = 4 + 9 
e = math.sqrt(d)
f = c - e
g = a / f
Problem: a chemist mixes one liter of pure water with x liters of a 45 % salt solution , and the resulting mixture is a 15 % salt solution . what is the value of x ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 1 , e ) 3
Rationale: "concentration of salt in pure solution = 0 concentration of salt in salt solution = 45 % concentration of salt in the mixed solution = 15 % the pure solution and the salt solution is mixed in the ratio of - - > ( 45 - 15 ) / ( 15 - 0 ) = 2 / 1 1 / x = 2 / 1 x = 1 / 2 answer : c"
Answer: c
Python program:
a = 45 - 15
b = 15 / a
Problem: the average weight of 5 person ' s increases by 10.0 kg when a new person comes in place of one of them weighing 40 kg . what might be the weight of the new person ?
Options: a ) 76 kg , b ) 76.5 kg , c ) 90 kg , d ) data inadequate , e ) none of these
Rationale: "explanation : total weight increased = ( 5 x 10.00 ) kg = 50 kg . weight of new person = ( 40 + 50 ) kg = 90 kg . answer : c"
Answer: c
Python program:
a = 5 * 10
b = a + 40
Problem: two trains 140 m and 170 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 ) 10.9 sec , b ) 10.1 sec , c ) 10.6 sec , d ) 10.8 sec , e ) 11.16 sec
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 140 + 170 = 310 m . required time = 310 * 9 / 250 = 11.16 sec . answer : e"
Answer: e
Python program:
a = 140 + 170 
b = 60 + 40 
c = b * const_0_2778
d = a / c
Problem: the units digit of ( 3 ) ^ ( 44 ) + ( 10 ) ^ ( 46 ) is :
Options: a ) 2 , b ) 4 , c ) 1 , d ) 8 , e ) 0
Rationale: "any power of anything ending in zero always has a units digit of 0 . so the first term has a units digit of 0 . the period is 4 . this means , 3 to the power of any multiple of 4 will have a units digit of 1 . 3 ^ 44 has a units digit of 1 . of course 0 + 1 = 1 c"
Answer: c
Python program:
a = reminder * (
b = reminder + (
Problem: if a ( a + 8 ) = 9 and b ( b + 8 ) = 9 , where a ≠ b , then a + b =
Options: a ) − 8 , b ) − 2 , c ) 2 , d ) 46 , e ) 48
Rationale: "a ( a + 8 ) = 9 = > we have a = 1 or - 9 also b ( b + 8 ) = 9 = > b = 1 or - 9 given a ≠ b 1 ) when a = 1 , b = - 9 and a + b = - 8 1 ) when a = - 9 , b = 1 and a + b = - 8 answer choice a"
Answer: a
Python program:
a = 9 / 10
b = 9 / 10
c = 9 / b
d = a + c
Problem: what is the thousandths digit in the decimal equivalent of 66 / 5000 ?
Options: a ) 0 , b ) 1 , c ) 3 , d ) 5 , e ) 6
Rationale: "66 / 5000 = 66 / ( 5 * 10 ^ 3 ) = ( 66 / 5 ) * 10 ^ - 3 = 13.2 * 10 ^ - 3 = . 0132 thousandths digit = 3 answer c"
Answer: c
Python program:
a = 66 / 5000
b = 100 * a
c = math.floor(b)
Problem: a contractor undertook to do a piece of work in 6 days . he employed certain number of laboures but 7 of them were absent from the very first day and the rest could finish the work in only 10 days . find the number of men originally employed ?
Options: a ) 17.2 , b ) 16.5 , c ) 17.5 , d ) 17.9 , e ) 17.3
Rationale: "let the number of men originally employed be x . 6 x = 10 ( x â € “ 7 ) or x = 17.5 answer c"
Answer: c
Python program:
a = 10 * 7
b = 10 - 6
c = a / b
Problem: a container holding 12 ounces of a solution that is 1 part alcohol to 2 parts water is added to a container holding 8 ounces of a solution that is 1 part alcohol to 3 parts water . what is the ratio of alcohol to water in the resulting solution ?
Options: a ) 2 : 5 , b ) 3 : 7 , c ) 3 : 5 , d ) 4 : 7 , e ) 7 : 3
Rationale: "container 1 has 12 ounces in the ratio 1 : 2 or , x + 2 x = 12 gives x ( alcohol ) = 4 and remaining water = 8 container 2 has 8 ounces in the ratio 1 : 3 or , x + 3 x = 8 gives x ( alcohol ) = 2 and remaining water = 6 mixing both we have alcohol = 4 + 2 and water = 8 + 6 ratio thus alcohol / water = 6 / 14 = 3 / 7 answer : b"
Answer: b
Python program:
a = 1 + 2 
b = 1 / a
c = 12 * b
d = 1 + 3 
e = 1 / d
f = 8 * e
g = c + f 
h = 12 + 8 
i = 1 + 2 
j = 1 / i
k = 12 * j
l = 1 + 3 
m = 1 / l
n = 8 * m
o = k + n 
p = h - o
q = g / p
Problem: the inside dimensions of a rectangular wooden box are 4 meters by 5 meters by 6 meters . a cylindrical drum is to be placed inside the box so that it stands upright when the closed box rests on one of its six faces . of all such drums that could be used , what is the volume , in cubic meters , of the one that has maximum volume ?
Options: a ) 20 π
b ) 24 π
c ) 25 π
d ) 96 π
e ) 100 π
Rationale: you have three options here . approach is to calculate volumes for all of them and see which one is greatest . 1 . cylinder ' s base rests on a 4 x 5 side of the box . so , height becomes 6 and the maximum possible radius becomes 4 / 2 . so , maximum volume = π . ( 4 / 2 ) ^ 2.6 = π 24 2 . cylinder ' s base rests on a 5 x 6 side of the box . so , height becomes 4 and the maximum possible radius becomes 5 / 2 . so , maximum volume = π . ( 5 / 2 ) ^ 2.4 = π 25 3 . cylinder ' s base rests on a 4 x 6 side of the box . so , height becomes 5 and the maximum possible radius becomes 4 / 2 . so , maximum volume = π . ( 4 / 2 ) ^ 2.5 = π 20 option 2 gives maximum value and so that should be the answer , π 25 . answer : c
Answer: c
Python program:
a = 4 / 2
b = max(volume_cylinder)
c = 4 / 2
d = max(b)
Problem: there are some people in party , 1 / 3 rd left the party . then 2 / 5 th of the remaining left the party , then 2 / 3 rd of the remaining left the party . at last 10 were remaining . how many people were in total ?
Options: a ) 45 , b ) 27 , c ) 28 , d ) 26 , e ) 75
Rationale: "sol : 45 if x persons were there in total , then x × ( 1 – 1 / 3 ) × ( 1 – 2 / 5 ) × ( 1 – 2 / 3 ) = 10 x × 2 / 3 × 3 / 5 × 1 / 3 = 10 x = 75 answer : e"
Answer: e
Python program:
a = 1 / 3
b = 1 - a
c = 2 / 5
d = 1 - c
e = b * d
f = 2 / 3
g = 1 - f
h = e * g
i = 10 / h
Problem: the hcf of two numbers is 40 and the other two factors of their lcm are 11 and 12 . what is the largest number .
Options: a ) 462 , b ) 450 , c ) 488 , d ) 480 , e ) 555
Rationale: "explanation : hcf of the two numbers = 40 hcf will be always a factor of lcm 40 is factor of lcm other two factors are 11 & 12 then the numbers are ( 40 * 11 ) and ( 40 x 12 ) = 440 and 480 answer : option d"
Answer: d
Python program:
a = 40 * 12
Problem: bert and rebecca were looking at the price of a condominium . the price of the condominium was 110 % more than bert had in savings , and separately , the same price was also 20 % more than rebecca had in savings . what is the ratio of what bert has in savings to what rebecca has in savings .
Options: a ) 1 : 5 , b ) 1 : 4 , c ) 2 : 3 , d ) 4 : 7 , e ) 1 : 2
Rationale: "suppose bert had 100 so price becomes 210 , this 210 = 1.2 times r ' s saving . . so r ' s saving becomes 175 so required ratio is 100 : 175 = 4 : 7 answer : d"
Answer: d
Python program:
a = 100 + 110 
b = 100 / a
c = 100 + 20 
d = 100 / c
e = b / d
Problem: at what rate percent on simple interest will rs . 800 amount to rs . 950 in 5 years ?
Options: a ) 3.75 % , b ) 5.93 % , c ) 4.75 % , d ) 5.33 % , e ) 6.33 %
Rationale: "150 = ( 800 * 5 * r ) / 100 r = 3.75 % answer : a"
Answer: a
Python program:
a = 950 - 800
b = a / 800
c = b / 5
d = c * 100
Problem: in a school with 5 classes , each class has 2 students less than the previous class . how many students are there in the largest class if the total number of students at school is 115 ?
Options: a ) 25 , b ) 26 , c ) 27 , d ) 28 , e ) 29
Rationale: "let x be the number of students in the largest class . then x + ( x - 2 ) + ( x - 4 ) + ( x - 6 ) + ( x - 8 ) = 115 5 x - 20 = 115 5 x = 135 x = 27 the answer is c ."
Answer: c
Python program:
a = 2 + 2 
b = 2 + a 
c = 2 + 2 
d = c + 2 
e = b + d 
f = 2 + 2 
g = f + 2 
h = g + 2 
i = e + h 
j = 115 - i
k = j / 5
l = 2 + 2 
m = l + 2 
n = m + 2 
o = k + n
Problem: the length of 3 ropes are in the ratio 4 : 5 : 6 . if the sum of the weights of the longest and the shortest rope is 100 metres more than the length of the third rope , what is the length of the shortest rope ?
Options: a ) 80 m , b ) 180 m , c ) 100 m , d ) 60 m , e ) of these
Rationale: let the lengths of the three ropes be 4 k , 5 k and 6 k respectively . 4 k + 6 k = 5 k + 100 = > 5 k = 100 = > k = 20 therefore the weight of the lightest boy = 4 k = 4 ( 20 ) = 80 m answer : a
Answer: a
Python program:
a = 6 + 4 
b = a - 5
c = 100 / b
d = c * 4
Problem: on a ranch , a rancher can place a loop of rope , called a lasso , once in every 2 throws around a cow ’ s neck . what is the probability that the rancher will be able to place a lasso around a cow ’ s neck at least once in 6 attempts ?
Options: a ) 3 / 4 , b ) 7 / 8 , c ) 15 / 16 , d ) 31 / 32 , e ) 63 / 64
Rationale: "p ( missing all 6 ) = ( 1 / 2 ) ^ 6 = 1 / 64 p ( success on at least one attempt ) = 1 - 1 / 64 = 63 / 64 the answer is e ."
Answer: e
Python program:
a = 1 / 2
b = a ** 6
c = 1 - b
Problem: two pipes can fill the cistern in 10 hr and 12 hr respectively , while the third empty it in 50 hr . if all pipes are opened simultaneously , then the cistern will be filled in
Options: a ) 6.12 hr , b ) 8 hr , c ) 8.5 hr , d ) 10 hr , e ) none of these
Rationale: solution : work done by all the tanks working together in 1 hour . 1 / 10 + 1 / 12 − 1 / 50 = 8 / 49 hence , tank will be filled in 49 / 8 = 6.12 hour option ( a )
Answer: a
Python program:
a = 1 / 10
b = 1 / 12
c = a + b 
d = 1 / 50
e = c - d
f = 1/(e)
Problem: 9 people decided to split the restaurant bill evenly . if the bill was $ 514.16 dollars , how much money did they 1 cent is the smallest unit ?
Options: a ) $ 514.16 , b ) $ 514.17 , c ) $ 514.18 , d ) $ 514.19 , e ) $ 514.20
Rationale: "this is equivalent to finding the first number that is divisible by 9 that occurs after 51416 . in order to divide the sum in 9 parts , the amount must be divisible by 9 divisibility rule of 9 : the sum of the digits must be divisible by 9 sum of digits of 51416 = 17 and 18 is divisible by 9 . hence , we need to add 1 to this number for it to be divisible by 9 correct option : b"
Answer: b
Python program:
a = 3 / 100
b = 514 + 16
Problem: a certain car increased its average speed by 5 miles per hour in each successive 5 - minute interval after the first interval . if in the first 5 - minute interval its average speed was 26 miles per hour , how many miles did the car travel in the third 5 - minute interval ?
Options: a ) 1.0 , b ) 1.5 , c ) 2.0 , d ) 2.5 , e ) 3.0
Rationale: in the third time interval the average speed of the car was 22 + 5 + 5 = 36 miles per hour ; in 5 minutes ( 1 / 12 hour ) at that speed car would travel 36 * 1 / 12 = 3 miles . answer : e .
Answer: e
Python program:
a = 26 + 5 
b = a + 5 
c = 5 / const_60
d = b * c
Problem: there are 13 boys and 10 girls in a class . if three students are selected at random , in how many ways that 1 girl & 2 boys are selected ?
Options: a ) 120 , b ) 480 , c ) 780 , d ) 720 , e ) 800
Rationale: n ( s ) = sample space = 23 c 3 = 1771 e = event that 1 girl and 2 boys are selected n ( e ) = we have to select 2 boys from 13 and 1 girl from 10 = 13 c 2 * 10 c 1 = 780 ans - c
Answer: c
Python program:
a = math.comb(13, 2)
b = math.comb(10, 1)
c = a * b