euclaise/mathqa_programs huggingface dataset:
Problem: an exam consists of 8 true / false questions . brian forgets to study , so he must guess blindly on each question . if any score above 90 % is a passing grade , what is the probability that brian passes ?
Options: a ) 1 / 16 , b ) 37 / 256 , c ) 1 / 2 , d ) 219 / 256 , e ) 15 / 16
Rationale: "if you have 8 t or f and brian is going to guess then each question he has a 50 % chance of getting correct . if a passing score is 70 % it means brian needs to get 6 / 8 = 75 % , 7 / 8 = 87.5 % , or 8 / 8 = 100 % to pass . each is a possibility . if brian gets a 5 / 8 ( = 62.5 % ) or below he fails . so first figure out the number of ways that brian can get 6 out of 8 , 7 out of 8 , and 8 out of 8 questions correct . which is 8 choose 6 , equals is 28 , 8 choose 7 , equals 8 , and 8 choose 8 , equals 1 . this sums to 37 . the number of possible questions outcomes - the sum of 8 choose 8 , 7 choose 8 , 6 choose 8 … . 2 choose 8 , 1 choose 8 , and 0 choose 8 is 256 , so the chance of him passing is 15 / 16 . e"
Answer: e
Python program:
a = 1 / 2
b = a ** 8
c = 1 / 2
d = c ** 8
e = 8 * d
f = b + e 
g = 8 * 3
h = 1 / 2
i = h ** 8
j = g * i
k = f + j 
l = 1 - k
m = l / 10
n = 1 / 2
o = n ** 8
p = 1 / 2
q = p ** 8
r = 8 * q
s = o + r 
t = 8 * 3
u = 1 / 2
v = u ** 8
w = t * v
x = s + w 
y = 1 - x
z = m + y
Problem: a fruit seller had some oranges . he sells 30 % oranges and still has 420 oranges . how many oranges he had originally ?
Options: a ) 420 , b ) 600 , c ) 220 , d ) 400 , e ) none of these
Rationale: "explanation : he sells 30 % of oranges and still there are 420 oranges remaining = > 70 % of oranges = 420 ⇒ ( 70 × total oranges ) / 100 = 420 ⇒ total oranges / 100 = 6 ⇒ total oranges = 6 × 100 = 600 answer : option b"
Answer: b
Python program:
a = 30 / 100
b = 420 * a
c = 420 + b
Problem: 70 is subtracted from 30 % of a number , the result is 20 . find the number ?
Options: a ) 150 , b ) 997 , c ) 266 , d ) 300 , e ) 271
Rationale: ( 30 / 100 ) * x – 70 = 20 3 x = 900 x = 300 answer : d
Answer: d
Python program:
a = 70 + 20 
b = 30 / 100
c = a / b
Problem: sonika deposited rs . 8000 which amounted to rs . 9200 after 3 years at simple interest . had the interest been 0.5 % more . she would get how much ?
Options: a ) 9320 , b ) 96288 , c ) 26667 , d ) 1662 , e ) 2882
Rationale: "( 8000 * 3 * 0.5 ) / 100 = 120 9200 - - - - - - - - 9320 answer : a"
Answer: a
Python program:
a = 0 / 5
b = 9200 - 8000
c = b / 3
d = c / 8000
e = a + d 
f = e * 8000
g = f * 3
h = g + 8000
Problem: the average of 11 numbers is 60 . out of 11 numbers the average of first 6 no . is 88 , and last 6 numbers is 65 then find 6 th number ?
Options: a ) a ) 258 , b ) b ) 65 , c ) c ) 58 , d ) d ) 62 , e ) e ) 48
Rationale: "6 th number = sum of 1 st 6 no . s + sum of last 6 no . s - sum of 11 no . s answer = 6 * 88 + 6 * 65 - 11 * 60 = 258 answer is a"
Answer: a
Python program:
a = 6 * 88
b = 6 * 65
c = a + b 
d = 11 * 60
e = c - d
Problem: what is the area of a square field whose sides have a length of 13 meters ?
Options: a ) 225 sq m , b ) 169 sq m , c ) 128 sq m , d ) 267 sq m , e ) 231 sq m
Rationale: "13 * 13 = 169 sq m the answer is b ."
Answer: b
Python program:
a = square_area / (
Problem: what is the cp of rs 100 stock at 6 discount , with 1 / 5 % brokerage ?
Options: a ) 96.9 , b ) 96.3 , c ) 94.2 , d ) 96.7 , e ) 96.21
Rationale: "explanation : use the formula , cp = 100 â € “ discount + brokerage % cp = 100 - 6 + 1 / 5 94.2 thus the cp is rs 94.2 . answer : c"
Answer: c
Python program:
a = 100 - 6
b = 1 / 5
c = a + b
Problem: the edges of cuboid are 4 cm ; 5 cm and 6 cm . find its surface area ?
Options: a ) 228
b ) 148
c ) 992
d ) 772
e ) 222
Rationale: 2 ( 4 * 5 + 5 * 6 + 4 * 6 ) = 148 answer : b
Answer: b
Python program:
a = 2 * 4
b = a * 5
c = 2 * 6
d = c * 4
e = 2 * 5
f = 6 * e
g = d + f 
h = b + g
Problem: x does a work in 15 days . y does the same work in 30 days . in how many days they together will do the same work ?
Options: a ) 10 , b ) 12 , c ) 20 , d ) 30 , e ) 15
Rationale: "x ' s 1 day ' s work = 1 / 15 y ' s 1 day ' s work = 1 / 30 ( x + y ) ' s 1 day ' s work = ( 1 / 15 + 1 / 30 ) = 1 / 10 both together will finish the work in 10 days . correct option is a"
Answer: a
Python program:
a = 1 / 15
b = 1 / 30
c = a + b 
d = 1/(c)
Problem: two trains of equal lengths take 10 sec and 20 sec respectively to cross a telegraph post . if the length of each train be 120 m , in what time will they cross other travelling in opposite direction ?
Options: a ) 16 sec , b ) 13 sec , c ) 17 sec , d ) 21 sec , e ) 23 sec
Rationale: "speed of the first train = 120 / 10 = 12 m / sec . speed of the second train = 120 / 20 = 6 m / sec . relative speed = 12 + 6 = 18 m / sec . required time = ( 120 + 120 ) / 18 = 13 sec . answer : b"
Answer: b
Python program:
a = 120 * 2
b = speed + ( 
c = a / b
Problem: set a contains all the even numbers between 4 and 50 inclusive . set b contains all the even numbers between 104 and 150 inclusive . what is the difference between the sum of elements of set b and the sum of the elements of set a ?
Options: a ) 2400 , b ) 2550 , c ) 5050 , d ) 6275 , e ) 11325
Rationale: "set a contains 4 , 6 . . . 50 set b contains 104 , 106 . . . 150 number of terms in each set = 24 difference between corresponding terms in set a and b = 100 difference between sum of set b and set a = 100 * 24 = 2400 answer a"
Answer: a
Python program:
a = 104 - 4
b = 50 - 4
c = b / 2
d = c + 1 
e = a * d
Problem: for any number y , y * is defined as the greatest positive even integer less than or equal to y . what is the value of 8.2 – 8.2 * ?
Options: a ) 0.2 , b ) 1.2 , c ) 1.8 , d ) 2.2 , e ) 4.0
Rationale: "since y * is defined as the greatest positive even integer less than or equal to y , then 8.2 * = 4 ( the greatest positive even integer less than or equal to 5.2 is 4 ) . hence , 8.2 – 8.2 * = 8.2 - 6 = 2.2 answer : d ."
Answer: d
Python program:
a = math.floor(8, 2)
b = a - 1
c = 8 - 2
Problem: ( 1000 ) 7 ÷ ( 10 ) 20 = ?
Options: a ) 10 , b ) 100 , c ) 1000 , d ) 10000 , e ) none of these
Rationale: "explanation : = ( 103 ) 7 / ( 10 ) 20 = ( 10 ) 21 / ( 10 ) 20 = 10 ( 1 ) = 10 option a"
Answer: a
Python program:
a = 1000 * 10
Problem: a number when divided by 5 gives a number which is 8 more than the remainder obtained on dividing the same number by 34 . such a least possible number v is
Options: a ) 74 , b ) v = 75 , c ) v = 175 , d ) v = 680 , e ) 690
Rationale: i solved this question by plugging in numbers from the answer choices . a . ) 74 starting with answer choice a , i immediately eliminated it because 74 is not even divisible by 5 . b . ) 75 i divide 75 / 5 and get 15 as an answer . i divide 75 / 34 and get a remainder of 7 . 15 - 7 = 8 so i know the correct answer isb
Answer: b
Python program:
a = 34 * 2
b = 34 * 2
c = 8 * 5
d = b - c
e = 5 - 1
f = d / e
g = a + f
Problem: in the hillside summer camp there are 50 children . 80 % of the children are boys and the rest are girls . the camp administrator decided to make the number of girls only 10 % of the total number of children in the camp . how many more boys must she bring to make that happen ?
Options: a ) 55 , b ) 50 , c ) 40 . , d ) 30 . , e ) 25 .
Rationale: "given there are 50 students , 80 % of 50 = 40 boys and remaining 10 girls . now here 80 % are boys and 20 % are girls . now question is asking about how many boys do we need to add , to make the girls percentage to 20 or 20 % . . if we add 50 to existing 40 then the count will be 90 and the girls number will be 10 as it . now boys are 90 % and girls are 10 % . ( out of 100 students = 90 boys + 10 girls ) . imo option b is correct ."
Answer: b
Python program:
a = 100 - 10
b = a / 100
c = b * 50
d = 10 / 100
e = d * 50
f = c + e
Problem: a man invests rs . 8,000 at the rate of 5 % per annum . how much more should he invest at the rate of 8 % , so that he can earn a total of 6 % per annum ?
Options: a ) rs . 1200 , b ) rs . 1300 , c ) rs . 1500 , d ) rs . 4000 , e ) none of these
Rationale: explanation : interest on rs . 8000 at 5 % per annum = ( 8000 × 5 × 1 ) / 100 = rs . 400 let his additional investment at 8 % = x interest on rs . x at 8 % per annum = ( x × 8 × 1 ) / 100 = 2 x / 25 . to earn 6 % per annum for the total , interest = ( 8000 + x ) × 6 × 1 / 100 . = > 400 + 2 x / 25 = ( 8000 + x ) × 6 × 1 / 100 . = > 40000 + 8 x = ( 8000 + x ) × 6 . = > 40000 + 8 x = 48000 + 6 x . = > 2 x = 8000 . = > x = 4000 . answer : d
Answer: d
Python program:
a = 8 * 1000
b = 6 - 5
c = 8 - 6
d = b / c
e = a * d
Problem: how many 3 digit odd numbers do not use any digit more than once
Options: a ) 1720 , b ) 216 , c ) 224 , d ) 2460 , e ) 280
Rationale: "the way i solved it is a b c ( hundreds , tens , units ) c can be 1 3 5 7 9 ( any of the 5 digits ) a can be anything except ( d or 0 ) so 8 possibilitie b can be anything execpt ( a d c ) so 7 possibilities total ways are 7 * 8 * 5 = 280 ans : e"
Answer: e
Python program:
a = 3 + 1 
b = 10 - 1
c = b - 1
d = a * c
e = 10 - 1
f = e - 1
g = d * f
h = 10 - 1
i = h - 1
j = i - 1
k = g * j
Problem: a sum of 25 was paid for a work which a can do in 32 days , b in 20 days , b and c in 12 days and d in 24 days . how much did c receive if all the 4 work together ?
Options: a ) 14 ⁄ 3 , b ) 16 ⁄ 3 , c ) 15 ⁄ 3 , d ) 17 ⁄ 3 , e ) none of these
Rationale: a ' s one day ' s work = 1 ⁄ 32 b ' s one day ' s work = 1 ⁄ 20 ( b + c ) ' s one day ' s work = 1 ⁄ 12 ∴ c ' s one day ' s work = 1 ⁄ 12 - 1 ⁄ 20 = 1 ⁄ 30 d ' s one day ' s work = 1 ⁄ 24 ∴ ( a + b + c + d ) ' s one day ' s work 1 / 32 + 1 / 20 + 1 / 30 + 1 / 24 = 75 + 120 + 80 + 100 / 2400 = 375 ⁄ 2400 = 15 ⁄ 96 = 5 ⁄ 32 ∴ out of 5 ⁄ 32 of work done 1 ⁄ 30 of the work is done by c . ⇒ out of 25 paid for the work , c will receive 1 / 30 / 5 / 32 × 25 , i . e , 1 ⁄ 30 × 32 ⁄ 5 × 25 , i . e , 16 ⁄ 3 answer b
Answer: b
Python program:
a = math.lcm(32, 20)
b = math.lcm(a, 24)
c = 1 / 12
d = 1 / 20
e = c - d
f = 1 / e
g = b / f
h = math.lcm(32, 20)
i = math.lcm(h, 24)
j = i / 32
k = math.lcm(32, 20)
l = math.lcm(k, 24)
m = l / 20
n = j + m 
o = math.lcm(32, 20)
p = math.lcm(o, 24)
q = 1 / 12
r = 1 / 20
s = q - r
t = 1 / s
u = p / t
v = n + u 
w = math.lcm(32, 20)
x = math.lcm(w, 24)
y = x / 24
z = v + y 
A = 25 / z
B = g * A
Problem: a room 13 m 47 cm long and 7 m 77 cm broad is to be paved with square tiles . find the least number of square tiles required to cover the floor .
Options: a ) 116636 , b ) 116406 , c ) 116647 , d ) 116291 , e ) 116675
Rationale: "explanation : area of the room = ( 1347 x 777 ) cm 2 . size of largest square tile = h . c . f . of 1347 cm and 777 cm = 3 cm . area of 1 tile = ( 3 x 3 ) cm 2 . number of tiles required = ( 1347 × 777 ) / ( 3 × 3 ) = 116291 answer : option d"
Answer: d
Python program:
a = 13 * 100
b = a + 47 
c = 7 * 100
d = c + 77 
e = b * d
f = 2 * 4
g = f + 2 
h = 47 - g
i = 2 * 4
j = i + 2 
k = 47 - j
l = h * k
m = e / l
Problem: if a number p is prime , and 2 p + 3 = q , where q is also prime , then the decimal expansion of 1 / q will produce a decimal with q - 1 digits . if this method produces a decimal with 166 digits , what is the units digit of the product of p and q ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "1 / 5 = 0.2 . . ( a repeating pattern one digit long ) a"
Answer: a
Python program:
a = 166 + 1 
b = a - 3
c = b / 2
d = 166 + 1 
e = d - 3
f = e / 2
g = f - 1
h = c - g
Problem: what will be the percentage increase in the area of the cube ' s surface if each of the cube ' s edges grows by 60 % ?
Options: a ) 150 % , b ) 160 % , c ) 156 % , d ) 158 % , e ) 162 %
Rationale: "the question is very easy . my logic is the following : a surface = 6 * a ^ 2 after 60 % increase a surface = 6 * ( ( 1.6 a ) ^ 2 ) = 6 * 2.56 * a ^ 2 the increase in the surface area = ( 6 * 2.56 * a ^ 2 - 6 * a ^ 2 ) / 6 * a ^ 2 = ( 6 * a ^ 2 ( 2.56 - 1 ) ) / ( 6 * a ^ 2 ) = 2.56 - 1 = 1.56 = 156 % answer : c"
Answer: c
Python program:
a = 60 / 100
b = 1 + a 
c = b ** 2
d = c - 1
e = d * 100
Problem: the workforce of company x is 60 % female . the company hired 20 additional male workers , and as a result , the percent of female workers dropped to 55 % . how many employees did the company have after hiring the additional male workers ?
Options: a ) 160 , b ) 220 , c ) 240 , d ) 360 , e ) 420
Rationale: let ' s xx be total quantity of employees 0.6 x = females before adding men 0.55 ( x + 20 ) = females after adding men as quantity of women does n ' t change we can make an equation : 0.6 x = 0.55 ( x + 20 ) 0.05 x = 11 x = 220 - this is quantity of employees before adding 2020 men so after adding it will be 240 answer is c
Answer: c
Python program:
a = 55 / 100
b = a * 20
c = 60 / 100
d = 55 / 100
e = c - d
f = b / e
g = f + 20
Problem: if | 20 x - 10 | = 90 , then find the product of the values of x ?
Options: a ) - 45 , b ) 50 , c ) - 62 , d ) 35 , e ) - 20
Rationale: "| 20 x - 10 | = 90 20 x - 10 = 90 or 20 x - 10 = - 90 20 x = 100 or 20 x = - 80 x = 5 or x = - 4 product = - 4 * 5 = - 20 answer is e"
Answer: e
Python program:
a = 90 - 10
b = 90 + 10 
c = a - b
d = c - 10
Problem: two brothers took the gmat exam , the higher score is x and the lower one is y . if the difference between the two scores is 1 / 3 , what is the value of x / y ?
Options: a ) 3 . , b ) 2 . , c ) 1 / 2 . , d ) 4 , e ) there is n ' t enough data to answer the question .
Rationale: answer is d : 4 x - y = ( x + y ) / 2 solving for x / y = 4
Answer: d
Python program:
a = 3 * 1
b = a / 3
c = 3 + b
Problem: let a be the event that a randomly selected two digit number is divisible by 2 and let b be the event that a randomly selected two digit number is divisible by 10 . what is p ( a and b ) ?
Options: a ) 1 / 20 , b ) 1 / 15 , c ) 1 / 12 , d ) 1 / 8 , e ) 1 / 2
Rationale: "p ( a and b ) = 1 / 2 * 1 / 10 = 1 / 20 the answer is a ."
Answer: a
Python program:
a = 2 - 1
b = 2 - 1
c = b * 2
d = a / c
e = 2 - 1
f = e * 2
g = 2 - 1
h = g * 2
i = f / h
j = d * i
Problem: in a flight of 600 km , an aircraft was slowed down due to bad weather . its average speed for the trip was reduced by 200 km / hr and the time of flight increased by 30 minutes . the duration of the flight is :
Options: a ) 1 hour , b ) 2 hour , c ) 3 hour , d ) 4 hour , e ) 5 hour
Rationale: "let the duration of the flight be x hours then 600 / x - 600 / x ( 1 / 2 ) = 200 = 600 / x - 1200 / 2 x + 1 = 200 = x ( 2 x + 1 ) = 3 = 2 xsquare + x - 3 = 0 = ( 2 x + 3 ) ( x - 1 ) = 0 = x = 1 hr ( neglecting the - ve value of x ) answer : option a"
Answer: a
Python program:
a = 200 * 30
b = a / 10
c = 600 / b
Problem: a person travels equal distances with speeds of 50 km / hr , 100 km / hr and 120 km / hr and takes a total time of 23 minutes . the total distance is ?
Options: a ) 15 km , b ) 30 km , c ) 45 km , d ) 50 km , e ) 60 km
Rationale: "let the total distance be 3 x km x / 50 + x / 100 + x / 120 = 23 / 60 23 x / 600 = 23 / 60 23 x = 230 x = 10 km total distance = 3 x = 30 km answer is b"
Answer: b
Python program:
a = 23 / const_60
b = 1 / 50
c = 1 / 100
d = b + c 
e = 1 / 120
f = d + e 
g = a / f
h = g * 3
i = h * 1000
Problem: two pipes can fill the cistern in 10 hr and 12 hr respectively , while the third empty it in 25 hr . if all pipes are opened simultaneously , then the cistern will be filled in
Options: a ) 7.5 hr , b ) 6.98 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 / 25 = 1 / 7 hence , tank will be filled in 6.98 hour option ( b )"
Answer: b
Python program:
a = 1 / 10
b = 1 / 12
c = a + b 
d = 1 / 25
e = c - d
f = 1/(e)
Problem: if 5 + 3 + 2 = 151022 , 9 + 2 + 4 = 183652 , then 7 + 2 + 5 = ?
Options: a ) 223888 , b ) 143547 , c ) 2607778 , d ) 126997 , e ) 127811
Rationale: if the given number is a + b + c then a . b | a . c | a . b + a . c - b ⇒ ⇒ 5 + 3 + 2 = 5.3 | 5.2 | 5.3 + 5.2 - 3 = 151022 ⇒ ⇒ 9 + 2 + 4 = 9.2 | 9.4 | 9.2 + 9.4 - 2 = 183652 7 + 2 + 5 = 7.2 | 7.5 | 7.2 + 7.5 - 2 = 143547 answer : b
Answer: b
Python program:
a = 7 * 2
b = a * 100
c = 7 * 5
d = b + c 
e = d * 100
f = 7 * 2
g = 7 * 5
h = f + g 
i = h - 2
j = e + i
Problem: the inner circumference of a circle race track 18 m wide is 880 m . find the radius of the outer circle .
Options: a ) 120 m
b ) 145 m
c ) 130 m
d ) 140 m
e ) 122 m
Rationale: let inner radius be r metres then 2 π r = 640 2 × 22 / 7 r = 880 44 / 7 r = 880 r = 880 × 7 / 44 = 140 m answer is d .
Answer: d
Python program:
a = 880 / math.pi
b = a / 2
Problem: 4 mat - weavers can weave 4 mats in 4 days . at the same rate , how many mats would be woven by 14 mat - weavers in 14 days ?
Options: a ) 25 , b ) 19 , c ) 39 , d ) 61 , e ) 49
Rationale: "let the required number of bottles be x . more weavers , more mats ( direct proportion ) more days , more mats ( direct proportion ) wavers 4 : 14 : : 4 : x days 4 : 14 4 * 4 * x = 14 * 14 * 4 x = ( 14 * 14 * 4 ) / ( 4 x 4 ) x = 49 . answer is e ."
Answer: e
Python program:
a = 14 / 4
b = 4 * a
c = 14 / 4
d = b * c
Problem: find √ ? / 15 = 4 ?
Options: a ) 76 , b ) 5776 , c ) 304 , d ) 3600 , e ) none
Rationale: "answer let √ n / 15 = 4 then √ n = 15 x 4 = 60 ∴ n = 60 x 60 = 3600 . correct option : d"
Answer: d
Python program:
a = 4 * 15
b = a ** 2
Problem: if a ( a - 1 ) = 20 and b ( b - 1 ) = 20 , where a ≠ b , then a + b =
Options: a ) − 48 , b ) − 1 , c ) 2 , d ) 46 , e ) 67
Rationale: "i . e . if a = 5 then b = - 4 or if a = - 4 then b = 5 but in each case a + b = - 5 + 4 = - 1 answer : option b"
Answer: b
Python program:
a = 1 + 20 
b = 1 - 20
c = a + b 
d = c - 1
e = d - 1
f = e - 1
g = f - 1
Problem: 10 % people of a village in sri lanka died by bombardment , 20 % of the remainder left the village on account of fear . if now the population is reduced to 3240 , how much was it in the beginning ?
Options: a ) a ) 3800 , b ) b ) 4200 , c ) c ) 4400 , d ) d ) 4500 , e ) e ) 4600
Rationale: "x * ( 90 / 100 ) * ( 80 / 100 ) = 3240 x = 4500 answer : d"
Answer: d
Python program:
a = 100 - 10
b = a / 100
c = 100 - 20
d = c / 100
e = b * d
f = 3240 / e
g = math.floor(f)
Problem: a sum of rs . 2743 is lent into two parts so that the interest on the first part for 8 years at 3 % per annum may be equal to the interest on the second part for 3 years at 5 % per annum . find the second sum ?
Options: a ) 1642 , b ) 1640 , c ) 1632 , d ) 1688 , e ) 6386
Rationale: "( x * 8 * 3 ) / 100 = ( ( 2743 - x ) * 3 * 5 ) / 100 24 x / 100 = 41145 / 100 - 15 x / 100 39 x = 41145 = > x = 1055 second sum = 2743 – 1055 = 1688 answer : d"
Answer: d
Python program:
a = 3 * 5
b = a * 2743
c = 3 * 5
d = 8 * 3
e = c + d 
f = b / e
g = 2743 - f
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 t 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 , t = 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: when positive integer n is divided by positive integer j , the remainder is 18 . if n / j = 134.08 , what is value of j ?
Options: a ) 22 , b ) 56 , c ) 78 , d ) 112 , e ) 225
Rationale: "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 134.08 here 134 is the quotient . given that remainder = 18 so , 134.08 = 134 + 18 / j so , j = 225 ans e"
Answer: e
Python program:
a = 4 * 10
b = a + 2 
c = 100 + b 
d = 134 - 8
e = 18 / d
Problem: a can finish a work in 18 days and b can do the same work in 15 days . b worked for 10 days and left the job . in how many days , a alone can finish the remaining work ?
Options: a ) 5 , b ) 5 1 / 2 , c ) 6 , d ) 8 , e ) none of these
Rationale: b ' s 10 day ' s work = ( 1 / 15 * 10 ) = 2 / 3 remaining work = ( 1 - 2 / 3 ) = 1 / 3 now , 1 / 18 work is done by a in 1 day 1 / 3 work is done by a in ( 18 * 1 / 3 ) = 6 days . correct option : c
Answer: c
Python program:
a = 1 / 15
b = a * 10
c = b * 18
d = c / 2
Problem: the difference of two numbers is 1375 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder . what is the smaller number ?
Options: a ) 240 , b ) 272 , c ) 295 , d ) 360 , e ) 252
Rationale: "let the smaller number be x . then larger number = ( x + 1375 ) . x + 1375 = 6 x + 15 5 x = 1360 x = 272 smaller number = 270 . answer b"
Answer: b
Python program:
a = 1375 + 15 
b = 6 - 1
c = a / b
Problem: the population of a town is 7600 . it decreases annually at the rate of 10 % p . a . what was its population 2 years ago ?
Options: a ) 9400 , b ) 8000 , c ) 8500 , d ) 9500 , e ) 10000
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 7600 ã — 100 / 90 ã — 100 / 90 = 9382 a )"
Answer: a
Python program:
a = 10 / 100
b = 7600 * a
c = 7600 - b
d = 10 / 100
e = 7600 * d
f = 7600 - e
g = 10 / 100
h = f * g
i = c - h
Problem: the average of first 10 prime numbers which are odd is ?
Options: a ) 22.2 , b ) 22.1 , c ) 15.3 , d ) 15.8 , e ) 14.6
Rationale: explanation : sum of first 10 prime no . which are odd = 158 average = 158 / 10 = 15.8 answer : d
Answer: d
Python program:
a = 1 + 3 
b = a + 1 
c = 3 + b 
d = 1 + 3 
e = d + 3 
f = c + e 
g = 10 + 1 
h = f + g 
i = 10 + 3 
j = h + i 
k = 1 + 3 
l = k + 3 
m = 10 + l 
n = j + m 
o = 1 + 3 
p = 1 + 3 
q = p + 1 
r = o + q 
s = 10 + r 
t = 1 + 3 
u = s + t 
v = n + u 
w = 1 + 3 
x = 1 + 3 
y = x + 1 
z = w + y 
A = 10 + z 
B = A + 10 
C = v + B 
D = 1 + 3 
E = 1 + 3 
F = E + 1 
G = D + F 
H = 1 + 3 
I = H + 3 
J = G + I 
K = 10 + 1 
L = J + K 
M = L + 10 
N = C + M 
O = 1 + 3 
P = 1 + 3 
Q = P + 1 
R = O + Q 
S = 10 + R 
T = N + S 
U = T / 10
Problem: on increasing the price of t . v . sets by 60 % , their sale decreases by 20 % . what is the effect on the revenue receipts of the shop ?
Options: a ) 4 , b ) 5 , c ) 56 , d ) 28 , e ) 7
Rationale: explanation : let the price be = rs . 100 , and number of units sold = 100 then , sale value = rs . ( 100 × 100 ) = rs . 10000 new sale value = rs . ( 160 × 80 ) = rs . 12800 increase % = 2800 / 10000 × 100 = 28 % answer : d
Answer: d
Python program:
a = 100 + 60 
b = 100 + 60 
c = b * 20
d = c / 100
e = d + 100 
f = a - e
Problem: a meal cost $ 35.50 adn there was no tax . if the tip was more than 2 pc but less than 12 pc of the price , then the total amount paid should be :
Options: a ) 40 - 43 , b ) 39 - 42 , c ) 39 - 42 , d ) 38 - 41 , e ) 36 - 40
Rationale: "2 % ( 35.5 ) = 0.71 12 % ( 35.5 ) = 4.26 total amount could have been 35.5 + 0.71 and 35.5 + 4.26 = > could have been between 36.21 and 39.76 = > approximately between 36 and 40 answer is e ."
Answer: e
Python program:
a = 35 * 50
b = a / 100
c = b + 35
Problem: in an office in singapore there are 60 % female employees . 50 % of all the male employees are computer literate . if there are total 62 % employees computer literate out of total 1200 employees , then the no . of female employees who are computer literate ?
Options: a ) 504 , b ) 674 , c ) 672 , d ) 960 , e ) none
Rationale: solution : total employees , = 1200 female employees , 60 % of 1200 . = ( 60 * 1200 ) / 100 = 720 . then male employees , = 480 50 % of male are computer literate , = 240 male computer literate . 62 % of total employees are computer literate , = ( 62 * 1200 ) / 100 = 744 computer literate . thus , female computer literate = 744 - 240 = 504 . answer : option a
Answer: a
Python program:
a = 62 / 100
b = 60 / 100
c = 1 - b
d = 50 / 100
e = c * d
f = a - e
g = f * 1200