euclaise/mathqa_programs huggingface dataset:
Problem: in x game of billiards , x can give y 20 points in 45 and he can give z 30 points in 45 . how many points can y give z in x game of 100 ?
Options: a ) 30 , b ) 20 , c ) 25 , d ) 40 , e ) 50
Rationale: "x scores 45 while y score 40 and z scores 30 . the number of points that z scores when y scores 100 = ( 100 * 30 ) / 25 = 60 . in x game of 100 points , y gives ( 100 - 60 ) = 40 points to c . d"
Answer: d
Python program:
a = 45 - 20
b = a * 3
c = 45 - 30
d = c * 3
e = b - d
Problem: bill spends two days driving from point a to point b . on the first day , he drove 2 hours longer and at an average speed 5 miles per hour faster than he drove on the second day . if during the two days he drove a total of 680 miles over the course of 18 hours , what was his average speed on the second day , in miles per hour ?
Options: a ) 20 , b ) 25 , c ) 28 , d ) 30 , e ) 35
Rationale: first recognize that we have two pieces of information regarding the time bill spent driving each day . on day 1 , bill drove 2 hours longer than he drove on day 2 . so , let x = # of driving hours on day 2 then x + 2 = # of driving hours on day 1 bill drove a total of 18 hours so , x + ( x + 2 ) = 18 simplify : 2 x + 2 = 18 solve , x = 8 so , bill drove 10 hours on day 1 and he drove 8 hours on day 2 now let ' s solve the question by starting with a word equation . let x = speed driven on day 2 so , x + 5 = speed driven on day 1 ( distance traveled on day 1 ) + ( distance traveled on day 2 ) = 680 distance = ( rate ) ( time ) we get : ( x + 5 ) ( 10 ) + ( x ) ( 8 ) = 680 expand : 10 x + 50 + 8 x = 680 simplify : 18 x + 50 = 680 18 x = 630 x = 35 ( mph ) answer : e
Answer: e
Python program:
a = 2 * 5
b = a * 5
c = 680 - b
d = 2 * 5
e = 2 * 4
f = d + e 
g = c / f
Problem: the expenditure of an woman increase consistently by 30 % per year . if her present expenditure is rs . 1000 then what will her expenditure be after 3 years ?
Options: a ) 2107 , b ) 2197 , c ) 2187 , d ) 2177 , e ) 2167
Rationale: explanation : expenditure = 1000 x 1.3 x 1.3 x 1.3 = 2197 answer : option b
Answer: b
Python program:
a = 30 / 100
b = 1 + a 
c = b ** 3
d = c * 1000
Problem: what percent of 6.3 kg is 25 gms ?
Options: a ) 39 , b ) 66 , c ) 288 , d ) 19 , e ) 17
Rationale: "explanation : required percentage = ( 25 / 63000 * 100 ) % = 39 / 100 % = 0.39 % answer : a ) . 39 %"
Answer: a
Python program:
a = 6 / 3
b = a * 100
Problem: the average of 45 results is 9 . the average of first 22 of them is 15 and that of last 22 is 20 . find the 23 result ?
Options: a ) 515 , b ) 480 , c ) 750 , d ) 650 , e ) 560
Rationale: "23 th result = sum of 45 results - sum of 44 results 9 * 45 - 15 * 22 + 20 * 22 = 450 - 330 + 440 = 515 answer is a"
Answer: a
Python program:
a = 45 * 9
b = 22 * 20
c = a - b
d = 22 * 15
e = c - d
Problem: at what rate percent per annum will a sum of money double in 5 years .
Options: a ) 20.0 % , b ) 13.5 % , c ) 11.5 % , d ) 14.5 % , e ) 21.5 %
Rationale: let principal = p , then , s . i . = p and time = 8 years rate = [ ( 100 x p ) / ( p x 5 ) ] % = 20.0 % per annum . answer : a
Answer: a
Python program:
a = 100 / 5
Problem: the percentage increase in the area of rectangle , if each of its side is increased by 20 % is ?
Options: a ) 30 % , b ) 44 % , c ) 50 % , d ) 55 % , e ) 60 %
Rationale: "let original length = x meters original breadth = y meters original area = xy m ^ 2 new length = 120 x / 100 new breadth = 120 y / 100 = 6 y / 5 new area = 6 x / 5 * 6 y / 5 = 36 xy / 25 m ^ 2 increase percent = 11 xy / 25 * 1 / xy * 100 = 44 % answer is b"
Answer: b
Python program:
a = 100 + 20 
b = a / 100
c = 100 + 20 
d = c / 100
e = b * d
f = e - 1
g = f * 100
Problem: a cube is painted such that one pair of surfaces is painted brown and the other pair of surfaces is painted orange . the cube is cut in to 64 small cubes of equal size . find how many cubes have both the color brown and orange ?
Options: a ) 22
b ) 16
c ) 11
d ) 12
e ) 10
Rationale: there are 6 surfaces to the cube . in which opposite surfaces are painted brown and other 2 opposite surfaces are painted orange . then 4 edges of the cube have both the colors . since the big cube cut in to 64 smaller cubes , the 4 edges of the cube have both the colors . since the big cube cut into 64 smaller cubes , the 4 edges of the big cube has 4 × 4 = 16 smaller cubes have both brown and orange colors . answer = 16 answer : b
Answer: b
Python program:
a = 64 / 2
b = a / 2
Problem: a bag contains 4 red , 4 blue and 2 green balls . if 2 ballsare picked at random , what is the probability that both are red ?
Options: a ) 2 / 15 , b ) 2 / 21 , c ) 5 / 26 , d ) 3 / 29 , e ) 4 / 27
Rationale: "p ( both are red ) , = 4 c 210 c 2 = 4 c 210 c 2 = 6 / 45 = 2 / 15 a"
Answer: a
Python program:
a = math.comb(4, 2)
b = 4 + 4 
c = b + 2 
d = math.comb(c, 2)
e = a / d
Problem: in the xy - coordinate system , if ( m , n ) and ( m + 3 , n + k ) are two points on the line with the equation x = 2 y + 5 , then k =
Options: a ) 1 / 2 , b ) 1 , c ) 2 , d ) 3 / 2 , e ) 4
Rationale: since ( m , n ) and ( m + 2 , n + k ) are two points on the line with the equation x = 2 y + 5 they should satisfy m = 2 n + 5 and m + 3 = 2 * ( n + k ) + 5 . by 1 st equation we have m - 2 n = 5 and by 2 nd equation m - 2 n = 2 k + 2 - - - > 5 = 2 k + 2 - - - > k = 3 / 2 . the answer is , therefore , ( d ) .
Answer: d
Python program:
a = 5 + 3 
b = a - 5
c = b / 2
Problem: each factor of 210 is inscribed on its own plastic ball , and all of the balls are placed in a jar . if a ball is randomly selected from the jar , what is the probability that the ball is inscribed with a multiple of 45 ?
Options: a ) 1 / 16 , b ) 5 / 42 , c ) 1 / 8 , d ) 3 / 16 , e ) 1 / 4
Rationale: "210 = 2 * 3 * 5 * 7 , so the # of factors 210 has is ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 16 ( see below ) ; 42 = 2 * 3 * 7 , so out of 16 factors only two are multiples of 42 : 42 and 210 , itself ; so , the probability is 2 / 16 = 5 / 42 . answer : b ."
Answer: b
Python program:
a = math.comb(45, 1)
b = a / 45
c = 3 ** 2
d = b / c
Problem: in a garden , 26 trees are planted at equal distances along a yard 300 metres long , one tree being at each end of the yard . what is the distance between two consecutive trees ?
Options: a ) 10 metres , b ) 20 metres , c ) 14 metres , d ) 12 metres , e ) 13 metres
Rationale: "between 26 trees , there are 25 gaps length of each gap = 300 / 25 = 12 i . e . , distance between two consecutive trees = 12 answer : d"
Answer: d
Python program:
a = 26 - 1
b = 300 / a
Problem: the product of 4 consecutive even numbers is always divisible by :
Options: a ) 384 , b ) 350 , c ) 400 , d ) 200 , e ) 250
Rationale: the product of 4 consecutive numbers is always divisible by 4 ! . since , we have 4 even numbers , we have an additional 2 available with each number . now , using both the facts , we can say that the product of 4 consecutive even numbers is always divisible by , 2 ^ 4 * 4 ! 16 * 24 = 384 answer a
Answer: a
Python program:
a = 2 ** 4
b = math.factorial(4)
c = a * b
Problem: workers at a campaign office have 2500 fliers to send out . if they send out 1 / 5 of them in the morning and 1 / 4 of the remaining ones out during the afternoon , how many are left for the next day ?
Options: a ) 300 , b ) 800 , c ) 1500 , d ) 1200 , e ) 1900
Rationale: ( 1 / 5 ) * 2500 = 500 remaining = 2500 - 500 = 2000 ( 1 / 4 ) of remaining = ( 1 / 4 ) * 2000 = 500 remaining now = 2000 - 500 = 1500 answer : option c
Answer: c
Python program:
a = 2500 / 5
b = 2500 - a
c = 2500 / 5
d = 2500 - c
e = d / 4
f = b - e
Problem: two numbers n and 24 have lcm = 48 and gcf = 8 . find n .
Options: a ) 16 , b ) 56 , c ) 76 , d ) 87 , e ) 24
Rationale: "the product of two integers is equal to the product of their lcm and gcf . hence . 24 * n = 48 * 8 n = 48 * 8 / 24 = 16 correct answer a"
Answer: a
Python program:
a = 48 * 8
b = a / 24
Problem: what is the sum of all the multiples of 8 between 30 and 100 ?
Options: a ) 485 , b ) 72 , c ) 547 , d ) 104 , e ) 624
Rationale: "you first have to know all the multiples of 8 between 30 and 100 . they are 8 , 16 , 24 , 32,40 , 48,56 , 64,72 , 80,88 and 96 . if you add all these numbers together , you get 624 . final answer : e"
Answer: e
Python program:
a = 12 + 2 
b = a + 1 
c = 12 + 2 
d = 2 + 4 
e = d + 4 
f = 10 - 1
g = e + f 
h = 2 + 4 
i = h + 4 
j = g + i 
k = 10 + 2 
l = j + k 
m = c + l 
n = b + m 
o = 12 + 2 
p = o + 1 
q = p + 1 
r = n + q 
s = r + 8 
t = 2 + 4 
u = s + t
Problem: a trailer carries 3 , 4 and 5 crates on a trip . each crate weighs no less than 1250 kg . what is the maximum weight of the crates on a single trip ?
Options: a ) 1250 , b ) 6250 , c ) 600 , d ) 7500 , e ) 375
Rationale: "max no . of crates = 5 . max weight = 1250 kg max . weight carried = 5 * 1250 = 6250 kg = b"
Answer: b
Python program:
a = 5 * 1250
Problem: what will be the difference between simple and compound interest @ 10 % per annum on a sum of $ 1000 after 4 years ?
Options: a ) $ 48.12 , b ) $ 52.64 , c ) $ 64.10 , d ) $ 72.85 , e ) $ 60.10
Rationale: "s . i . = 1000 * 10 * 4 / 100 = $ 400 c . i . = 1000 * ( 1 + 10 / 100 ) ^ 4 - 1000 = $ 464.10 difference = 464.10 - 400 = $ 64.10 answer is c"
Answer: c
Python program:
a = 10 / 100
b = a + 1 
c = b ** 4
d = 1000 * c
e = d - 1000
f = 10 / 100
g = 1000 * f
h = g * 4
i = e - h
Problem: if n is a positive integer and n ^ 2 is divisible by 150 , then what is the largest positive integer that must divide n ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: "150 = 2 * 3 * 5 ^ 2 if 150 divides n ^ 2 , then n must be divisible by 2 * 3 * 5 = 30 the answer is c ."
Answer: c
Python program:
a = 150 / 2
b = math.sqrt(a)
c = b * 2
Problem: the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 5 . if the sum of their ages is 196 , what is the difference between the ages of patrick and monica ?
Options: a ) 27 , b ) 64 , c ) 45 , d ) 72 , e ) 18
Rationale: "ages of p and mi = 3 x : 5 x ages of mi and mo = 3 x : 5 x rationalizing their ages . ratio of their ages will be 9 x : 15 x : 25 x sum = 49 x = 196 x = 4 difference if ages of pa and mo = 25 x - 9 x = 16 x = 16 * 4 = 64 answer b"
Answer: b
Python program:
a = 5 * 5
b = 3 * 3
c = 3 * 5
d = b + c 
e = 5 * 5
f = d + e 
g = 196 / f
h = a * g
i = 3 * 3
j = 3 * 3
k = 3 * 5
l = j + k 
m = 5 * 5
n = l + m 
o = 196 / n
p = i * o
q = h - p
Problem: if tim had lunch at $ 50.50 and he gave 20 % tip , how much did he spend ?
Options: a ) $ 30.60 , b ) $ 60.60 , c ) $ 70.60 , d ) $ 40.60 , e ) $ 50.60
Rationale: "the tip is 20 % of what he paid for lunch . hence tip = 20 % of 50.50 = ( 20 / 100 ) * 50.50 = 101 / 100 = $ 10.10 total spent 50.50 + 10.10 = $ 60.60 correct answer b"
Answer: b
Python program:
a = 50 * 50
b = a / 100
c = 50 + 50
Problem: 20 . a certain church bell rings the bell twice at half past the hour and 4 times at the hour plus an additional number of rings equal to what ever time it is . how many rings will the clock make from 6 : 20 in the morning to 09 : 50 in the morning ?
Options: a ) 44 . , b ) 36 . , c ) 42 . , d ) 46 . , e ) 50 .
Rationale: unless i understood the problem correctly , i get 58 @ 6 : 30 - 2 @ 7 - 4 + 7 = 11 @ 7 : 30 - 2 @ 8 - 12 @ 8 : 30 - 2 @ 9 - 13 @ 9 : 30 - 2 totals to a = 44
Answer: a
Python program:
a = 4 * 2
b = 4 * 4
c = a + b 
d = 3 + 4 
e = 4 + 1 
f = d + e 
g = f + 6 
h = c + g
Problem: if a book is sold at 7 % profit instead of 7 % loss , it would have brought rs 14 more . find out the cost price of the book
Options: a ) 75 , b ) 100 , c ) 60 , d ) 70 , e ) 80
Rationale: "let c . p . of the book be rs . ’ x ’ given , 1.07 x - 0.93 x = 14 = > 0.14 x = 14 = 14 / 0.14 = rs 100 answer : b"
Answer: b
Python program:
a = 7 / 2
b = 100 * a
c = b / 7
Problem: mahesh marks an article 15 % above the cost price of rs . 540 . what must be his discount percentage if he sells it at rs . 460 ?
Options: a ) 18 % , b ) 21 % , c ) 25.9 % , d ) 19 % , e ) none of these
Rationale: cp = rs . 540 , mp = 540 + 15 % of 540 = rs . 621 sp = rs . 460 , discount = 621 - 460 = 161 discount % = 161 / 621 * 100 = 25.9 % answer : c
Answer: c
Python program:
a = 100 + 15 
b = a / 100
c = 540 * b
d = c - 460
e = d * 100
f = 100 + 15 
g = f / 100
h = 540 * g
i = e / h
Problem: a shopkeeper has 280 kg of apples . he sells 50 % of these at 20 % profit and remaining 60 % at 30 % profit . find his % profit on total .
Options: a ) 24 % , b ) 25 % , c ) 26 % , d ) 28 % , e ) 35 %
Rationale: "if the total quantity was 100 then 50 x 20 % + 60 x 30 % = 28 this profit will remain same for any total quantity unless the % of products remains the same . hence ' d ' is the answer"
Answer: d
Python program:
a = 280 * 50
b = a / 100
c = 100 + 20 
d = c / 100
e = b * d
f = 280 * 60
g = f / 100
h = 100 + 30 
i = h / 100
j = g * i
k = e + j 
l = k - 280
m = l * 100
n = m / 280
Problem: s ( n ) is a n - digit number formed by attaching the first n perfect squares , in order , into one integer . for example , s ( 1 ) = 1 , s ( 2 ) = 14 , s ( 3 ) = 149 , s ( 4 ) = 14916 , s ( 5 ) = 1491625 , etc . how many digits y are in s ( 99 ) ?
Options: a ) y = 350 , b ) y = 353 , c ) y = 354 , d ) y = 356 , e ) y = 357
Rationale: "focus on the points where the number of digits in squares change : 1 , 2 , 3 - single digit squares . first 2 digit number is 10 . 4 , 5 , . . . 9 - two digit squares . to get 9 , the last number with two digit square , think that first 3 digit number is 100 which is 10 ^ 2 . so 9 ^ 2 must be the last 2 digit square . 10 , 11 , 12 , . . . 31 - three digit squares . to get 31 , think of 1000 - the first 4 digit number . it is not a perfect square but 900 is 30 ^ 2 . 32 ^ 2 = 2 ^ 10 = 1024 , the first 4 digit square . 32 - 99 - four digit squares . to get 99 , think of 10,000 - the first 5 digit number which is 100 ^ 2 . so number of digits in s ( 99 ) = 3 * 1 + 6 * 2 + 22 * 3 + 68 * 4 = 3 + 12 + 66 + 272 = 353 . b"
Answer: b
Python program:
a = const_60 + 4 
b = a + 4 
c = const_60 + 4 
d = c + 4 
e = d * 4
f = b + e 
g = 3 * 1
h = 3 * 2
i = h * 2
j = g + i 
k = f + j
Problem: a can do a piece of work in 12 days and b can do a piece of work in 18 days how many days will the work be completed if both of them work together ?
Options: a ) 15 , b ) 7.2 , c ) 7.7 , d ) 7.4 , e ) 8
Rationale: "a ' s 1 day work = 1 / 12 , b ' s 1 day work = 1 / 18 ; ( a + b ) 1 day work = 1 / 12 + 1 / 18 = 5 / 36 ; they can finish the work in = 36 / 5 = 7.2 answer : b"
Answer: b
Python program:
a = 1/(12)
b = 1/(18)
c = a + b 
d = 1/(c)
Problem: how many two - digit numbers yield a remainder of 2 when divided by both 7 and 16 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "easier to start with numbers that are of the form 16 p + 2 - - - > 18,34 , 50,66 , 82,98 . out of these no number is also of the form 7 q + 2 . thus 0 is the answer . a is the correct answer ."
Answer: a
Python program:
a = 16 * 7
b = 2 + a 
c = 16 * 7
d = b - c
Problem: in track last week , the boys ran 34 laps . the girls ran 20 more laps . each lap is a 1 / 6 th of a mile . how many miles did the girls run ?
Options: a ) 9 miles , b ) 10 miles , c ) 11 miles , d ) 12 miles , e ) 13 miles
Rationale: the girls ran 34 + 20 = 54 laps . 54 x 1 / 6 = 54 / 6 , which reduces to 9 . the girls ran 9 miles correct answer a
Answer: a
Python program:
a = 34 + 20 
b = a / 6
Problem: the average weight of a group of boys is 30 kg . after a boy of weight 40 kg joins the group , the average weight of the group goes up by 1 kg . find the number of boys in the group originally ?
Options: a ) 14 , b ) 5 , c ) 6 , d ) 7 , e ) 9
Rationale: "let the number off boys in the group originally be x . total weight of the boys = 30 x after the boy weighing 40 kg joins the group , total weight of boys = 30 x + 40 so 30 x + 40 = 31 ( x + 1 ) = > x = 9 . answer : e"
Answer: e
Python program:
a = 30 + 1 
b = 40 - a
c = b + 1
Problem: in a garment industry , 12 men working 8 hours per day complete a piece of work in 10 days . to complete the same work in 8 days , working 20 hours a day , the number of men required is :
Options: a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: explanation : let the required number of men be x . less days , more men ( indirect proportion ) more working hrs per day , less men ( indirect proportion ) days 8 : 10 working hrs 20 : 8 : : 12 : x = > 8 x 20 x x = 10 x 8 x 12 = > x = 10 x 8 x 12 / ( 8 x 20 ) = > x = 6 answer : c
Answer: c
Python program:
a = 12 * 8
b = a * 10
c = b / 20
d = c / 8
Problem: find the minimum value of n such that 50 ! is perfectly divisible by 2520 ^ n .
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: 50 ! / 2520 ^ n 2520 - > 2 ^ 3 * 3 ^ 2 * 5 ^ 1 * 7 ^ 1 here 7 is the largest prime factor . . . so in order to find the minimum value of ` ` n ' ' , it is enough to find the minimum power of ` ` 7 ' ' . . . nd for maximum value of ` ` n ' ' , find max power of 7 . . . for max . value of n , find 50 / 7 ^ 1 + 50 / 7 ^ 2 = 7 + 1 = 8 [ quotient only ] max . value of n which is perfectly divisible by 2520 ^ n is ( 8 ) min . value is 1 max value : 8 min value : 1 answer : b
Answer: b
Python program:
a = 50 / 100
b = a * 2
Problem: a can finish a work in 10 days and b can do same work in half the time taken by a . then working together , what part of same work they can finish in a day ?
Options: a ) 1 / 5 , b ) 1 / 6 , c ) 1 / 7 , d ) 3 / 10 , e ) none of these
Rationale: "explanation : please note in this question , we need to answer part of work for a day rather than complete work . it was worth mentioning here because many do mistake at this point in hurry to solve the question so lets solve now , a ' s 1 day work = 1 / 10 b ' s 1 day work = 1 / 5 [ because b take half the time than a ] ( a + b ) ' s one day work = ( 1 / 10 + 1 / 5 ) = 3 / 10 so in one day 3 / 10 work will be done answer : d"
Answer: d
Python program:
a = 1 / 10
b = 1 / 10
c = b * 2
d = a + c
Problem: 81 men working 8 hours per day dig 30 m deep . how many extra men should be put to dig to a depth of 50 m working 6 hours per day ?
Options: a ) a ) 99 , b ) b ) 77 , c ) c ) 66 , d ) d ) 55 , e ) e ) 88
Rationale: "( 81 * 8 ) / 30 = ( x * 6 ) / 50 = > x = 180 180 – 81 = 99 answer : a"
Answer: a
Python program:
a = 81 * 8
b = a / 30
c = b * 50
d = c / 6
e = d - 81
Problem: fog + fog + fog + fog = 1464 . if f , o and g are digits in a 3 - digit number in the preceding equation the f + o + g = ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: given , fog + fog + fog + fog = 1464 4 ( fog ) = 1464 = > fog = 366 face value of f is : 3 face value of o is : 6 face value of g is : 6 so f + o + g = 3 + 6 + 6 = 15 answer : e
Answer: e
Python program:
a = 3 * 2
b = 3 + a 
c = 3 * 2
d = b + c
Problem: a is an integer greater than 39 but less than 51 , b is an integer greater than 49 but less than 61 , what is the range of a / b ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 3 / 4 , d ) 1 , e ) 5 / 4
Rationale: "min value of a / b will be when b is highest and a is lowest - - - > a = 40 and b = 60 so , a / b = 2 / 3 max value of a / b will be when b is lowest and a is highest - - - > a = 50 and b = 50 so , a / b = 1 range is 1 - ( 2 / 3 ) = 1 / 3 . answer should be b ."
Answer: b
Python program:
a = 51 - 1
b = 49 + 1 
c = a / b
d = 39 + 1 
e = 61 - 1
f = d / e
g = c - f
Problem: two sets of 6 consecutive positive integers have exactly one integer in common . the sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set ?
Options: a ) 14 , b ) 42 , c ) 28 , d ) 12 , e ) it can not be determined from the information given .
Rationale: "a = ( 1,2 , 3,4 , 5,6 ) , sum of this = 21 b = ( 6 , 7,8 , 9,10 , 11,12 ) , sum of this = 63 , the differenct between 63 - 21 = 42 hence , 42 is the answer i . e . b"
Answer: b
Python program:
a = 6 * 10
b = 4 * 6
c = a - b
Problem: how many paying stones , each measuring 2 1 / 2 m * 2 m are required to pave a rectangular court yard 50 m long and 16 1 / 2 m board ?
Options: a ) 99 , b ) 18 , c ) 165 , d ) 10 , e ) 15
Rationale: 50 * 33 / 2 = 5 / 2 * 2 * x = > x = 165 answer : c
Answer: c
Python program:
a = 1 / 2
b = 16 + a 
c = 50 * b
d = 1 / 2
e = 2 + d 
f = e * 2
g = c / f
Problem: how many digits are required to number a book containing 260 pages ?
Options: a ) 784 , b ) 672 , c ) 492 , d ) 372 , e ) 300
Rationale: "9 pages from 1 to 9 will require 9 digits . 90 pages from 10 to 99 will require 90 * 2 = 180 digits . 260 - ( 90 + 9 ) = 161 pages will require 161 * 3 = 483 digits . the total number of digits is 9 + 180 + 483 = 672 . the answer is b ."
Answer: b
Python program:
a = 10 - 1
b = 10 - 1
c = b * 10
d = c * 2
e = a + d 
f = 260 - 100
g = f + 1 
h = g * 3
i = e + h
Problem: log 3 n + log 15 n what is 3 digit number n that will be whole number
Options: a ) 3375 , b ) 7292 , c ) 8291 , d ) 3929 , e ) 2727
Rationale: "no of values n can take is 1 15 ^ 3 = 3375 answer : a"
Answer: a
Python program:
a = 15 ** 3
Problem: the sum of squares of 3 numbers is 764 and sum of their products taken two at a time is 500 . what is their sum ?
Options: a ) 48 , b ) 42 , c ) 52 , d ) 32 , e ) 33
Rationale: description : let the numbers be x , y , z . = > x 2 + y 2 + z 2 = 764 = > 2 ( xy + yz + xz ) = 2 * 500 = 1000 = > ( x + y + z ) 2 = ( x 2 + y 2 + z 2 ) + 2 ( xy + yz + xz ) = 1764 = > ( x + y + z ) = sqrt ( 1764 ) = 42 answer b
Answer: b
Python program:
a = 500 / 3
b = a / 3
c = b - 10
d = c - 3
Problem: a doctor prescribed 18 cubic centimeters of a certain drug to a patient whose body weight was 120 pounds . if the typical dosage is 2 cubic centimeters per 10 pounds of the body weight , by what percent was the prescribed dosage lesser than the typical dosage ?
Options: a ) 8 % , b ) - 37.5 % , c ) 11 % , d ) 12.5 % , e ) 14.8 %
Rationale: typical dosage per 10 pound of the body weight = 2 c . c typical dosage per 120 pound of the body weight = 2 * ( 120 / 10 ) = 2 * 12 = 24 c . c dosage prescribed by doctor for 120 pound patient = 18 c . c % prescribed dosage greater than the typical dosage = ( 18 - 24 / 16 ) * 100 % = ( - 6 / 16 ) * 100 % = - 37.5 % answer b
Answer: b
Python program:
a = 2 / 10
b = a * 120
c = b - 18
d = 2 / 10
e = d * 120
f = c / e
g = f * 100
Problem: the maximum number of students among them 1340 pens and 1280 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils ?
Options: a ) 25 , b ) 30 , c ) 20 , d ) 45 , e ) 90
Rationale: "number of pens = 1340 number of pencils = 1280 required number of students = h . c . f . of 1340 and 1280 = 20 answer is c"
Answer: c
Python program:
a = math.gcd(1340, 1280)
Problem: if the remainder is 10 when the integer n is divided by 18 , what is the remainder when 2 n is divided by 9 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "n = 18 k + 10 2 n = 2 ( 18 k + 10 ) = 4 k * 9 + 20 = 4 k * 9 + 2 * 9 + 2 = 9 j + 2 the answer is c ."
Answer: c
Python program:
a = 10 * 2
b = a - 18
Problem: the sum of two numbers is 15 and their geometric mean is 20 % lower than arithmetic mean . find the numbers .
Options: a ) 11,4 , b ) 12,3 , c ) 9,6 , d ) 3,2 , e ) 2,1
Rationale: "let a and b are two numbers so a + b = 15 . . . . ( 1 ) now gm = am * 80 / 100 or , sqrt ( ab ) = [ ( a + b ) / 2 ] * 80 / 100 squaring both sides . . . and after that putting the value of ( a + b ) . . . we get . . . . . ab = 36 now go through from option then we get 12 * 3 = 36 answer : b"
Answer: b
Python program:
a = 15 ** 2
b = 20 - a
c = b / 2
Problem: the value of ( 34.5 * 0.473 * 1.567 ) / ( 0.0673 * 23.25 * 7.57 ) is close to
Options: a ) 2 , b ) 1.15 , c ) 2.05 , d ) 2.16 , e ) 2.35
Rationale: "( 34.5 * 0.473 * 1.567 ) / ( 0.0673 * 23.25 * 7.57 ) = 25.5710895 / 11.845 = 2.16 answer : d"
Answer: d
Python program:
a = 34 * 5
b = a * 1
c = 7 * 57
d = c * 0
e = b / d
f = e / 10