euclaise/mathqa_programs huggingface dataset:
Problem: the ratio of expenditure and savings is 3 : 2 . if the income increases by 15 % and the savings increases by 6 % , then by how much percent should his expenditure increases ?
Options: a ) 22 , b ) 21 , c ) 88 , d ) 76 , e ) 29
Rationale: answer : b ) 21
Answer: b
Python program:
a = 15 - 6
b = a * 2
c = 15 * 3
d = b + c 
e = d / 3
Problem: in an election between the two candidates , the candidates who gets 70 % of votes polled is winned by 160 vote ’ s majority . what is the total number of votes polled ?
Options: a ) 750 , b ) 400 , c ) 800 , d ) 850 , e ) none of these
Rationale: "explanation : note : majority ( 40 % ) = difference in votes polled to win ( 70 % ) & defeated candidates ( 30 % ) 40 % = 70 % - 30 % 40 % - - - - - > 160 ( 40 * 4 = 160 ) 100 % - - - - - > 400 ( 100 * 4 = 400 ) answer : option b"
Answer: b
Python program:
a = 100 * 160
b = 100 - 70
c = 70 - b
d = a / c
Problem: the sum of three consecutive even numbers is 48 . find the middle number of the three ?
Options: a ) 14 , b ) 16 , c ) 18 , d ) 24 , e ) 64
Rationale: "three consecutive even numbers ( 2 p - 2 ) , 2 p , ( 2 p + 2 ) . ( 2 p - 2 ) + 2 p + ( 2 p + 2 ) = 48 6 p = 48 = > p = 8 . the middle number is : 8 p = 64 . answer : e"
Answer: e
Python program:
a = 48 - 10
b = a - 2
c = b / 4
d = c + 2 
e = d + 2 
f = e ** 2
g = 48 - 10
h = g - 2
i = h / 4
j = i + 2 
k = j + 2 
l = k + 2 
m = l ** 2
n = f + m 
o = 48 - 10
p = o - 2
q = p / 4
r = q ** 2
s = 48 - 10
t = s - 2
u = t / 4
v = u + 2 
w = v ** 2
x = r + w 
y = n + x
Problem: there are 8 stores in town that had a total of 24 visitors on a particular day . however , only 12 people went shopping that day ; some people visited more than one store . if 9 people visited exactly two stores each , and everyone visited at least one store , what is the largest number of stores anyone could have visited ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "9 people visited 2 stores each for 18 visits . to maximize the number of stores that one person visited , let ' s assume that 2 people visited 1 store each . the number of remaining visits is 24 - 18 - 2 = 4 , which is the maximum that one person could have visited . the answer is c ."
Answer: c
Python program:
a = 8 * 2
b = 24 - a
c = 12 - 8
d = c - 1
e = b - d
Problem: if a train , travelling at a speed of 80 kmph , crosses a pole in 5 sec , then the length of train is ?
Options: a ) 110.111 m , b ) 121.111 m , c ) 111.11 m , d ) 141.111 m , e ) 181.111 m
Rationale: "d = 80 * 5 / 18 * 5 = 111.11 m answer : c"
Answer: c
Python program:
a = 80 * const_0_2778
b = a * 5
Problem: in how many ways can the integer 120 be expressed as a product of two different positive integers ?
Options: a ) 10 , b ) 8 , c ) 5 , d ) 4 , e ) 2
Rationale: "120 = ( 2 ^ 3 ) * 3 * 5 since 120 is not a perfect square , no of ways = 5 answer c"
Answer: c
Python program:
a = 120 / 1
b = a / 3
c = b - 3
Problem: a fruit - salad mixture consists of apples , peaches , and grapes in the ratio 4 : 5 : 2 , respectively , by weight . if 44 pounds of the mixture is prepared , the mixture includes how many more pounds of apples than grapes ?
Options: a ) 15 , b ) 12 , c ) 8 , d ) 6 , e ) 4
Rationale: "we can first set up our ratio using variable multipliers . we are given that a fruit - salad mixture consists of apples , peaches , and grapes , in the ratio of 4 : 5 : 2 , respectively , by weight . thus , we can say : apples : peaches : grapes = 4 x : 5 x : 2 x we are given that 39 pounds of the mixture is prepared so we can set up the following question and determine a value for x : 4 x + 5 x + 2 x = 44 11 x = 44 x = 4 now we can determine the number of pounds of apples and of grapes . pounds of grapes = ( 2 ) ( 4 ) = 8 pounds of apples = ( 4 ) ( 4 ) = 16 thus we know that there are 16 – 8 = 8 more pounds of apples than grapes . answer is c ."
Answer: c
Python program:
a = 4 * 2
b = 2 * 2
c = a - b
Problem: if an integer n is to be selected at random from 1 to 99 , inclusive , what is probability n ( n + 1 ) will be divisible by 3 ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4
Rationale: "for n ( n + 1 ) to be a multiple of 3 , either n or n + 1 has to be a multiple of 3 . thus n must be of the form 3 k or 3 k - 1 , but not 3 k + 1 . the probability is 2 / 3 . the answer is d ."
Answer: d
Python program:
a = 2 / 3
Problem: a sum of money deposited at c . i . amounts to rs . 2420 in 2 years and to rs . 3267 in 3 years . find the rate percent ?
Options: a ) 11 , b ) 10 , c ) 28 , d ) 24 , e ) 35
Rationale: "explanation : 2420 - - - 847 100 - - - ? = > 35 % answer : option e"
Answer: e
Python program:
a = 3267 - 2420
b = a / 2420
c = b * 100
Problem: workers in a factory store products inside two different sized boxes . the bigger of the boxes can store 50 products while the smaller box can store 40 products . if a fresh batch of products numbering 212 in total were to be stored , what is the least number of products that will not be boxed ?
Options: a ) 23 , b ) 11 , c ) 2 , d ) 10 , e ) 12
Rationale: total products to be stored 212 the big box can store 50 small box can store 40 storing 212 products in big box 212 / 50 = 4 r 12 least number of toys that will be left unboxed = 12 answer : e
Answer: e
Python program:
a = 50 * 4
b = 212 - a
Problem: a recipe requires 2 1 / 2 ( mixed number ) cups of flour 2 3 / 4 ( mixed number ) cups of sugar and 1 1 / 3 ( mixed number ) cups of milk to make one cake . victor has 15 cups if flour , 16 cups of sugar and 8 cups of milk . what is the greatest number of cakes william can make using this recipe ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "less work up front : go through each item and see what the greatest number of cakes you can make with each . the lowest of these will be the right answer . flour : 15 cups , we need 2.5 cups each . just keep going up the line to see how many cakes we can make : that means i can make 2 cakes with 5 cups , so 6 cakes overall with 15 cups . i ' ve already got the answer narrowed to either a or b . sugar : 16 cups , we need 2.75 cups each . same principle . i can make 2 cups with 5.5 cups , so to make 6 cakes i ' d need 16.5 cups . i do n ' t have that much sugar , so we ' re limited to 5 cakes . no need to even do milk because we ' re already at 5 . sugar will be the limiting factor . answer is a"
Answer: a
Python program:
a = 1 / 2
b = 2 + a 
c = 15 / b
d = 3 / 4
e = d + 2 
f = 16 / e
g = math.floor(f)
h = min(c)
i = 1 / 3
j = i + 1 
k = 8 / j
l = min(h)
Problem: in a hostel , the number of students decreased by 5 % and the price of food increased by 20 % over the previous year . if each student consumes the same amount of food then by how much should the consumption of food be cut short by every student , so that the total cost of the food remains the same as that of the previous year ?
Options: a ) 19 % , b ) 12.3 % , c ) 25 % , d ) 40 % , e ) 9.4 %
Rationale: cost of food ( c ) = food consumed per student ( f ) * number of students ( n ) * price of food ( p ) originally , c = fnp when number of students decrease by 5 % , and the price of food increases by 20 % , c = f ( new ) * ( 0.95 n ) * ( 1.2 p ) = > f ( new ) = f / ( 0.95 * 1.2 ) = > f ( new ) = 0.877 f therefore the new cost of food must be 87.7 % of the old cost , or the cost of food must decrease by 12.28 % ( optionb )
Answer: b
Python program:
a = 100 * 100
b = 100 - 5
c = 100 + 20 
d = b * c
e = a / d
f = 1 - e
g = f * 100
Problem: at 15 : 00 there were 21 students in the computer lab . at 15 : 03 and every three minutes after that , 3 students entered the lab . if at 15 : 10 and every ten minutes after that 8 students left the lab , how many students were in the computer lab at 15 : 44 ?
Options: a ) 7 , b ) 14 , c ) 25 , d ) 27 , e ) 30
Rationale: initial no of students + 3 * ( 1 + no of possible 3 minute intervals between 15 : 03 and 15 : 44 ) - 8 * ( 1 + no of possible 10 minute intervals between 15 : 10 and 15 : 44 ) 20 + 3 * 14 - 8 * 4 = 27 d
Answer: d
Python program:
a = 44 / 3
b = math.floor(a)
c = b * 3
d = c + 21 
e = 44 / 8
f = math.floor(e)
g = f * 8
h = d - g
i = h + 3
Problem: if a speaks the truth 70 % of the times , b speaks the truth 60 % of the times . what is the probability that they tell the truth at the same time
Options: a ) 0.49 , b ) 0.48 , c ) 0.41 , d ) 0.42 , e ) 0.411
Rationale: "explanation : probability that a speaks truth is 70 / 100 = 0.7 probability that b speaks truth is 60 / 100 = 0.6 since both a and b are independent of each other so probability of a intersection b is p ( a ) × p ( b ) = 0.7 × 0.6 = 0.42 answer : d"
Answer: d
Python program:
a = 4 * 5
b = a * 5
c = 70 / b
d = 4 * 5
e = d * 5
f = 60 / e
g = c * f
Problem: find the curved surface area , if the radius of a cone is 21 m and slant height is 15 m ?
Options: a ) 660
b ) 770
c ) 880
d ) 900
e ) 990
Rationale: cone curved surface area = ï € rl 22 / 7 ã — 21 ã — 15 = 66 ã — 15 = 990 m ( power 2 ) answer is e .
Answer: e
Python program:
a = 21 * 15
b = math.pi * a
Problem: of the goose eggs laid at a certain pond , 2 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year . if 130 geese survived the first year and if no more than one goose hatched from each egg , how many goose eggs were laid at the pond ?
Options: a ) 280 , b ) 400 , c ) 540 , d ) 650 , e ) 840
Rationale: "of the goose eggs laid at a certain pond , 2 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month : 2 / 3 * 3 / 4 = 1 / 2 survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year : ( 1 - 3 / 5 ) * 1 / 2 = 1 / 5 survived the first year . 130 geese survived the first year : 1 / 5 * ( total ) = 130 - - > ( total ) = 650 . answer : d ."
Answer: d
Python program:
a = 3 / 5
b = 1 - a
c = 130 / b
d = 3 / 4
e = c / d
f = 2 / 3
g = e / f
Problem: a goods train runs at the speed of 72 km / hr and crosses a 250 m long platform in 22 sec . what is the length of the goods train ?
Options: a ) 299 , b ) 190 , c ) 276 , d ) 270 , e ) 281
Rationale: "speed = 72 * 5 / 18 = 20 m / sec . time = 22 sec . let the length of the train be x meters . then , ( x + 250 ) / 22 = 20 x = 190 m . answer : b"
Answer: b
Python program:
a = 72 / 3600
b = a * 1000
c = b * 22
d = c - 250
Problem: john was thrice as old as tom 6 years ago . john will be 9 / 7 times as old as tom in 6 years . how old is tom today ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: "j - 6 = 3 ( t - 6 ) , so j = 3 t - 12 j + 6 = 9 / 7 * ( t + 6 ) 7 j + 42 = 9 t + 54 7 ( 3 t - 12 ) + 42 = 9 t + 54 12 t = 96 t = 8 the answer is b ."
Answer: b
Python program:
a = 9 / 7
b = 6 * a
Problem: how many integers from 0 to 48 , inclusive , have a remainder of 1 when divided by 3 ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: "my ans is also c . 17 . explanation : 1 also gives 1 remainder when divided by 3 , another number is 4 , then 7 and so on . hence we have an arithmetic progression : 1 , 4 , 7 , 10 , . . . . . 46 , which are in the form 3 n + 1 . now we have to find out number of terms . tn = a + ( n - 1 ) d , where tn is the nth term of an ap , a is the first term and d is the common difference . so , 46 = 1 + ( n - 1 ) 3 or , ( n - 1 ) 3 = 45 or , n - 1 = 15 or , n = 16 b"
Answer: b
Python program:
a = 48 / 10
Problem: what is the prime factors ’ number of 36 ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "prime factors ’ number , as i assume , for a number x = a ^ n * b ^ m * c ^ o * d ^ p . . . is = n + m + o + p . . . so , 24 = 2 ^ 2 * 3 ^ 2 prime factors ’ number will be 2 + 2 = 4 . hence , answer is c ."
Answer: c
Python program:
a = 1 + 1 
b = 1 + a 
c = b + 1 
d = c + 1
Problem: how much time will a train of length 250 m moving at a speed of 72 kmph take to cross another train of length 300 m , moving at 36 kmph in the same direction ?
Options: a ) 55 , b ) 99 , c ) 88 , d ) 76 , e ) 12
Rationale: "the distance to be covered = sum of their lengths = 250 + 300 = 550 m . relative speed = 72 - 36 = 36 kmph = 36 * 5 / 18 = 10 mps . time required = d / s = 550 / 10 = 55 sec . answer : a"
Answer: a
Python program:
a = 250 + 300 
b = 72 - 36
c = b * const_0_2778
d = a / c
Problem: for all real numbers v , an operation is defined by the equation v * = v - v / 3 . if ( v * ) * = 20 , then v =
Options: a ) 36 , b ) 39 , c ) 42 , d ) 45 , e ) 48
Rationale: "( v * ) * = ( v - v / 3 ) - ( v - v / 3 ) / 3 20 = 2 v / 3 - 2 v / 9 = 4 v / 9 v = 45 the answer is d ."
Answer: d
Python program:
a = 1 / 3
b = 1 - a
c = 20 / b
d = 1 / 3
e = 1 - d
f = c / e
Problem: ( 4300231 ) - ? = 2535618
Options: a ) 1865113 , b ) 1775123 , c ) 1764613 , d ) 1675123 , e ) none of them
Rationale: "let 4300231 - x = 2535618 then x = 4300231 - 2535618 = 1764613 answer is c"
Answer: c
Python program:
a = 4 + 1 
b = a ** 4
c = 4300231 * b
Problem: the difference of 2 digit no . & the no . obtained by interchanging the digits is 36 . what is the difference the sum and the number if the ratio between the digits of the number is 1 : 2 ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 13
Rationale: let the number be xy . given xy – yx = 36 . this means the number is greater is than the number got on reversing the digits . this shows that the ten ’ s digit x > unit digit y . also given ratio between digits is 1 : 2 = > x = 2 y ( 10 x + y ) – ( 10 y + x ) = 36 = > x – y = 4 = > 2 y – y = 4 . hence , ( x + y ) – ( x – y ) = 3 y – y = 2 y = 8 b
Answer: b
Python program:
a = 10 * 2
b = a - 10
c = b - 1
d = 36 / c
e = 10 * 2
f = e - 10
g = f - 1
h = 36 / g
i = h * 2
j = d + i 
k = 10 * 2
l = k - 10
m = l - 1
n = 36 / m
o = n * 2
p = 10 * 2
q = p - 10
r = q - 1
s = 36 / r
t = o - s
u = j - t
Problem: the average of 5 numbers is calculated as 15 . it is discovered later on that while calculating the average , one number namely 36 was wrongly read as 26 . the correct average is ?
Options: a ) 12.5 , b ) 26.2 , c ) 6.5 , d ) 7.5 , e ) 12
Rationale: "5 * 15 + 36 – 26 = 75 / 10 = 7.5 answer : d"
Answer: d
Python program:
a = 36 - 26
b = a / 5
c = 15 + b
Problem: the length of a rectangle is reduced by 10 % . by what % would the width have to be increased to maintain the original area ?
Options: a ) 10 % , b ) 11.1 % , c ) 25 % , d ) 30 % , e ) 35 %
Rationale: "sol . required change = ( 10 * 100 ) / ( 100 - 10 ) = 11.1 % b"
Answer: b
Python program:
a = 100 - 10
b = a / 100
c = 1 - b
d = 100 - 10
e = d / 100
f = c / e
g = f * 100
Problem: rs 3500 is divided into two parts such that one part is put out at 3 % and the other at 5 % . if the annual interest earned from both the investments be rs 144 , find the first part .
Options: a ) s 4000 , b ) s 2800 , c ) s 1800 , d ) s 1500 , e ) s 1550
Rationale: "explanation : average rate = ( 144 / 3500 ) * 100 = 4.11 ratio = 8.85 : 11.14 so , first part = ( 8.85 / 20 ) * 3500 = rs 1550 . answer : e"
Answer: e
Python program:
a = 5 / 100
b = 3500 * a
c = b - 144
d = 5 / 100
e = 3 / 100
f = d - e
g = c / f
Problem: a train 110 m long is running with a speed of 60 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 7 sec , b ) 6 sec , c ) 4 sec , d ) 2 sec , e ) 9 sec
Rationale: "speed of train relative to man = 60 + 6 = 66 km / hr . = 66 * 5 / 18 = 55 / 3 m / sec . time taken to pass the men = 110 * 3 / 55 = 6 sec . answer : b"
Answer: b
Python program:
a = 60 + 6 
b = a * const_0_2778
c = 110 / b
Problem: what is the sum of all 4 digit integers formed using the digits 2 , 3 , 4 and 5 ( repetition is allowed )
Options: a ) 444440 , b ) 610000 , c ) 666640 , d ) 995456 , e ) 880000
Rationale: n = 4 * 4 * 4 * 4 = 256 < x > = ( 5555 + 2222 ) / 2 = 3888.5 sum = number of integers x average value n * < x > = 256 * 3888.5 = 711040 answer = d
Answer: d
Python program:
a = 4 ** 3
b = 5 + 4 
c = b + 3 
d = c + 2 
e = a * d
f = 100 * 10
g = f + 100 
h = g + 10 
i = h + 1 
j = e * i
Problem: length of a rectangular plot is 10 mtr more than its breadth . if the cost of fencing the plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ?
Options: a ) 55 m , b ) 60 m , c ) 80 m , d ) 82 m , e ) 84 m
Rationale: "let breadth = x metres . then , length = ( x + 10 ) metres . perimeter = 5300 m = 200 m . 26.50 2 [ ( x + 10 ) + x ] = 200 2 x + 10 = 100 2 x = 90 x = 45 . hence , length = x + 10 = 55 m a"
Answer: a
Python program:
a = 5300 / 26
b = 2 * 10
c = a + b 
d = c / 4
Problem: what is the diagonal of a square field whose perimeter is 24 m ?
Options: a ) 8 m
b ) 2 m
c ) 7 m
d ) 10 m
e ) 6 √ 2 m
Rationale: sol : let the side of the square be x meters . therefore , 4 x = 24 x = 6 diagonal of the square is = √ 2 * ( 6 ) ^ 2 = 6 √ 2 answer : e
Answer: e
Python program:
a = math.sqrt(2)
b = 24 / 4
c = a * b
Problem: due to construction , the speed limit along an 5 - mile section of highway is reduced from 55 miles per hour to 35 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) 3.12 , b ) 8 , c ) 10 , d ) 15 , e ) 24
Rationale: "old time in minutes to cross 5 miles stretch = 5 * 60 / 55 = 5 * 12 / 11 = 5.45 new time in minutes to cross 5 miles stretch = 5 * 60 / 35 = 5 * 12 / 7 = 8.57 time difference = 3.12 ans : a"
Answer: a
Python program:
a = 55 + 5 
b = a - 1
c = 5 / 35
d = 5 / 55
e = c - d
f = b * e
g = max(f)
Problem: the average age of an adult class is 40 years . 2 new students with an avg age of 32 years join the class . therefore decreasing the average by 4 year . find what was the original strength of class ?
Options: a ) 10 , b ) 12 , c ) 16 , d ) 2 , e ) 22
Rationale: "let original strength = y then , 40 y + 2 x 32 = ( y + 2 ) x 36 â ‡ ’ 40 y + 64 = 36 y + 72 â ‡ ’ 4 y = 8 â ˆ ´ y = 2 d"
Answer: d
Python program:
a = 40 - 4
b = 2 * a
c = 2 * 32
d = b - c
e = d / 4
Problem: two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 16 hours and 9 hours respectively . the ratio of their speeds is ?
Options: a ) 4 : 5 , b ) 4 : 3 , c ) 4 : 4 , d ) 4 : 9 , e ) 3 : 4
Rationale: "let us name the trains a and b . then , ( a ' s speed ) : ( b ' s speed ) = √ b : √ a = √ 9 : √ 16 = 3 : 4 answer : e"
Answer: e
Python program:
a = math.sqrt(9)
b = math.sqrt(16)
c = a / b
Problem: a person travels equal distances with speeds of 3 km / hr , 4 km / hr , 5 km / hr . and takes a total time of 47 minutes . find the total distance ?
Options: a ) 3 , b ) 2 , c ) 5 , d ) 4 , e ) 6
Rationale: "let the each distance be x km total distance = 3 x then total time , ( x / 3 ) + ( x / 4 ) + ( x / 5 ) = 47 / 60 x = 1 total distance = 3 * 1 = 3 km correct option is a"
Answer: a
Python program:
a = 47 / const_60
b = 1 / 3
c = 1 / 4
d = b + c 
e = 1 / 5
f = d + e 
g = a / f
h = g * 3
i = h * 1000
Problem: the product of a and b is equal to 11 more than twice the sum of a and b . if b = 5 , what is the value of b - a ?
Options: a ) - 2 , b ) 5 , c ) 7 , d ) 24 , e ) 35
Rationale: "ab = 11 + 2 ( a + b ) 5 a = 11 + 2 a + 10 3 a = 21 a = 7 b - a = 5 - 7 = - 2 a is the answer"
Answer: a
Python program:
a = 5 * 2
b = a + 11 
c = 5 - 2
d = b / c
e = 5 - d
Problem: in town x , 64 percent of the population are employed , and 48 percent of the population are employed males . what percent of the employed people in town x are females ?
Options: a ) 16 % , b ) 25 % , c ) 32 % , d ) 40 % , e ) 52 %
Rationale: "let population be 100 total employed people = 64 % of the population = 64 employed males = 48 % of the population = 48 employed females = 16 % of the population = 16 employed females % in terms of employed people = ( 16 / 64 ) * 100 = 25 % answer is b ."
Answer: b
Python program:
a = 64 - 48
b = a / 64
c = b * 100
Problem: if s is a positive integer , and if the units ' digit of s ^ 2 is 4 and the units ' digit of ( s + 1 ) ^ 2 is 1 , what is the units ' digit of ( s + 2 ) ^ 2 ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: a for me . _ 1 ² = _ 1 _ 2 ² = _ 4 _ 3 ² = _ 9 _ 4 ² = _ 6 _ 5 ² = _ 5 _ 6 ² = _ 6 _ 7 ² = _ 9 _ 8 ² = _ 4 _ 9 ² = _ 1 _ 0 ² = _ 0 on the list , the only number that squared has the units digit = 4 preceding a number that squared has the units digit = 1 is the _ 8 . so , s = _ 8 , that has square 4 . the next square is 1 andnext nextsquare is 0 .
Answer: a
Python program:
a = 2 ** 2
b = 3 * 3
c = a * b
d = 4 + c
Problem: in a group of 65 people , 40 like cricket , 10 like both cricket and tennis . how many like tennis ?
Options: a ) 30 , b ) 35 , c ) 40 , d ) 45 , e ) 50
Rationale: "make a venn diagram , and enter your data . let the number of people who like only tennis be x x + 10 + 30 = 65 x = 25 so number who like tennis = 10 + 25 = 35 answer b"
Answer: b
Python program:
a = 40 - 10
b = 10 + a 
c = b + 10
Problem: the arithmetic mean and standard deviation of a certain normal distribution are 14.0 and 1.5 , respectively . what value is exactly 2 standard deviations less than the mean ?
Options: a ) 10.5 , b ) 11 , c ) 11.5 , d ) 12 , e ) 12.5
Rationale: "the value which isexactlytwo sd less than the mean is : mean - 2 * sd = 14.0 - 2 * 1.5 = 11 . answer : b ."
Answer: b
Python program:
a = 2 * 1
b = 14 - 0
Problem: if a * b denotes the greatest common divisor of a and b , then ( ( 16 * 20 ) * ( 18 * 24 ) ) = ?
Options: a ) 24 , b ) 12 , c ) 6 , d ) 4 , e ) 2
Rationale: the greatest common divisor of 16 and 20 is 4 . hence 16 * 20 = 4 ( note that * here denotes the function not multiplication ) . the greatest common divisor of 18 and 24 is 6 . hence 18 * 24 = 6 . hence ( ( 16 * 20 ) * ( 18 * 24 ) ) = 4 * 6 . the greatest common divisor of 4 and 6 is 2 . answer ; e .
Answer: e
Python program:
a = 18 / 3
b = a / 3
Problem: the average weight of a group of boys is 30 kg . after a boy of weight 39 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 ) a ) 4 , b ) b ) 8 , c ) c ) 6 , d ) d ) 2 , e ) e ) 1
Rationale: "let the number off boys in the group originally be x . total weight of the boys = 30 x after the boy weighing 39 kg joins the group , total weight of boys = 30 x + 39 so 30 x + 39 = 31 ( x + 1 ) = > x = 8 . answer : b"
Answer: b
Python program:
a = 30 + 1 
b = 39 - a
c = b + 1
Problem: a man sitting in a train which is traveling at 60 kmph observes that a goods train , traveling in opposite direction , takes 12 seconds to pass him . if the goods train is 300 m long , find its speed
Options: a ) 52 kmph , b ) 56 kmph , c ) 58 kmph , d ) 30 kmph , e ) 34 kmph
Rationale: "explanation : relative speed = 300 / 12 m / sec = ( ( 300 / 12 ) × ( 18 / 5 ) ) kmph = 90 kmph . speed of goods train = ( 90 - 60 ) kmph = 30 kmph answer : option d"
Answer: d
Python program:
a = 300 / 12
b = a * const_3_6
c = b - 60
Problem: solution p is 20 percent lemonade and 80 percent carbonated water by volume ; solution q is 45 percent lemonade and 55 percent carbonated water by volume . if a mixture of pq contains 65 percent carbonated water , what percent of the volume of the mixture is p ?
Options: a ) 20 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 80 %
Rationale: "65 % is 15 % - points below 80 % and 10 % - points above 55 % . so the ratio of solution p to solution q is 2 : 3 . mixture p is 2 / 5 = 40 % of the volume of mixture pq . the answer is b ."
Answer: b
Python program:
a = 65 / 100
b = 55 / 100
c = a - b
d = 65 / 100
e = 55 / 100
f = d - e
g = 80 / 100
h = 65 / 100
i = g - h
j = f + i 
k = c / j
l = k * 100