euclaise/mathqa_programs huggingface dataset:
Problem: a rectangular tank measuring 5 m × 4.5 m × 2.1 m is dug in the centre of the field measuring 13.5 m × 2.5 . the earth dug out is spread evenly over the remaining portion of a field . how much is the level of the field raised ?
Options: a ) 4.0 m , b ) 4.1 m , c ) 4.2 m , d ) 4.3 m , e ) none of these
Rationale: area of the field = 13.5 × 2.5 = 33.75 m 2 area covered by the rectangular tank = 5 × 4.5 = 22.50 m 2 area of the field on which the earth dug out is to be spread = 33.75 – 22.50 = 11.25 m 2 let the required height be h . then , 11.25 × h = 5 × 4.5 × 2.1 or h = 4.2 m answer c
Answer: c
Python program:
a = 5 * 4
b = a * 2
c = 13 * 5
d = 5 * 4
e = c - d
f = b / e
Problem: a batsman makes a score of 80 runs in the 11 th inning and thus increases his average by 5 . find his average after 11 th inning .
Options: a ) 40 , b ) 50 , c ) 62 , d ) 30 , e ) 56
Rationale: "let the average after 11 th inning = x then , average after 10 th inning = x - 5 10 ( x - 5 ) + 80 = 11 x x = 80 - 50 = 30 answer is d"
Answer: d
Python program:
a = 11 * 5
b = 80 - a
c = b + 5
Problem: paul has to secure 50 % marks to clear his exam of class 7 th . he got 50 marks and failed by 10 marks . what is the maximum marks ?
Options: a ) 100 , b ) 110 , c ) 120 , d ) 210 , e ) 200
Rationale: c 120 to pass the exam ravish needs 50 + 10 = 60 marks . = > ( 60 / 50 ) * 100 = 120
Answer: c
Python program:
a = 50 + 10 
b = a * 100
c = b / 50
Problem: on a two - dimensional coordinate plane , the line s = x ^ 2 - x ^ 3 touches the x - axis in how many places ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "apparently it ' s s = x ^ 2 - x ^ 3 instead of s = x ^ 2 - s ^ 3 . in this case : the x - intercept is the value ( s ) of x for s = 0 . 0 = x ^ 2 - x ^ 3 ; 0 = x ^ 2 ( 1 - x ) ; x = 0 or x = 1 . answer : c ."
Answer: c
Python program:
a = max(3)
b = a - 1
Problem: two vertical ladders length of 6 m and 11 m are kept vertically at a distance of 12 m . find the top distance of both ladders ?
Options: a ) 22 , b ) 27 , c ) 13 , d ) 19 , e ) 17
Rationale: so distance between the top points = ad = 122 + 52 − − − − − − − √ = 13122 + 52 = 13 so in paper b he did well . answer : c
Answer: c
Python program:
a = 11 - 6
b = a ** 2
c = 12 ** 2
d = b + c 
e = math.sqrt(d)
Problem: the volume of a certain substance is always directly proportional to its weight . if 48 cubic inches of the substance weigh 112 ounces , what is the volume , in cubic inches , of 84 ounces of this substance ?
Options: a ) 27
b ) 36
c ) 42
d ) 64
e ) 147
Rationale: 112 ounces of a substance has a volume of 48 cubic inches 84 ounces of a substance has a volume of ( 48 / 112 ) * 84 = 36 cubic inches answer b
Answer: b
Python program:
a = 48 / 112
b = a * 84
Problem: a batsman makes a score of 95 runs in the 11 th inning and thus increases his average by 5 . find his average after 11 th inning .
Options: a ) 40 , b ) 50 , c ) 62 , d ) 45 , e ) 56
Rationale: "let the average after 11 th inning = x then , average after 10 th inning = x - 5 10 ( x - 5 ) + 95 = 11 x x = 95 - 50 = 45 answer is d"
Answer: d
Python program:
a = 11 * 5
b = 95 - a
c = b + 5
Problem: of the three - digit positive integers that have no digits equal to zero , how many have two digits that are equal to each other and the remaining digit different from the other two ?
Options: a ) 24 , b ) 36 , c ) 72 , d ) 1 , e ) 216
Rationale: "assume : a , b , c is the digit and a , b , c not = 0 thus a , b , c could be 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , and 9 count the possible way to get three digit number abc . a = b , and c must be different from a , b thus , there are 3 possible ways of digit arrangement : aac , aca , caa case i : aac = > ( digit 1 st ) x ( digit 2 nd ) x ( digit 3 rd ) = > 9 x 1 x 8 { pick any number from group = 9 possible ways } x { pick number the same as the first pick = 1 way } x { pick any number from the rest = 8 possible ways } = 9 x 1 x 8 = 72 possible ways case ii : aca = > same as case i you have 72 possible ways case iii : caa = > same as case i you have 72 possible ways total of this set of number = 72 + 72 + 72 = 216 e ) is the answer"
Answer: e
Python program:
a = 10 - 1
b = 10 - 2
c = a * b
d = c * 1
Problem: a cistern can be filled by a tap in 7 hours while it can be emptied by another tap in 9 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
Options: a ) 4.5 hrs , b ) 5 hrs , c ) 6.5 hrs , d ) 17.2 hrs , e ) 31.5 hrs
Rationale: "net part filled in 1 hour = 1 / 7 - 1 / 9 = 2 / 63 therefore the cistern will be filled in 63 / 2 hours or 31.5 hours . answer : e"
Answer: e
Python program:
a = 1 / 7
b = 1 / 9
c = a - b
d = 1 / c
Problem: 16.036 divided by 0.04 gives :
Options: a ) 40.09 , b ) 4.06 , c ) 40.06 , d ) 400.9 , e ) 400.6
Rationale: = 16.036 / 0.04 = 1603.6 / 4 = 400.9 answer is d .
Answer: d
Python program:
a = 16 / 36
Problem: a canoe has two oars , left and right . each oar either works or breaks . the failure or non - failure of each oar is independent of the failure or non - failure of the other . you can still row the canoe with one oar . the probability that the left oar works is 3 / 5 . the probability that the right oar works is also 3 / 5 . what is the probability r that you can still row the canoe ?
Options: a ) 9 / 25 , b ) 10 / 25 , c ) 6 / 10 , d ) 2 / 3 , e ) 21 / 25
Rationale: "simply look at the question from the other side . what is the probability that you can ’ t row the canoe ? this would be 2 / 5 x 2 / 5 = 4 / 25 . using the idea that the probability of something happening is 1 – the probability that it doesn ’ t happen , you can use the following equation to reach the right answer r : 1 – 4 / 25 = 21 / 25 . answer choice e ."
Answer: e
Python program:
a = 3 / 5
b = 3 / 5
c = a * b
d = 3 / 5
e = 2 / 5
f = d * e
g = 3 / 5
h = 2 / 5
i = g * h
j = f + i 
k = c + j
Problem: a is the average ( arithmetic mean ) of the first 7 positive multiples of 8 and b is the median of the first 3 positive multiples of positive integer n . if the value of a ^ 2 – b ^ 2 is zero , what is the value of n ?
Options: a ) 10 , b ) 12 , c ) 16 , d ) 24 , e ) 32
Rationale: "if a ^ 2 - b ^ 2 = 0 , then let ' s assume that a = b . a must equal the 4 th positive multiple of 4 , thus a = 32 , which also equals b . b is the second positive multiple of n , thus n = 32 / 2 = 16 . the answer is c ."
Answer: c
Python program:
a = 8 * 4
b = a / 2
Problem: the population of a bacteria culture doubles every 3 minutes . approximately how many minutes will it take for the population to grow from 1,000 to 500,000 bacteria
Options: a ) 27 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: this one ' s easy . 1000 * 2 ^ t = 500,000 2 ^ t = 500 now gauging , since 2 ^ 8 = 256 , then 2 ^ 9 = 512 so t = 9 but be careful , ' t ' is in time intervals of 3 minutes so answer is 9 * 3 = 27 minutes answer ( a )
Answer: a
Python program:
a = 4 + 1 
b = a * 1000
c = b * 100
d = c / 1000
e = math.log(d)
f = e * 3
Problem: shopkeeper rise price by 36 % and gives successive discount of 10 % and 15 % . what is overall % gain or loss ?
Options: a ) 5.04 % , b ) 4.04 % , c ) 3.04 % , d ) 6.04 % , e ) 7.04 %
Rationale: "let d initial price be 100 36 % rise now price = 136 / 100 * 100 = 136 10 % discount then price = 136 * 90 / 100 = 122.4 15 % discount then price = 122.4 * 85 / 100 = 104.04 so gain = 104.04 - 100 = 4.04 gain % = gain * 100 / cp = = > 4.04 * 100 / 100 = 4.04 % answer : b"
Answer: b
Python program:
a = 100 + 36 
b = 100 - 10
c = b / 100
d = a * c
e = 100 - 15
f = e / 100
g = d * f
h = g - 100
Problem: set j consists of 18 consecutive even numbers . if the smallest term in the set is - 22 , what is the range of the positive integers in set j ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "since there are only 18 integers , another approach is the just list all 18 . we get : - 22 , - 20 , - 18 , - 16 , - 14 , - 12 , - 10 , - 8 , - 6 , - 4 , - 2 , 0 , 2 , 4 , 6 , 8 , 10 , 12 range of positive integers = 12 - 2 = 10 answer : e"
Answer: e
Python program:
a = negate + ( 
b = 18 - 1
c = b * 22
d = a - c
Problem: suresh and ramesh started a business investing rs . 24,000 and rs . 40,000 respectively . out of total profit of rs . 18,000 , what is suresh ' s share ?
Options: a ) s . 6750 , b ) s . 7750 , c ) s . 8750 , d ) s . 9372 , e ) s . 9750
Rationale: explanation : ratio of suresh and ramesh ' s share = 24,000 : 40,000 = 3 : 5 suresh ' s share = rs . ( 18000 x 3 / 8 ) = rs . 6750 answer : a
Answer: a
Python program:
a = 2 * 3
b = a * 4
c = 2 + 3 
d = 2 * c
e = d * 100
f = b * e
g = 2 * 3
h = 3 * g
i = 2 + 3 
j = 2 * i
k = j * 100
l = h * k
m = 2 * 3
n = m * 4
o = 2 + 3 
p = 2 * o
q = p * 100
r = n * q
s = 2 + 3 
t = 2 * s
u = 4 * t
v = u + 2 
w = 2 + 3 
x = 2 * w
y = x * 100
z = v * y
A = r + z 
B = l / A
C = f * B
Problem: what is the square root of 36 , divided by 6 ?
Options: a ) 9 , b ) 36 , c ) 122 , d ) 6 , e ) 1
Rationale: "square root is a number times itself square root of 36 = 6 , 6 / 6 = 1 ( e ) 1"
Answer: e
Python program:
a = math.sqrt(36)
b = a / 6
Problem: a man swims downstream 32 km and upstream 24 km taking 4 hours each time , what is the speed of the man in still water ?
Options: a ) 9 , b ) 8 , c ) 6 , d ) 7 , e ) 2
Rationale: "32 - - - 4 ds = 8 ? - - - - 1 24 - - - - 4 us = 6 ? - - - - 1 m = ? m = ( 8 + 6 ) / 2 = 7 answer : d"
Answer: d
Python program:
a = 24 / 4
b = 32 / 4
c = a + b 
d = c / 2
Problem: during a sale , the price of a pair of shoes is marked down 15 % from the regular price . after the sale ends , the price goes back to the original price . what is the percent of increase to the nearest percent from the sale price back to the regular price for the shoes ?
Options: a ) 9 % , b ) 10 % , c ) 11 % , d ) 18 % , e ) 90 %
Rationale: assume the price = 100 price during sale = 85 price after sale = 100 percent increase = 15 / 85 * 100 = 18 % approx . correct option : d
Answer: d
Python program:
a = 15 * 100
b = 100 - 15
c = a / b
Problem: a and b can do a piece of work in 18 and 9 days respectively . a does the work for a few days and left , then b continued for 6 days . how many days did a and b work together ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: a and b work together for 2 days . a 1 day work 1 / 18 b 1 day work 1 / 9 let a work x days . then equation form is ( x / 18 ) + ( ( x + 6 ) / 9 ) = 1 from this equation x value is 2 . answer : b
Answer: b
Python program:
a = 6 * 3
b = a / 9
Problem: a and b can finish a work in 10 days while a alone can do the same work in 20 days . in how many days b alone will complete the work ?
Options: a ) 20 days , b ) 48 days , c ) 98 days , d ) 31 days , e ) 22 days
Rationale: "b = 1 / 10 – 1 / 20 = 1 / 20 = > 20 days answer : a"
Answer: a
Python program:
a = 1/(10)
b = 1/(20)
c = a - b
d = 1/(c)
Problem: a combustion reaction forms carbon dioxide . a carbon dioxide molecule contains one carbon and two oxygen atoms . if , over a period of 12 minutes , a combustion reaction creates 12,000 molecules of carbon dioxide then approximately how many more atoms of oxygen than carbon are created on average per minute ?
Options: a ) 20 , b ) 60 , c ) 600 , d ) 1,000 , e ) 1,200
Rationale: "solution : 12,000 carbon dioxide molecules are created over a period of 12 minutes . therefore 12,000 / 12 = 1,000 carbon dioxide molecules are created on average per minute each carbon dioxide molecule contains one carbon atom and two oxygen atoms . so 1,000 carbon dioxide molecules contain 1 × 1,000 = 1,000 carbon atoms and 2 × 1,000 = 2,000 oxygen atoms . the difference is 2,000 – 1,000 = 1,000 . the correct answer is d ."
Answer: d
Python program:
a = 12 * 2
b = a - 12
c = b * 1000
d = c / 12
e = d / 1000
Problem: 8 ! / ( 8 - 2 ) ! = ?
Options: a ) 36 , b ) 46 , c ) 56 , d ) 66 , e ) 96
Rationale: 8 ! / ( 8 - 2 ) ! = 8 ! / 6 ! = 8 * 7 = 56 . hence , the correct answer is c .
Answer: c
Python program:
a = math.factorial(8)
b = 8 - 2
c = math.factorial(b)
d = a / c
Problem: sally , mark , sarah , steve and jim are inheriting the money from their grandmother . she left them $ 527500 to split equally between all of them . if the money is split equally , how much money will each person receive ?
Options: a ) $ 135875 , b ) $ 52700 , c ) $ 127900 , d ) $ 105500 , e ) $ 105000
Rationale: there are 5 people inheriting the money . we have to take the total of the inheritance and divide it by 5 for each person receiving money . $ 527500 / 5 = $ 105500 . therefore the correct answer is d .
Answer: d
Python program:
a = 4 + 1 
b = 527500 / a
Problem: if the cost price of 165 chocolates is equal to the selling price of 150 chocolates , the gain percent is
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "let c . p . of each chocolate be re . 1 . then , c . p . of 150 chocolates = rs . 150 ; s . p . of 150 chocolates = rs . 165 . gain % = 15 / 150 * 100 = 10 % answer : c"
Answer: c
Python program:
a = 165 - 150
b = 150 / a
c = 100 / b
Problem: jack and jill work at a hospital with 2 other workers . for an internal review , 2 of the 4 workers will be randomly chosen to be interviewed . what is the probability that jack and jill will both be chosen ?
Options: a ) 1 / 3 , b ) 1 / 6 , c ) 1 / 15 , d ) 3 / 8 , e ) 2 / 3
Rationale: "1 / 4 c 2 = 1 / 6 . answer : b ."
Answer: b
Python program:
a = math.factorial(4)
b = math.factorial(2)
c = math.factorial(2)
d = b * c
e = a / d
f = 1/(e)
Problem: if 15 % of 30 % of 50 % of a number is 126 , then what is the number ?
Options: a ) 5000 , b ) 5600 , c ) 5400 , d ) 4500 , e ) none of these
Rationale: "let the number be a given , 15 / 100 * 30 / 100 * 50 / 100 * a = 126 = > 3 / 20 * 3 / 10 * 1 / 2 * a = 126 = > a = 10 * 20 * 10 * 2 = 5600 . answer : b"
Answer: b
Python program:
a = 50 / 100
b = 30 / 100
c = a * b
d = 15 / 100
e = c * d
f = 126 / e
Problem: a full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet . oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck ' s tank is completely filled . if the truck ' s tank has a radius of 5 feet and a height of 12 feet , how far ( in feet ) did the oil level drop in the stationary tank ?
Options: a ) 2.5 , b ) 0.025 , c ) 0.05 , d ) 0.03 , e ) 3
Rationale: "the volume of oil pumped to the tank = the volume of oil taken away from stationary cylinder . pi * 25 * 12 = pi * h * 100 * 100 ( h is distance that the oil level dropped ) h = 300 / 10,000 = 3 / 100 = 0.03 ft the answer is d ."
Answer: d
Python program:
a = volume_cylinder / (
Problem: company x provides bottled water to its employees in 5 liter bottles , $ 2 each . at least how many 5 l bottles must company x buy monthly , so that new contract with $ 100 fixed monthly rate and $ 1 for 10 l bottle each paid off ? ( assume that no other costs apply )
Options: a ) 121 , b ) 125 , c ) 132 , d ) 134 , e ) 138
Rationale: let the no . of 5 liter bottles be x , so the no . of 10 l bottles will be x / 2 ( to equate the vol . ) since the total cost will be equal , 2 x = 100 + x / 2 so x = 133.33 or 134 . answer is ( d ) .
Answer: d
Python program:
a = 1 / 1
b = 5 - a
c = 100 / b
Problem: when the price of an article was reduced by 35 % its sale increased by 80 % . what was the net effect on the sale ?
Options: a ) 17 % increase , b ) 44 % decrease , c ) 60 % increase , d ) 66 % increase , e ) 66 % decrease
Rationale: "if n items are sold for $ p each , revenue is $ np . if we reduce the price by 35 % , the new price is 0.65 p . if we increase the number sold by 80 % , the new number sold is 1.8 n . so the new revenue is ( 0.65 p ) ( 1.8 n ) = 1.17 np , which is 1.17 times the old revenue , so is 17 % greater . answer : a"
Answer: a
Python program:
a = 80 + 100 
b = 100 - 35
c = a * b
d = c / 100
e = d - 100
Problem: two trains travel in opposite directions at 36 kmph and 45 kmph and a man sitting in slower train passes the faster train in 10 seconds . the length of the faster train is
Options: a ) 225 m , b ) 100 m , c ) 120 m , d ) 180 m , e ) none
Rationale: "solution relative speed = ( 36 + 45 ) km / hr = ( 81 x 5 / 18 ) m / sec = ( 45 / 2 ) m / sec length of the train = ( 45 / 2 x 10 ) m = 225 m . answer a"
Answer: a
Python program:
a = 36 + 45 
b = a * const_0_2778
c = b * 10
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 r are in s ( 99 ) ?
Options: a ) r = 350 , b ) r = 353 , c ) r = 354 , d ) r = 356 , e ) 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 = r = 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: with a uniform speed a car covers the distance in 8 hours . had the speed been increased by 6 km / hr , the same distance could have been covered in 7 1 / 2 hours . what is the distance covered ?
Options: a ) 187 km , b ) 480 km , c ) 720 km , d ) 297 km , e ) 671 km
Rationale: "let the distance be x km . then , x / ( 7 1 / 2 ) - x / 8 = 6 2 x / 15 - x / 8 = 6 = > x = 720 km . answer : c"
Answer: c
Python program:
a = 1 / 2
Problem: if a and b are positive integers and ( 2 ^ a ) ^ b = 2 ^ 2 , what is the value of 2 ^ a * 2 ^ b ?
Options: a ) 8 , b ) 4 , c ) 16 , d ) 32 , e ) 64
Rationale: "2 ^ ab = 2 ^ 2 therefore ab = 2 either a = 1 or 2 or b = 2 or 1 therefore 2 ^ a * 2 ^ b = 2 ^ ( a + b ) = 2 ^ 3 = 8 a"
Answer: a
Python program:
a = 2 ** 2
b = a * 2
Problem: when 242 is divided by a certain divisor the remainder obtained is 4 . when 698 is divided by the same divisor the remainder obtained is 8 . however , when the sum of the two numbers 242 and 698 is divided by the divisor , the remainder obtained is 7 . what is the value of the divisor ?
Options: a ) 5 , b ) 17 , c ) 13 , d ) 23 , e ) none of these
Rationale: "let that divisor be x since remainder is 4 or 8 it means divisor is greater than 8 . now 242 - 4 = 238 = kx ( k is an integer and 234 is divisble by x ) similarly 698 - 8 = 690 = lx ( l is an integer and 689 is divisible by x ) adding both 698 and 242 = ( 238 + 690 ) + 4 + 8 = x ( k + l ) + 12 when we divide this number by x then remainder will be equal to remainder of ( 12 divided by x ) = 7 hence x = 12 - 7 = 5 hence a"
Answer: a
Python program:
a = 4 + 8 
b = a - 7
Problem: in a college , the ratio of the number of boys to girls is 6 : 5 . if there are 200 girls , the total number of students in the college is
Options: a ) 440 , b ) 520 , c ) 620 , d ) 720 , e ) 820
Rationale: "explanation : let the boy are 6 x and girls are 5 x = > 5 x = 200 = > x = 40 total students = 6 x + 5 x = 11 x = 11 ( 40 ) = 440 option a"
Answer: a
Python program:
a = 200 / 5
b = a * 6
c = 200 + b
Problem: what is the greater of the two numbers whose product is 1280 , given that the sum of the two numbers exceeds their difference by 32 ?
Options: a ) a ) 90 , b ) b ) 100 , c ) c ) 110 , d ) d ) 70 , e ) 80
Rationale: "let the greater and the smaller number be g and s respectively . g * s = 1288 g + s exceeds g - s by 32 i . e . , g + s - ( g - s ) = 32 i . e . , 2 s = 32 = > s = 16 . g = 1280 / s = 80 . answer : e"
Answer: e
Python program:
a = 2 ** 4
b = a * 2
c = 1280 / b
Problem: p , q and r have rs . 8000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ?
Options: a ) rs . 3200 , b ) rs . 3600 , c ) rs . 2400 , d ) rs . 4000 , e ) none of these
Rationale: "let the amount with r be rs . r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 8000 - r ) = > 3 r = 16000 - 2 r = > 5 r = 16000 = > r = 3200 . answer : a"
Answer: a
Python program:
a = 2 / 3
b = 1 + a 
c = 8000 / b
d = 2 / 3
e = c * d
Problem: in a race of 1000 m , a can beat by 100 m , in a race of 800 m , b can beat c by 100 m . by how many meters will a beat c in a race of 1000 m ?
Options: a ) 122.9 m , b ) 127.5 m . , c ) 122.2 m , d ) 222.9 m , e ) 212.5 m
Rationale: when a runs 1000 m , b runs 900 m and when b runs 800 m , c runs 700 m . when b runs 900 m , distance that c runs = ( 900 * 700 ) / 800 = 6300 / 8 = 787.5 m . in a race of 1000 m , a beats c by ( 1000 - 787.5 ) = 212.5 m to c . in a race of 1000 m , the number of meters by which a beats c = ( 1000 * 212.5 ) / 1000 = 212.5 m . answer : e
Answer: e
Python program:
a = 1000 - 100
b = 800 - 100
c = a * b
d = c / 800
e = 1000 - d
Problem: how many positive integers between 1 and 300 are there such that they are multiples of 9 ?
Options: a ) 31 , b ) 33 , c ) 35 , d ) 36 , e ) 23
Rationale: "multiples of 9 = 9 , 18,27 , - - - - - 297 number of multiples of 15 = > 9 * 33 = 297 answer is b"
Answer: b
Python program:
a = 300 - 1
b = a / 9
Problem: a squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 5 feet . how many feet does the squirrel travels if the post is 25 feet tall and 3 feet in circumference ?
Options: a ) 10 feet
b ) 12 feet
c ) 13 feet
d ) 15 feet
e ) 18 feet
Rationale: total circuit = 25 / 5 = 5 total feet squirrel travels = 5 * 3 = 15 feet answer : d
Answer: d
Python program:
a = 25 / 5
b = a * 3
Problem: a man swims downstream 48 km and upstream 42 km taking 6 hours each time ; what is the speed of the current ?
Options: a ) 3 kmph , b ) 0.5 kmph , c ) 13 kmph , d ) 6.5 kmph , e ) 7 : 3 kmph
Rationale: "explanation : 48 - - - 6 ds = 8 ? - - - - 1 42 - - - - 6 us = 7 ? - - - - 1 s = ? s = ( 8 - 7 ) / 2 = 0.5 answer : option b"
Answer: b
Python program:
a = 42 / 6
b = 48 / 6
c = a + b 
d = c / 2
Problem: the average weight of 16 girls in a class is 50.25 kg and that of the remaining 8 girls is 45.15 kg . find the average weights of all the girls in the class .
Options: a ) a ) 48.55 , b ) b ) 49 , c ) c ) 51 , d ) d ) 61 , e ) e ) 62
Rationale: required average = ( 50.25 x 16 + 45.15 x 8 ) / ( 16 + 8 ) = ( 804 + 361.20 ) / 24 = 1165.20 / 24 = 48.55 kg answer is a
Answer: a
Python program:
a = 16 * 50
b = 8 * 45
c = a + b 
d = 16 + 8 
e = c / d
Problem: if rs . 782 is divided into 3 parts , proportional to 1 / 2 : 2 / 3 : 3 / 4 find the first part .
Options: a ) 190 , b ) 204 , c ) 220 , d ) 230 , e ) none of these
Rationale: explanation : 1 / 2 : 2 / 3 : 3 / 4 = 6 : 8 : 9 first part = 782 ∗ 6 / 23 = 204 option b
Answer: b
Python program:
a = 12 / 2
b = 12 / 2
c = 12 / 3
d = c * 2
e = b + d 
f = 12 / 4
g = f * 3
h = e + g 
i = a / h
j = 782 * i
Problem: the hcf of two numbers is 50 and the other two factors of their lcm are 11 and 12 . what is the largest number .
Options: a ) 462 , b ) 450 , c ) 480 , d ) 504 , e ) 600
Rationale: "explanation : hcf of the two numbers = 50 hcf will be always a factor of lcm 50 is factor of lcm other two factors are 11 & 12 then the numbers are ( 50 * 11 ) and ( 50 x 12 ) = 550 and 600 answer : option e"
Answer: e
Python program:
a = 50 * 12
Problem: find the value for m ? 21 ( m + n ) + 21 = 21 ( - m + n ) + 21
Options: a ) 0 , b ) - 1 , c ) 1 , d ) 2 , e ) 3
Rationale: 21 m + 21 n - 21 = - 21 m + 21 n + 21 42 m = 42 = > m = 1 c
Answer: c
Python program:
a = 2 * 10
b = 21 - a
Problem: find 40 % of 320
Options: a ) 96 , b ) 94 , c ) 128 , d ) 74 , e ) 110
Rationale: "we know that r % of m is equal to r / 100 × m . so , we have 40 % of 320 40 / 100 × 320 = 128 answer : c"
Answer: c
Python program:
a = 40 / 320