euclaise/mathqa_programs huggingface dataset:
Problem: in how many no . between 10 and 30 exactly two of the digits is 3 ?
Options: a ) 1 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: it ' s simple can be solved by elimination of answer choices . option b and c are too large , not possible . even de are large to have correct choice . ans : a
Answer: a
Python program:
a = 30 / 10
b = a / 3
Problem: ( 208 % of 1265 ) ÷ 6 = ?
Options: a ) a ) 125 , b ) b ) 439 , c ) c ) 225 , d ) d ) 375 , e ) e ) 524
Rationale: "explanation : ? = ( 208 x 1265 / 100 ) ÷ 6 = 263120 / 600 = 439 answer : option b"
Answer: b
Python program:
a = 208 / 100
b = a * 1265
c = b / 6
Problem: by selling an article at rs . 120 , a profit of 25 % is made . find its cost price ?
Options: a ) s . 96 , b ) s . 45 , c ) s . 120 , d ) s . 180 , e ) s . 189
Rationale: "sp = 120 cp = ( sp ) * [ 100 / ( 100 + p ) ] = 120 * [ 100 / ( 100 + 25 ) ] = 120 * [ 100 / 125 ] = rs . 96 answer : a"
Answer: a
Python program:
a = 120 * 100
b = 100 + 25 
c = a / b
Problem: the average score of a cricketer in 2 matches is 40 and in other 3 matches is 10 . then find the average score in all the 5 matches ?
Options: a ) 25 , b ) 22 , c ) 30 , d ) 35 , e ) 42
Rationale: "average in 5 matches = ( 2 * 40 + 3 * 10 ) / 2 + 3 = 80 + 30 / 5 = 110 / 5 = 22 answer is b"
Answer: b
Python program:
a = 2 * 40
b = 3 * 10
c = a + b 
d = c / 5
Problem: which number need to add to 8679921 to get a number exactly divisible by 330 ?
Options: a ) 69 , b ) 62 , c ) 61 , d ) 63 , e ) 64
Rationale: 8679921 / 330 = 26302 and reminder = 261 . 330 - 261 = 69 so , the next number divisible by 339 is 69 places in front of 8679921 which means 69 + 8679921 = 8679990 69 should be added to 8679921 a
Answer: a
Python program:
a = 8679921 / 330
b = math.floor(a)
c = b + 1 
d = 8679921 / 330
e = c - d
f = 330 * e
Problem: at a certain college , 60 percent of the total number of students are freshmen . if 40 percent of the fresh - men are enrolled in the school of liberal arts and , of these , 20 percent are psychology majors , what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts ?
Options: a ) 4 % , b ) 8 % , c ) 4.2 % , d ) 4.8 % , e ) 5 %
Rationale: "let ' s say there is a total of 100 students at this college . 60 percent of the total number of students are freshmen . # of freshmen = 60 % of 100 = 60 40 percent of the fresh - men are enrolled in the school of liberal arts . . . number of liberal arts freshmen = 40 % of 60 = 24 . . . and , of these , 20 percent are psychology majors . . . number of liberal arts freshmen who are psychology majors = 20 % of 24 = 4.8 what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts ? 4.8 / 100 = 4.8 % answer : d"
Answer: d
Python program:
a = 60 * 40
b = a / 100
c = b * 20
d = c / 100
Problem: what annual installment will discharge a debt of rs . 1008 due in 3 years at 12 % simple interest ?
Options: a ) 300 , b ) 345 , c ) 325 , d ) 335 , e ) none of them
Rationale: "let each installment be rs . x then , ( x + ( ( x * 12 * 1 ) / 100 ) ) + ( x + ( ( x * 12 * 2 ) / 100 ) ) + x = 1008 = ( ( 28 x / 25 ) + ( 31 x / 25 ) + x ) = 1008 ï ƒ › ( 28 x + 31 x + 25 x ) = ( 1008 * 25 ) x = ( 1008 * 25 ) / 84 = rs . 300 . therefore , each installment = rs . 300 . answer is a ."
Answer: a
Python program:
a = 12 / 1008
b = 100 * 0
c = b * 3
Problem: what is the smallest integer k for which 64 ^ k > 4 ^ 16 ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "64 ^ k > 4 ^ 16 4 ^ ( 3 k ) > 4 ^ 16 3 k > 16 k = 6 the answer is c ."
Answer: c
Python program:
a = 16 / 3
b = math.floor(a)
c = b + 1
Problem: a 1200 m long train crosses a tree in 120 sec , how much time will i take to pass a platform 1000 m long ?
Options: a ) 220 sec , b ) 190 sec , c ) 167 sec , d ) 197 sec , e ) 179 sec
Rationale: "l = s * t s = 1200 / 120 s = 10 m / sec . total length ( d ) = 2200 m t = d / s t = 2200 / 10 t = 220 sec answer : a"
Answer: a
Python program:
a = 1200 + 1000 
b = 1200 / 120
c = a / b
Problem: if t = 5 / 9 * ( k - 32 ) , and if t = 50 , then what is the value of k ?
Options: a ) 116 , b ) 119 , c ) 122 , d ) 125 , e ) 128
Rationale: "k - 32 = 9 t / 5 k = 9 t / 5 + 32 k = 9 ( 50 ) / 5 + 32 = 122 the answer is c ."
Answer: c
Python program:
a = 50 * 9
b = a / 5
c = b + 32
Problem: let q represent a set of 7 distinct prime numbers . if the sum of the numbers in q is even and x is a member of q , then what is the least possible value that x can be ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 7
Rationale: q = p 1 + p 2 + p 3 + p 4 + p 5 + p 6 + p 7 = even ( and all primes are distinct ) if the least prime is 2 then we have sum of q = even . ans . c . 3
Answer: c
Python program:
a = 7 / 7
b = a + 2
Problem: how many digits are in the number 50 ^ 8 × 8 ^ 3 × 11 ^ 2 x 10 ^ 4 ?
Options: a ) 22 , b ) 20 , c ) 19 , d ) 18 , e ) 17
Rationale: whenever you are asked to find the number of digits , try to bring the number in multiples of 10 . this way , we can wasily calculate the umber of 0 ' s through the powers of 10 50 ^ 8 × 8 ^ 3 × 11 ^ 2 x 10 ^ 4 = ( 5 ^ 2 * 2 ) ^ 8 * 2 ^ 9 * 11 ^ 2 * 10 ^ 4 = 5 ^ 16 * 2 ^ 17 * 11 ^ 2 * 10 ^ 4 = 2 * 11 ^ 2 * 10 ^ 16 * 10 ^ 4 = 242 * 10 ^ 16 x 10 ^ 4 hence we would have 16 trailing 0 ' s and the three digits from 242 total digits = 3 + 20 = 23 correct option : d
Answer: d
Python program:
a = 10 * 2
b = a - 2
Problem: sheila works 8 hours per day on monday , wednesday and friday , and 6 hours per day on tuesday and thursday . she does not work on saturday and sunday . she earns $ 432 per week . how much does she earn in dollars per hour ?
Options: a ) 2 , b ) 8 , c ) 9 , d ) 11 , e ) 12
Rationale: "explanation : total hours worked = 8 x 3 + 6 x 2 = 36 total earned = 432 . hourly wage = 432 / 36 = 12 answer : e"
Answer: e
Python program:
a = 8 * 3
b = 6 * 2
c = a + b 
d = 432 / c
Problem: x , y , and z are consecutive numbers and x > y > z . also , 2 x + 3 y + 3 z = 5 y + 11 . what is the value of z ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "if x , y , and z are consecutive numbers and x > y > z , then y = z + 1 and x = z + 2 . 2 x + 3 y + 3 z = 5 y + 11 2 z + 4 + 3 z + 3 + 3 z = 5 z + 5 + 11 3 z = 9 z = 3 the answer is b ."
Answer: b
Python program:
a = 4 * 2
b = 2 * 3
c = a - b
d = 11 - c
e = d / 3
Problem: a and b are two circles . the radius of a is 5 times as large as the radius of b . what is the ratio between the areas of the circles ?
Options: a ) 1 : 8 .
b ) 1 : 2 .
c ) 1 : 4 .
d ) 1 : 25 .
e ) 1 : 6 .
Rationale: given : the radius of a is 5 times as large as the radius of b . = > r ( a ) = 5 r ( b ) . the radius are in ratio of 1 : 5 thus the area will be in the ratio of square of radius . 1 : 25 . hence d .
Answer: d
Python program:
a = math.pi * 1
b = 5 ** 2
c = math.pi * b
d = a / c
Problem: [ ( 3.242 x 10 ) / 100 ] = ?
Options: a ) 0.045388 , b ) 4.5388 , c ) 0.03242 , d ) 473.88 , e ) none of these
Rationale: "answer multiplying 3.242 x 10 = 3.242 now divide 3.242 by 100 so , 3.242 ÷ 100 = 0.03242 ∴ shift the decimal two places to the left as 100 correct option : c"
Answer: c
Python program:
a = 3 * 242
b = a / 100
c = b / 10
Problem: pipe a can fill a pool in 12 hours at a constant rate . if pipe a does the job for 8 hours and pipe b does the rest of the job , which works at 1 / 3 constant rate of pipe a . how long will it take for pipe b alone to do the rest of the job ?
Options: a ) 12 hrs , b ) 6 hrs , c ) 8 hrs , d ) 10 hrs , e ) 24 hrs
Rationale: pipe a will do 8 / 12 in 8 hrs , so a does 2 / 3 of the work . . therefore , b will do the remaining 1 / 3 rd work alone . . as the speed of b is 1 / 3 rate of a , b will do the 1 / 3 rd work in same time that a takes to complete full job . . . ans 12 a
Answer: a
Python program:
a = 12 - 8
b = 1/(3)
c = a / b
Problem: rs . 1210 were divided among a , b , c so that a : b = 5 : 4 and b : c = 9 : 10 . then , c gets :
Options: a ) rs . 340 , b ) rs . 400 , c ) rs . 450 , d ) rs . 475 , e ) none
Rationale: "solution a : b = 5 : 4 , b : c = 9 : 10 = ( 9 x 4 / 9 ) : ( 10 x 4 / 90 = 4 : 40 / 9 ∴ a : b : c = 5 : 4 : 40 / 9 = 45 : 36 : 40 . sum of ratio terms = ( 45 + 36 + 40 ) = 121 ∴ c ’ s share = rs . ( 1210 x 40 / 121 ) = rs . 400 . answer b"
Answer: b
Python program:
a = 5 + 5 
b = a + 4 
c = 1210 - b
d = c / 3
e = d + 4 
f = e + 5
Problem: two sacks together contained 40 kilograms of sugar . if after 1 kilogram of sugar was taken from the first sack and poured into the second the weight of the sugar in the first sack became 60 % the weight of the sugar in the second , what was the original difference in the weights of the sacks ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: say the weight of the second sack after change is x kilograms , then the weight of the first sack after change would be 0.6 x . since the total weight of sugar in both sacks remained the same then x + 0.6 x = 40 , which gives x = 25 . now , if the weight of the second sack after change is 25 kilograms then initially it was 25 − 1 = 24 kilograms and the initial weight of the first sack was 40 − 24 = 16 kilograms , so the difference was 24 − 16 = 8 kilograms . answer : c
Answer: c
Python program:
a = 60 / 100
b = 1 + a 
c = 40 / b
d = c - 1
e = 60 / 100
f = 1 + e 
g = 40 / f
h = g - 1
i = 40 - h
j = d - i
Problem: find a positive number , which when increased by 8 is equal to 128 times reciprocal of the number .
Options: a ) 5 , b ) 6 , c ) 8 , d ) 7 , e ) 9
Rationale: explanation : let the number be x . then , x + 8 = 128 x ( 1 / x ) = > x < sup > 2 < / sup > + 8 x - 128 = 0 = > ( x + 16 ) ( x - 8 ) = 0 = > x = 8 answer : option c
Answer: c
Python program:
a = 128 * 4
b = 8 ** 2
c = a + b 
d = math.sqrt(c)
e = d - 8
f = e / 2
Problem: find the value of x : 2 a ^ 2 - 7 a + 10 = 14
Options: a ) 7 , b ) 5 , c ) 6 , d ) 4 , e ) 2
Rationale: "using the elimination method substitute options for x and find the correct option . answer : d"
Answer: d
Python program:
a = 7 + 2 
b = 2 ** 2
c = a / b
Problem: sheela deposits rs . 3400 in bank savings account . if this is 15 % of her monthly income . what is her monthly income in ?
Options: a ) 22666 , b ) 20000 , c ) 25000 , d ) 22235 , e ) none of these
Rationale: "explanation : 15 % of income = rs . 3400 100 % of income = 3400 x 100 / 15 = rs . 22666 answer : a"
Answer: a
Python program:
a = 3400 * 100
b = a / 15
Problem: when a person aged 39 is added to a group of n people , the average age increases by 2 . when a person aged 15 is added instead , the average age decreases by 1 . what is the value of r ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "a simple and elegant solution . as addition of 39 , shifts mean by 2 , and addition of 15 , shifts mean by 1 to the other side , we have the mean lying between 3915 , and in a ratio of 2 : 1 39 - 15 = 24 24 divide by 3 is 8 . meaning mean of the n terms is 15 + 8 = 39 - 16 = 23 now , from first statement , when a person aged 39 is added to a group of n people , the average age increases by 2 . r * 23 + 39 = 25 * ( r + 1 ) r = 7 ans . ( a )"
Answer: a
Python program:
a = 39 - 15
b = 2 + 1 
c = a / b
d = c - 1
Problem: a number when multiplied by 3 is odd and divisible by 9 . this number when multiplied by 4 is 108 . what is the original number ?
Options: a ) 10 , b ) 18 , c ) 13 , d ) 21 , e ) 27
Rationale: working backward , 108 divided by 4 is 27 . this number fits the rules of three and nine , where the digits add up to a sum divisible by nine . answer is e .
Answer: e
Python program:
a = 108 / 4
Problem: in the coordinate plane , line a has a slope of - 1 and an x - intercept of 1 . line b has a slope of 5 and a y - intercept of - 5 . if the two lines intersect at the point ( a , b ) , what is the sum a + b ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "the equation of line a is y = - x + 1 the equation of line b is y = 5 x - 5 5 x - 5 = - x + 1 x = 1 y = 0 the point of intersection is ( 1,0 ) and then a + b = 1 . the answer is b ."
Answer: b
Python program:
a = 5 - 5
b = a - 1
c = b / 1
Problem: the interest on a certain deposit at 4.5 % p . a . is rs . 405 in one year . how much will the additional interest in one year be on the same deposit at 5 % p . a . ?
Options: a ) rs . 50 , b ) rs . 45 , c ) rs . 40.5 , d ) rs . 48.5 , e ) rs . 49.5
Rationale: s . i . = rs . 405 r = 4.5 % t = 1 year principal = ( 100 * 405 ) / ( 4.5 * 1 ) = rs . 9000 s . i at 5 % interest = ( 9000 * 5 * 1 ) / 100 = rs . 450 difference in interest = 450 – 405 = rs . 45 answer : b
Answer: b
Python program:
a = 4 / 5
b = 405 / a
c = b * 5
d = c / 100
e = d - 405
Problem: a metallic sphere of radius 12 cm is melted and drawn into a wire , whose radius of cross section is 16 cm . what is the length of the wire ?
Options: a ) 45 cm , b ) 18 cm , c ) 90 cm , d ) 180 cm , e ) none of these
Rationale: volume of the wire ( in cylindrical shape ) is equal to the volume of the sphere . π ( 16 ) 2 * h = ( 4 / 3 ) π ( 12 ) 3 = > h = 9 cm answer : e
Answer: e
Python program:
a = 12 ** 3
b = 16 ** 2
c = a / b
d = 4 * c
e = d / 3
Problem: in a box of 12 pens , a total of 4 are defective . if a customer buys 3 pens selected at random from the box , what is the probability that neither pen will be defective ?
Options: a ) 1 / 6 , b ) 2 / 55 , c ) 14 / 55 , d ) 12 / 55 , e ) 3 / 4
Rationale: "method - 1 there are 9 fine pieces of pen and 4 defective in a lot of 12 pens i . e . probability of first pen not being defective = ( 8 / 12 ) i . e . probability of second pen not being defective = ( 7 / 11 ) i . e . probability of third pen not being defective = ( 6 / 10 ) probability of both pen being non - defective = ( 8 / 12 ) * ( 7 / 11 ) * ( 6 / 10 ) = 14 / 55 answer : option c"
Answer: c
Python program:
a = 12 - 4
b = a / 12
c = 12 - 4
d = c - 1
e = 12 - 1
f = d / e
g = b * f
Problem: two friends plan to walk along a 33 - km trail , starting at opposite ends of the trail at the same time . if friend p ' s rate is 20 % faster than friend q ' s , how many kilometers will friend p have walked when they pass each other ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: "if q complete x kilometers , then p completes 1.2 x kilometers . x + 1.2 x = 33 2.2 x = 33 x = 15 then p will have have walked 1.2 * 15 = 18 km . the answer is d ."
Answer: d
Python program:
a = 20 / 100
b = a + 1 
c = b + 1 
d = 33 / c
e = 20 / 100
f = e + 1 
g = d * f
Problem: the number of degrees that the hour hand of a clock moves through between noon and 2.30 in the afternoon of the same day is
Options: a ) 720 , b ) 180 , c ) 75 , d ) 65 , e ) none of these
Rationale: "explanation : the hour hand moves from pointing to 12 to pointing to half way between 2 and 3 . the angle covered between each hour marking on the clock is 360 / 12 = 30 . since the hand has covered 2.5 of these divisions the angle moved through is 75 . answer : c"
Answer: c
Python program:
a = math.floor(2, 30)
b = math.floor(2, 30)
c = 2 - 30
d = c / const_60
e = d * 100
f = a + e 
g = f * 3
h = g * 10
Problem: a train running at the speed of 90 km / hr crosses a pole in 15 seconds . what is the length of the train ?
Options: a ) 325 , b ) 350 , c ) 375 , d ) 400 , e ) 425
Rationale: "speed = ( 90 x ( 5 / 18 ) m / sec = ( 25 ) m / sec . length of the train = ( speed x time ) . length of the train = ( ( 25 ) x 15 ) m = 375 m c"
Answer: c
Python program:
a = 90 * 1000
b = a / 3600
c = b * 15
Problem: two cars a and b start from boston and new york respectively simultaneously and travel towards each other at constant speeds along the same route . after meeting at a point between boston and new york the two cars a and b proceed to their respective destinations of new york and boston . car a reaches new york 60 minutes after the two cars have met and car b reaches boston 90 minutes after they have met . how long did car a take to cover the distance between boston and new york ?
Options: a ) 1 hour , b ) 1 hour 10 minutes , c ) 2 hours 30 minutes , d ) 2 hours , e ) 2 hours 10 minutes
Rationale: "both cars leave at the same time both cars travel at constant speed stealing a useful piece of information from paragkan : if two objects a and b start from opposite points and , after having met en route , reach their respective destinations in a and b mins ( or any other measure of time ) respectively , then the ratio of their speeds ratio of speed : ( a / b ) = sq . rt ( b / a ) sq . rt ( b / a ) sq . rt ( 90 / 60 ) sq . rt ( 3 / 2 ) so , for every three units of distance a travels , b travels two . because we know the ratio of speed and the time it took b to travel the distance a has n ' t yet covered , we can find the time it took a to cover the distance b did in 90 minutes . 90 * ( 2 / 3 ) where represents the lesser amount of time it took a to travel the distance b did in 90 minutes . = 60 minutes . therefore , a took 60 minutes to travel the first portion then 60 minutes to travel the distance b did in 90 minutes . a spent ( 60 + 60 ) = 120 minutes on the road . d . 2 hours"
Answer: d
Python program:
a = 60 / 90
b = math.sqrt(a)
c = b * 90
d = c + 60
Problem: four numbers are in the ratio 2 : 3 : 4 : 5 add up to give a sum of 1344 . find the biggest number .
Options: a ) 480 , b ) 239 , c ) 270 , d ) 282 , e ) 112
Rationale: answer : a
Answer: a
Python program:
a = 2 * 4
b = a * 100
c = 3 * 4
d = b + c
Problem: five machines , each working at the same constant rate , together can complete a certain job in 20 days . how many additional machines , each working at the same constant rate , will be needed to complete the job in 10 days ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 5 , e ) 10
Rationale: rate of one machine = 1 job / ( 20 * 5 ) days let x = number of machines needed to complete the job in 10 days 1 / ( 5 * 20 ) * 10 * x = 1 job x = 10 10 - 5 = 5 answer : d
Answer: d
Python program:
a = 4 + 1 
b = 20 * a
c = b / 10
d = 4 + 1 
e = c - d
Problem: find ( 7 x + 4 y ) / ( x - 2 y ) if x / 2 y = 5 / 2 ?
Options: a ) 13 , b ) 25 , c ) 26 , d ) 27 , e ) 29
Rationale: "x / 2 y = 3 / 2 = > x = 10 y / 2 = 5 y = > ( 7 x + 4 y ) / ( x - 2 y ) = ( ( 7 * ( 5 y ) ) + 4 y ) / ( 5 y - 2 y ) = > 39 y / 3 y = 13 answer : a"
Answer: a
Python program:
a = 5 / 2
b = a * 2
c = b * 7
d = c + 4 
e = 5 / 2
f = e * 2
g = f - 2
h = d / g
Problem: there is 60 % increase in an amount in 6 years at si . what will be the ci of rs . 11,000 after 3 years at the same rate ?
Options: a ) 3641 , b ) 2572 , c ) 4542 , d ) 2343 , e ) 3972
Rationale: "let p = rs . 100 . then , s . i . rs . 60 and t = 6 years . r = 100 x 60 = 10 % p . a . 100 x 6 now , p = rs . 11000 . t = 3 years and r = 10 % p . a . c . i . = rs . 11000 x 1 + 10 3 - 1 100 = rs . 11000 x 331 1000 = 3641 . a"
Answer: a
Python program:
a = 100 * 100
b = 60 / 6
c = 100 * b
d = c * 3
e = a + d 
f = 60 / 6
g = f / 100
h = 1 + g 
i = 60 / 6
j = i / 100
k = 1 + j 
l = h * k
m = 60 / 6
n = m / 100
o = 1 + n 
p = l * o
q = e * p
r = 100 * 100
s = 60 / 6
t = 100 * s
u = t * 3
v = r + u 
w = q - v
Problem: the ratio between the present ages of a and b is 4 : 3 respectively . the ratio between a ' s age 4 years ago and b ' s age 4 years hence is 1 : 1 . what is the ratio between a ' s age 4 years hence and b ' s age 4 years ago ?
Options: a ) 3 : 4 , b ) 3 : 0 , c ) 3 : 1 , d ) 3 : 2 , e ) 9 : 5
Rationale: let the present ages of a and b be 4 x and 3 x years respectively . then , ( 4 x - 4 ) / ( 3 x + 4 ) = 1 / 1 1 x = 8 = > x = 8 required ratio = ( 4 x + 4 ) : ( 3 x - 4 ) = 36 : 20 = 9 : 5 . answer : e
Answer: e
Python program:
a = 4 + 4 
b = 4 - 3
c = a / b
d = 4 * c
e = d + 4 
f = 4 + 4 
g = 4 - 3
h = f / g
i = 3 * h
j = i - 4
k = e / j
Problem: find value of x ( 11 ^ 2 + 12 ^ 2 + 13 ^ 2 + . . . + 20 ^ 2 ) = x
Options: a ) 1200 , b ) 1340 , c ) 1234 , d ) 1203 , e ) 2485
Rationale: ( 11 ^ 2 + 12 ^ 2 + 13 ^ 2 + . . . + 20 ^ 2 ) = ( 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + . . . + 20 ^ 2 ) - ( 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + . . . + 10 ^ 2 ) 6 = 20 x 21 x 41 - 10 x 11 x 21 6 6 = ( 2870 - 385 ) = 2485 e
Answer: e
Python program:
a = 20 + 1 
b = 20 * a
c = 2 * 20
d = c + 1 
e = b * d
f = 2 * 3
g = e / f
h = 10 + 1 
i = 10 * h
j = 2 * 10
k = j + 1 
l = i * k
m = 2 * 3
n = l / m
o = g - n
Problem: in a mixture 60 litres , the ratio of milk and water 2 : 1 . if the this ratio is to be 1 : 2 , then the quanity of water to be further added is
Options: a ) 20 liters , b ) 30 liters , c ) 50 liters , d ) 60 liters , e ) none of these
Rationale: "explanation : quantity of milk = 60 * ( 2 / 3 ) = 40 liters quantity of water = 60 - 40 = 20 liters as per question we need to add water to get quantity 2 : 1 = > 40 / ( 20 + x ) = 1 / 2 = > 20 + x = 80 = > x = 60 liters option d"
Answer: d
Python program:
a = 2 + 1 
b = 60 / a
c = 60 - b
d = c * 2
e = 2 + 1 
f = 60 / e
g = d - f
Problem: of the 13 employees in a certain department , 1 has an annual salary of 38,000 , 2 have an annual salary of 45,600 each , 2 have an annual salary of 42,500 each , 3 have an annual salary of 40,000 each and 5 have an annual salary of 48,500 each . what is the median annual salary for the 13 employees ?
Options: a ) 38,000 , b ) 40,000 , c ) 42,600 , d ) 45,600 , e ) 48,500
Rationale: "median is just the value in the middle when you arrange all values in the ascending order in this question , the 7 th value would be the median ( since there are 13 employees ) 38 , 40 , 40 , 40 , 42.5 , 42.5 , 45.6 so , answer is d ."
Answer: d
Python program:
a = 100 * 100
b = a * 4
Problem: if m and n are positive integers and m ^ 2 + n ^ 2 = 58 , what is the value of m ^ 3 + n ^ 3 ?
Options: a ) 72 , b ) 224 , c ) 370 , d ) 512 , e ) 1,600
Rationale: "you need to integers which squared are equal 58 . which could it be ? let ' s start with the first integer : 1 ^ 2 = 1 2 ^ 2 = 4 3 ^ 2 = 9 4 ^ 2 = 16 5 ^ 2 = 25 6 ^ 2 = 36 7 ^ 2 = 49 stop . the integers ca n ' t be greater than 7 or we will score above 58 . the second integer need to be picked up the same way . 1 ^ 2 = 1 2 ^ 2 = 4 3 ^ 2 = 9 4 ^ 2 = 16 5 ^ 2 = 25 6 ^ 2 = 36 7 ^ 2 = 49 the only pair that matches is 7 ^ 2 + 3 ^ 2 = 58 . so 7 ^ 3 + 3 ^ 3 = 370 . answer c . )"
Answer: c
Python program:
a = math.gcd(58, 4)
Problem: a circular ground whose radius is 15 metres , has a 1.2 metre - broad garden around it . what is the area of the garden in square metres ?
Options: a ) 118.67
b ) 116.67
c ) 117.67
d ) 120.56
e ) 120.57
Rationale: req . area = ï € [ ( 16.2 ) 2 â € “ ( 15 ) 2 ] = 22 â  „ 7 ã — ( 31.2 ã — 1.2 ) [ since a 2 - b 2 = ( a + b ) ( a - b ) ] = ( 22 ã — 31.2 ã — 1.2 ) / 7 = 117.67 sq m answer c
Answer: c
Python program:
a = 15 + 1 
b = circle_area - (
Problem: rahim bought 65 books for rs . 1160 from one shop and 50 books for rs . 920 from another . what is the average price he paid per book ?
Options: a ) rs . 18.28 , b ) rs . 20 , c ) rs . 18.08 , d ) rs . 28.08 , e ) rs . 38.08
Rationale: average price per book = ( 1160 + 920 ) / ( 65 + 50 ) = 2080 / 115 = rs . 18.08 answer : c
Answer: c
Python program:
a = 1160 + 920 
b = 65 + 50 
c = a / b
Problem: the ratio of the volumes of two cubes is 512 : 729 . what is the ratio of their total surface areas ?
Options: a ) 1 : 22 , b ) 81 : 12 , c ) 41 : 46 , d ) 41 : 19 , e ) 84 : 12
Rationale: "ratio of the sides = ³ √ 512 : ³ √ 729 = 8 : 9 ratio of surface areas = 82 : 92 = 41 : 46 answer : c"
Answer: c
Python program:
a = 512 / 729
b = 1 / 3
c = a ** b
Problem: x starts a business with rs . 45000 . y joins in the business after 7 months with rs . 30000 . what will be the ratio in which they should share the profit at the end of the year ?
Options: a ) 1 : 2 , b ) 18 : 5 , c ) 1 : 5 , d ) 3 : 1 , e ) 1 : 1
Rationale: "explanation : ratio in which they should share the profit = ratio of the investments multiplied by the time period = 45000 ã — 12 : 30000 ã — 5 = 45 ã — 12 : 30 ã — 5 = 3 ã — 12 : 2 ã — 5 = 18 : 5 answer : option b"
Answer: b
Python program:
a = 45000 * 12
b = 4 + 3 
c = 30000 * b
d = a / c
Problem: if rs . 782 be divided into 3 parts , proportional to 1 / 2 : 1 / 3 : 3 / 4 , then the first part is ?
Options: a ) a ) 426 , b ) b ) 526 , c ) c ) 247 , d ) d ) 204 , e ) e ) 297
Rationale: given ratio = 1 / 2 : 2 / 3 : 3 / 4 = 6 : 4 : 9 1 st part = 782 * 6 / 19 = rs . 247 answer : c
Answer: c
Python program:
a = 1 / 2
b = 1 / 2
c = 1 / 3
d = b + c 
e = 3 / 4
f = d + e 
g = a / f
h = g * 782