euclaise/mathqa_programs huggingface dataset:
Problem: reena took a loan of $ . 1200 with simple interest for as many years as the rate of interest . if she paid $ 192 as interest at the end of the loan period , what was the rate of interest ?
Options: a ) 3.6 , b ) 6 , c ) 4 , d ) can not be determined , e ) none of these
Rationale: "let rate = r % and time = r years . then , 1200 x r x r / 100 = 192 12 r 2 = 192 r 2 = 16 r = 4 . answer : c"
Answer: c
Python program:
a = 192 * 100
b = a / 1200
c = math.sqrt(b)
Problem: √ ( 25 ) ^ 2
Options: a ) 5 , b ) 14 , c ) 25 , d ) 21 , e ) none of these
Rationale: "explanation √ ( 25 ) ^ 2 = ? or , ? = 25 answer c"
Answer: c
Python program:
a = 25 ** 2
b = math.sqrt(a)
Problem: x can finish a work in 15 days . y can finish the same work in 20 days . y worked for 12 days and left the job . how many days does x alone need to finish the remaining work ?
Options: a ) 5 , b ) 3 , c ) 4 , d ) 7 , e ) 8
Rationale: "work done by x in 1 day = 1 / 15 work done by y in 1 day = 1 / 20 work done by y in 12 days = 12 / 20 = 3 / 5 remaining work = 1 – 3 / 5 = 2 / 5 number of days in which x can finish the remaining work = ( 1 / 3 ) / ( 1 / 15 ) = 5 a"
Answer: a
Python program:
a = 1 / 20
b = 12 * a
c = 1 - b
d = 1 / 15
e = c / d
Problem: the average of first 18 natural numbers is ?
Options: a ) 5.6 , b ) 9.5 , c ) 9.1 , d ) 9.8 , e ) 5.2
Rationale: "sum of 18 natural no . = 342 / 2 = 171 average = 171 / 18 = 9.5 answer : b"
Answer: b
Python program:
a = 18 + 1
Problem: what is the sum of 20 consecutive integers from - 9 inclusive , in a increasing order ?
Options: a ) - 9 , b ) 9 , c ) - 10 , d ) 10 , e ) 20
Rationale: "from - 9 to - 1 - - > 9 nos . zero - - > 1 number from + 1 to + 9 - - > 9 nos . when we add up nos . from - 9 to + 9 sum will be zero . total 19 nos will be added . 20 th number will be 10 . sum of these 20 nos . = 10 . d is the answer ."
Answer: d
Python program:
a = 9 + 1
Problem: if log 1087.5 = 2.9421 , then the number of digits in ( 875 ) 10 is ?
Options: a ) 30 , b ) 28 , c ) 27 , d ) 26 , e ) 40
Rationale: "x = ( 875 ) 10 = ( 87.5 x 10 ) 10 therefore , log 10 x = 10 ( log 2087.5 + 1 ) = 10 ( 2.9421 + 1 ) = 10 ( 3.9421 ) = 39.421 x = antilog ( 39.421 ) therefore , number of digits in x = 40 . answer : e"
Answer: e
Python program:
a = 4 * 2
b = math.log(100)
c = math.log(10)
d = b / c
e = a + d
Problem: annie and sam set out together on bicycles traveling at 15 and 12 km per hour respectively . after 40 minutes , annie stops to fix a flat tire . if it takes annie 20 minutes to fix the flat tire and sam continues to ride during this time , how many minutes will it take annie to catch up with sam assuming that annie resumes riding at 15 km per hour ?
Options: a ) 20 , b ) 40 , c ) 60 , d ) 80 , e ) 100
Rationale: "annie gains 3 km per hour ( or 1 km every 20 minutes ) on sam . after 40 minutes annie is 2 km ahead . sam rides 1 km every 5 minutes . in the next 20 minutes , sam rides 4 km so sam will be 2 km ahead . it will take annie 40 minutes to catch sam . the answer is b ."
Answer: b
Python program:
a = 15 - 12
b = 40 / const_60
c = a * b
d = 12 / c
e = 15 - 12
f = 40 / const_60
g = e * f
h = d - g
i = 15 - 12
j = h / i
k = j * const_60
Problem: last year the range of the annual yield on equal amount of investments in 100 mutual funds was $ 10000 . if the annual yield this year for each of the 100 mutual funds has improved by 15 percent this year than it was last year , what is the range of the annual yield on mutual funds this year ?
Options: a ) $ 12700 , b ) $ 13000 , c ) $ 23000 , d ) $ 11500 , e ) $ 33000
Rationale: let the lowest yield be x . therefore , highest yield is x + 10000 . now yield of each mutual fund investment is improved by 10 % . therefore the yields will remain arranged in the same order as before . or lowest yield = 1.15 x and highest = 1.15 * ( x + 10000 ) or range = highest - lowest = 1.15 * ( x + 10000 ) - 1.15 x = 11500 , hence , d
Answer: d
Python program:
a = 15 / 100
b = 10000 * a
c = 10000 + b
Problem: a customer purchased a package of ground beef at a cost of $ 1.80 per pound . for the same amount of money , the customer could have purchased a piece of steak that weighed 25 percent less than the package of ground beef . what was the cost per pound of the steak ?
Options: a ) $ 2.00 , b ) $ 2.15 , c ) $ 2.30 , d ) $ 2.40 , e ) $ 2.65
Rationale: "for simplicity , let ' s assume the customer bought 1 pound of ground beef for $ 1.80 . let x be the price per pound for the steak . then 0.75 x = 180 x = 180 / 0.75 = $ 2.40 the answer is d ."
Answer: d
Python program:
a = const_0_25 * 2
b = const_0_33 * 1
c = a + b 
d = 1 / 80
Problem: two trains a and b starting from two points and travelling in opposite directions , reach their destinations 9 hours and 4 hours respectively after meeting each other . if the train a travels at 100 kmph , find the rate at which the train b runs .
Options: a ) 40 , b ) 60 , c ) 150 , d ) 80 , e ) 100
Rationale: "if two objects a and b start simultaneously from opposite points and , after meeting , reach their destinations in ‘ a ’ and ‘ b ’ hours respectively ( i . e . a takes ‘ a hrs ’ to travel from the meeting point to his destination and b takes ‘ b hrs ’ to travel from the meeting point to his destination ) , then the ratio of their speeds is given by : sa / sb = √ ( b / a ) i . e . ratio of speeds is given by the square root of the inverse ratio of time taken . sa / sb = √ ( 4 / 9 ) = 2 / 3 this gives us that the ratio of the speed of a : speed of b as 2 : 3 . since speed of a is 100 kmph , speed of b must be 100 * ( 3 / 2 ) = 150 kmph answer c"
Answer: c
Python program:
a = 9 / 4
b = math.sqrt(a)
c = 100 * b
Problem: a soft drink company had 6000 small and 15000 big bottles in storage . if 12 % of small 14 % of big bottles have been sold , then the total bottles remaining in storage is
Options: a ) 15360 , b ) 16010 , c ) 18180 , d ) 14930 , e ) 16075
Rationale: "6000 + 15000 - ( 0.12 * 6000 + 0.14 * 15000 ) = 18180 . answer : c ."
Answer: c
Python program:
a = 6000 + 15000 
b = 12 / 100
c = 6000 * b
d = 14 / 100
e = d * 15000
f = c + e 
g = a - f
Problem: in a box of 10 pencils , a total of 2 are defective . if a customer buys 3 pencils selected at random from the box , what is the probability that neither pencils will be defective ?
Options: a ) 1 / 12 , b ) 7 / 15 , c ) 2 / 13 , d ) 2 / 15 , e ) 1 / 17
Rationale: "first , there are 8 c 3 ways you can select 3 good pencils from 4 good ones . second , there are 10 c 3 ways you select 3 pencils from 6 ones in the box . then , the probability that neither pen will be defective is : 8 c 3 / 10 c 3 = 56 / 120 = 7 / 15 answer is b"
Answer: b
Python program:
a = 10 - 2
b = math.factorial(a)
c = 10 - 2
d = c - 3
e = math.factorial(d)
f = math.factorial(3)
g = e * f
h = b / g
i = math.factorial(10)
j = 10 - 3
k = math.factorial(j)
l = math.factorial(3)
m = k * l
n = i / m
o = h / n
Problem: company workers decided to raise rs . 3 lakhs by equal contribution from each . had they contributed rs . 50 each extra , the contribution would have been rs . 3.25 lakhs . how many workers were they ?
Options: a ) 300 , b ) 400 , c ) 500 , d ) 600 , e ) 700
Rationale: explanation : n * 50 = ( 325000 - 300000 ) = 25000 n = 25000 / 50 = 500 option c
Answer: c
Python program:
a = 100 * 1000
b = 3 * 25
c = 100 * 1000
d = 3 * c
e = b - d
f = e / 50
Problem: the average of 7 numbers is 20 . if each number be multiplied by 5 . find the average of new set of numbers ?
Options: a ) a ) 100 , b ) b ) 122 , c ) c ) 120 , d ) d ) 125 , e ) e ) 145
Rationale: "explanation : average of new numbers = 20 * 5 = 100 answer : option a"
Answer: a
Python program:
a = 20 * 5
Problem: right triangle pqr is the base of the prism in the figure above . if pq = pr = â ˆ š 5 and the height of the prism is 10 , what is the volume of the prism ?
Options: a ) 5
b ) 10
c ) 15
d ) 20
e ) 25
Rationale: volume of prism = area of base * height = 1 / 2 * ( square root of 5 ) * ( square root of 5 ) * 10 = 25 answer : e
Answer: e
Python program:
a = math.sqrt(5)
b = math.sqrt(5)
c = triangle_area * (
Problem: each of the positive integers a and c is a 4 - digit integer . if each of the digits 0 through 9 appears in one of these 3 integers , what is the maximum possible value of the sum of a and c ?
Options: a ) 18695 , b ) 18325 , c ) 18365 , d ) 18395 , e ) 18485
Rationale: according to the stem we should use the digits 0 through 9 to construct 2 four - digit integers , so that their sum is as big as possible . to maximize the sum , maximize the thousands digits of a and c , so make them 9 and 8 . next , maximize hundreds digits . make them 7 and 6 . next maximize 10 ' s digit place by 5 and 4 use the remaining digits ( 3 , and 2 ) for units digits . so , a would be 9753 , and c would be 8642 . 9753 + 8642 = 18395 answer : d .
Answer: d
Python program:
a = 9 * 1000
b = 3 + 4 
c = b * 100
d = a + c 
e = 4 + 1 
f = e * 10
g = d + f 
h = g + 3 
i = 4 * 2
j = i * 1000
k = 3 * 2
l = k * 100
m = j + l 
n = 4 * 10
o = m + n 
p = o + 2 
q = h + p
Problem: the length of a rectangle is doubled while its width is doubled . what is the % change in area ?
Options: a ) 250 % , b ) 300 % , c ) 500 % , d ) 650 % , e ) 700 %
Rationale: "the original area is l * w the new area is 2 l * 2 w = 4 * l * w = l * w + 3 * l * w the area increased by 300 % . the answer is b ."
Answer: b
Python program:
a = 2 * 3
b = a - 1
c = b * 10
Problem: riya and priya set on a journey . riya moves eastward at a speed of 18 kmph and priya moves westward at a speed of 24 kmph . how far will be priya from riya after 15 minutes
Options: a ) 25 kms , b ) 11 kms , c ) 50 kms , d ) 30 kms , e ) 40 kms
Rationale: total eastward distance = 18 kmph * 1 / 4 hr = 4.5 km total westward distance = 24 kmph * 1 / 4 hr = 6 km total distn betn them = 4.5 + 6 = 10.5 m ans 11 km answer : b
Answer: b
Python program:
a = 18 + 24 
b = speed * (
Problem: 36 persons can repair a road in 12 days , working 5 hours a day . in how many days will 30 persons , working 6 hours a day , complete the work ?
Options: a ) 12 , b ) 16 , c ) 13 , d ) 18 , e ) 19
Rationale: "let the required number of days be x . less persons , more days ( indirect proportion ) more working hours per day , less days ( indirect proportion ) persons 30 : 36 : : 12 : x working hours / day 6 : 5 30 x 6 x x = 36 x 5 x 12 x = ( 36 x 5 x 12 ) / ( 30 x 6 ) x = 12 answer a"
Answer: a
Python program:
a = 36 * 12
b = a * 5
c = 30 * 6
d = b / c
Problem: a shopkeeper buys two articles for rs . 1000 each and then sells them , making 10 % profit on the first article and 10 % loss on second article . find the net profit or loss percent ?
Options: a ) 200 , b ) 278 , c ) 100 , d ) 202 , e ) 270
Rationale: profit on first article = 10 % of 1000 = 100 . this is equal to the loss he makes on the second article . that , is he makes neither profit nor loss . answer : c
Answer: c
Python program:
a = 100 - 10
b = 100 / a
c = b * 1000
d = 100 + 10 
e = 100 / d
f = e * 1000
g = c + f 
h = 1000 + 1000 
i = g - h
j = i * 100
k = 100 - 10
l = 100 / k
m = l * 1000
n = 100 + 10 
o = 100 / n
p = o * 1000
q = m + p 
r = j / q
s = r * 100
Problem: a can run 4 times as fast as b and gives b a start of 63 m . how long should the race course be so that a and b might reach in the same time ?
Options: a ) 70 m , b ) 60 m , c ) 80 m , d ) 65 m , e ) 84 m
Rationale: "speed of a : speed of b = 4 : 1 means in a race of 4 m a gains 3 m . then in a race of 63 m he gains 63 * ( 4 / 3 ) i . e 84 m answer : e"
Answer: e
Python program:
a = 63 / 4
b = 4 - 1
c = a / b
d = 4 * c
e = d + 63
Problem: if c is 25 % of a and 10 % of b , what percent of a is b ?
Options: a ) 2.5 % , b ) 15 % , c ) 25 % , d ) 35 % , e ) 250 %
Rationale: "c is 25 % of a - - > c = a / 4 ; c is 10 % of b - - > c = b / 10 ; thus a / 4 = b / 10 - - > b = 5 / 2 * a = 2.5 a . therefore , b is 250 % of a . answer : e"
Answer: e
Python program:
a = 25 / 100
b = 10 / 100
c = a / b
d = c * 100
Problem: car x began traveling at an average speed of 35 miles per hour . after 72 minutes , car y began traveling at an average speed of 40 miles per hour . when both cars had traveled the same distance , both cars stopped . how many miles did car x travel from the time car y began traveling until both cars stopped ?
Options: a ) 205 , b ) 220 , c ) 240 , d ) 247 , e ) 294
Rationale: "car y began travelling after 72 minutes or 1.2 hours . let t be the time for which car y travelled before it stopped . both cars stop when they have travelled the same distance . so , 35 ( t + 1.2 ) = 40 t t = 8.4 distance traveled by car x from the time car y began traveling until both cars stopped is 35 x 8.4 = 294 miles answer : - e"
Answer: e
Python program:
a = 72 / const_60
b = a * 35
c = 40 - 35
d = b / c
e = 35 * d
Problem: what is the ratio between perimeters of two squares one having 2.5 times the diagonal then the other ?
Options: a ) 4 : 5 , b ) 1 : 3 , c ) 2.5 : 1 , d ) 3.5 : 1 , e ) 3 : 2
Rationale: "d = 2.5 d d = d a √ 2 = 2.5 d a √ 2 = d a = 2.5 d / √ 2 a = d / √ 2 = > 2.5 : 1 answer : c"
Answer: c
Python program:
a = 2 / 5
b = 2 / 5
Problem: a number when divided by 899 gives a remainder 63 . what remainder will be obtained by dividing the same number by 29
Options: a ) 8 , b ) 5 , c ) 7 , d ) 6 , e ) 9
Rationale: 63 / 29 , thereforerequired number is : 5 , correct answer ( b )
Answer: b
Python program:
a = 29 * 2
b = 63 - a
Problem: a and b can do a piece of work in 10 days , while b and c can do the same work in 15 days and c and a in 25 days . they started working together , after 4 days a left . after another 4 days b left . in how many days c can finish the remaining work ?
Options: a ) 16 , b ) 32 , c ) 64 , d ) 96 , e ) none of these
Rationale: "let the rates of a , b and c be a , b , and c respectively . a and b can do a piece of work in 10 days : a + b = 1 / 10 ; b and c can do the same work in 15 days : b + c = 1 / 15 ; c and a can do the same work in 25 days : c + a = 1 / 25 . sum the above 3 equations : 2 ( a + b + c ) = 31 / 150 - - > a + b + c = 31 / 300 subtract a + b = 1 / 10 from above to get c = 1 / 300 . for 4 days all 3 worked and completed 4 * ( a + b + a ) = 124 / 300 of the work . for the next 4 days b and c worked and they completed 4 ( b + c ) = 4 / 15 = 80 / 300 of the work . so , by the time c is left alone 1 - ( 124 / 300 + 80 / 300 ) = 96 / 300 of the work is left to be completed by c alone . time = job / rate = ( 96 / 300 ) / ( 1 / 300 ) = 96 days . answer : d"
Answer: d
Python program:
a = 1 / 10
b = 1 / 15
c = a + b 
d = 1 / 25
e = c + d 
f = e / 2
g = f * 4
h = 1 - g
i = 1 / 10
j = 1 / 15
k = i + j 
l = 1 / 25
m = k + l 
n = m / 2
o = 1 / 15
p = n - o
q = h / p
Problem: 17 men take 21 days of 8 hours each to do a piece of work . how many days of 6 hours each would 21 women take to do the same . if 3 women do as much work as 2 men ?
Options: a ) 34 , b ) 87 , c ) 30 , d ) 99 , e ) 77
Rationale: "3 w = 2 m 17 m - - - - - - 21 * 8 hours 21 w - - - - - - x * 6 hours 14 m - - - - - - x * 6 17 * 21 * 8 = 14 * x * 6 x = 34 answer : a"
Answer: a
Python program:
a = 21 * 8
b = 17 * 3
c = a * b
d = 21 * 2
e = d * 6
f = c / e
g = math.floor(f)
h = g + 1
Problem: if xy = 9 , x / y = 36 , for positive numbers x and y , y = ?
Options: a ) 1 / 2 , b ) 2 , c ) 1 / 3 , d ) 3 , e ) 1 / 6
Rationale: very easy question . 2 variables and 2 easy equations . xy = 9 - - - > x = 9 / y - ( i ) x / y = 36 - - - > replacing ( i ) here - - - > 9 / ( y ^ 2 ) = 36 - - - > y ^ 2 = 9 / 36 = 1 / 4 - - - > y = 1 / 2 or - 1 / 2 the question states that x and y are positive integers . therefore , y = 1 / 2 is the answer . answer a .
Answer: a
Python program:
a = 9 / 36
b = math.sqrt(a)
Problem: in one year , the population , of a village increased by 20 % and in the next year , it decreased by 20 % . if at the end of 2 nd year , the population was 9600 , what was it in the beginning ?
Options: a ) 10000 , b ) 8000 , c ) 1988 , d ) 1277 , e ) 2081
Rationale: x * 120 / 100 * 80 / 100 = 9600 x * 0.96 = 9600 x = 9600 / 0.96 = > 10000 answer : a
Answer: a
Python program:
a = 20 / 100
b = 1 - a
c = 9600 / b
d = 20 / 100
e = 1 + d 
f = c / e
Problem: two numbers are in the ratio of 15 : 11 . if their h . c . f . is 13 , find the numbers .
Options: a ) 195,143 , b ) 185,133 , c ) 175,123 , d ) 165,113 , e ) none of them
Rationale: let the required numbers be 15 . x and llx . then , their h . c . f . is x . so , x = 13 . the numbers are ( 15 x 13 and 11 x 13 ) i . e . , 195 and 143 . answer is a .
Answer: a
Python program:
a = 15 * 13
Problem: a bag contains 7 red , 5 blue and 4 green balls . if 2 ballsare picked at random , what is the probability that both are red ?
Options: a ) 2 / 15 , b ) 2 / 21 , c ) 7 / 40 , d ) 3 / 29 , e ) 4 / 27
Rationale: "p ( both are red ) , = 7 c 216 c 2 = 7 c 216 c 2 = 21 / 120 = 7 / 40 c"
Answer: c
Python program:
a = math.comb(7, 2)
b = 7 + 5 
c = b + 4 
d = math.comb(c, 2)
e = a / d
Problem: a boat can travel with a speed of 22 km / hr in still water . if the speed of the stream is 5 km / hr , find the time taken by the boat to go 216 km downstream
Options: a ) 5 hours , b ) 4 hours , c ) 3 hours , d ) 2 hours , e ) 8 hours
Rationale: "explanation : speed of the boat in still water = 22 km / hr speed of the stream = 5 km / hr speed downstream = ( 22 + 5 ) = 27 km / hr distance travelled downstream = 216 km time taken = distance / speed = 216 / 27 = 8 hours . answer : option e"
Answer: e
Python program:
a = 22 + 5 
b = 216 / a
Problem: a certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996 . if total revenues from car sales and truck sales in 1997 were up 1 percent from 1996 , what is the ratio w of revenue from car sales in 1996 to revenue from truck sales in 1996 ?
Options: a ) 1 : 2 , b ) 4 : 5 , c ) 1 : 1 , d ) 3 : 2 , e ) 5 : 3
Rationale: a . . i have probably solved this question 3 - 4 times by now . . remember the answer . . 1 : 2
Answer: a
Python program:
a = 100 + 7 
b = 100 + 1 
c = a - b
d = 100 + 1 
e = 100 - 11
f = d - e
g = c / f
Problem: in 1979 approximately 1 / 3 of the 37.3 million airline passengers traveling to or from the united states used kennedy airport . if the number of such passengers that used miami airport was 1 / 2 the number that used kennedy airport and 5 times the number that used logan airport , approximately how many millions of these passengers used logan airport that year ?
Options: a ) 18.6 , b ) 9.3 , c ) 1.2 , d ) 3.1 , e ) 1.6
Rationale: "number of passengers using kennedy airport = 37 / 3 = ~ 12.43 passengers using miami airport = 12.43 / 2 = ~ 6.2 passengers using logan airport = 6.2 / 5 = ~ 1.24 so c"
Answer: c
Python program:
a = 37 / 3
b = 5 * 2
c = a / b
Problem: the average of 5 numbers is 6.8 . if one of the numbers is multiplied by a factor of 3 , the average of the numbers increases to 12.8 . what number is multiplied by 3 ?
Options: a ) 15.0 , b ) 13.0 , c ) 13.9 , d ) 10.0 , e ) 6.0
Rationale: "the average of 5 numbers is 6.8 the sum of 5 numbers will be 6.8 x 5 = 34 the average of 5 number after one of the number is multiplied by 3 is 12.8 the sum of the numbers will now be 12.8 x 5 = 64 so the sum has increased by 64 - 34 = 30 let the number multiplied by 3 be n then , 3 n = n + 30 or 2 n = 30 or n = 15 answer : - a"
Answer: a
Python program:
a = 12 * 8
b = 6 * 8
c = a - b
Problem: in covering a distance of 18 km , abhay takes 2 hours more than sameer . if abhay doubles his speed , then he would take 1 hour less than sameer . abhay ' s speed is :
Options: a ) 3 kmph , b ) 6 kmph , c ) 6.25 kmph , d ) 7.5 kmph , e ) 7.8 kmph
Rationale: let abhay ' s speed be x km / hr . then , 18 / x - 18 / 2 x = 3 6 x = 18 x = 3 km / hr . answer : option a
Answer: a
Python program:
a = 18 / 2
b = 18 - a
c = 1 + 2 
d = b / c
Problem: a portion of the 50 % solution of chemicals was replaced with an equal amount of 60 % solution of chemicals . as a result , 55 % solution of chemicals resulted . what part of the original solution was replaced ?
Options: a ) 3 / 4 , b ) 1 / 4 , c ) 3 / 4 , d ) 2 / 5 , e ) 1 / 2
Rationale: "this is a weighted average question . say x % of the solution was replaced - - > equate the amount of chemicals : 0.5 ( 1 - x ) + 0.6 * x = 0.55 - - > x = 1 / 2 . answer : e ."
Answer: e
Python program:
a = 50 - 55
b = 50 - 60
c = a / b
Problem: ram get 450 marks in his exam which is 90 % of total marks . what is the total marks ?
Options: a ) 475 , b ) 600 , c ) 550 , d ) 500 , e ) 525
Rationale: x * ( 90 / 100 ) = 450 x = 5 * 100 x = 500 answer : d
Answer: d
Python program:
a = 3 + 2 
b = a * 10
c = 450 + b
Problem: all the faces of a cube are painted with blue colour . then it is cut into 125 small equal cubes . how many small cubes will be formed having only one face coloured ?
Options: a ) 54 , b ) 8 , c ) 16 , d ) 24 , e ) 34
Rationale: no . of small cubes will have only one face painted = ( x - 2 ) 2 * 6 here x = side of the small cube = 5 therfore ( x - 2 ) 2 * 6 = 54 answer : a
Answer: a
Python program:
a = 1 / 3
b = 125 ** a
c = b - 2
d = c ** 2
e = d * const_60
f = e / 10
Problem: in a certain country 1 / 7 of 8 = 5 . assuming the same proportion , what would be the value of 1 / 5 of 40 ?
Options: a ) 54 , b ) 25 , c ) 45 , d ) 35 , e ) 52
Rationale: "d 35"
Answer: d
Python program:
a = 7 / 8
b = a * 40
Problem: mr . kramer , the losing candidate in a two - candidate election , received 942,568 votes , which was exactly 30 percent of all votes cast . approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast ?
Options: a ) 10 % , b ) 12 % , c ) 15 % , d ) 29 % , e ) 20 %
Rationale: let me try a simpler one . lets assume that candidate got 30 % votes and total votes is 100 . candidate won = 30 remaining = 70 to get 50 % , candidate requires 20 votes from 100 which is 20 % and 20 votes from 70 . 20 / 70 = 2 / 7 = . 285 = 28.5 % which is approx 29 % . hence the answer is d .
Answer: d
Python program:
a = 50 / 100
b = 30 / 100
c = a - b
d = 30 / 100
e = 1 - d
f = c / e
g = f * 100
Problem: in the junior basketball league there are 18 teams , 2 / 3 of them are bad and ½ are rich . what ca n ' t be the number of teams that are rich and bad ?
Options: a ) 4 . , b ) 6 . , c ) 7 . , d ) 8 . , e ) 10
Rationale: otal teams = 18 bad teams = ( 2 / 3 ) * 18 = 12 rich teams = 9 so maximum value that the both rich and bad can take will be 9 . so e = 10 can not be that value . answer : e
Answer: e
Python program:
a = 1 / 2
b = 18 * a
c = b + 1
Problem: working alone , john finishes cleaning half the house in a third of the time it takes nick to clean the entire house alone . john alone cleans the entire house in 6 hours . how many hours will it take nick and john to clean the entire house if they work together ?
Options: a ) 1.5 , b ) 2 , c ) 2.4 , d ) 3 , e ) 3.6
Rationale: answer is 3.6 hours . john does the complete house in 6 hours while nick does it in 9 hours . 1 / ( 1 / 6 + 1 / 9 ) = 3.6 answer is e
Answer: e
Python program:
a = 1/(6)
b = 3 / 2
c = b * 6
d = 1/(c)
e = a + d 
f = 1/(e)
Problem: the radius of a cylinder is 2 r units and height is 3 r units . find the curved surface ?
Options: a ) 18 π r 2 , b ) 12 π r 2 , c ) 3 π r 2 , d ) 6 π r 2 , e ) 9 π r 2
Rationale: "explanation : 2 * π * 2 r * 3 r = 12 π r 2 answer : b"
Answer: b
Python program:
a = circumface * (
Problem: on the richter scale , which measures the total amount of energy released during an earthquake , a reading of x - 1 indicates one - tenth the released energy as is indicated by a reading of x . on that scale , the frequency corresponding to a reading of 7 is how many times as great as the frequency corresponding to a reading of 5 ?
Options: a ) 10 ^ 2 , b ) 10 ^ 3 , c ) 10 ^ 4 , d ) 10 ^ 5 , e ) 10 ^ 6
Rationale: "if richter scale reading goes from x - 1 to x it will be 10 if richter scale reading goes from 5 to 6 it will be 10 similarly if richter scale reading goes from 6 to 7 it will be 10 so it will from 5 to 7 i . e 6,7 = 10 * 10 = 10 ^ 2 answer is a"
Answer: a
Python program:
a = 7 - 5
b = 10 ** a