euclaise/mathqa_programs huggingface dataset:
Problem: two consultants can type up a report in 12.5 hours and edit it in 7.5 hours . if mary needs 30 hours to type the report and jim needs 12 hours to edit it alone , how many e hours will it take if jim types the report and mary edits it immediately after he is done ?
Options: a ) 41.4 , b ) 34.1 , c ) 13.4 , d ) 12.4 , e ) 10.8
Rationale: "break down the problem into two pieces : typing and editing . mary needs 30 hours to type the report - - > mary ' s typing rate = 1 / 30 ( rate reciprocal of time ) ( point 1 in theory below ) ; mary and jim can type up a report in 12.5 and - - > 1 / 30 + 1 / x = 1 / 12.5 = 2 / 25 ( where x is the time needed for jim to type the report alone ) ( point 23 in theory below ) - - > x = 150 / 7 ; jim needs 12 hours to edit the report - - > jim ' s editing rate = 1 / 12 ; mary and jim can edit a report in 7.5 and - - > 1 / y + 1 / 12 = 1 / 7.5 = 2 / 15 ( where y is the time needed for mary to edit the report alone ) - - > y = 20 ; how many e hours will it take if jim types the report and mary edits it immediately after he is done - - > x + y = 150 / 7 + 20 = ~ 41.4 answer : a ."
Answer: a
Python program:
a = 1 / 12
b = 1 / 30
c = a - b
d = 1/(c)
e = 1 / 7
f = 1 / 12
g = e - f
h = 1/(g)
i = d + h
Problem: a man saves 20 % of his monthly salary . if an account of dearness of things he is to increase his monthly expenses by 10 % , he is only able to save rs . 500 per month . what is his monthly salary ?
Options: a ) rs . 4500 , b ) rs . 4000 , c ) rs . 4167 , d ) rs . 4200 , e ) rs . 3000
Rationale: income = rs . 100 expenditure = rs . 80 savings = rs . 20 present expenditure 80 + 80 * ( 10 / 100 ) = rs . 88 present savings = 100 – 88 = rs . 12 if savings is rs . 12 , salary = rs . 100 if savings is rs . 500 , salary = 100 / 12 * 500 = 4167 answer : c
Answer: c
Python program:
a = 500 * 100
b = 100 - 20
c = 100 - 20
d = 10 / 100
e = c * d
f = b + e 
g = 100 - f
h = a / g
Problem: a started a business with an investment of rs . 70000 and after 6 months b joined him investing rs . 120000 . if the profit at the end of a year is rs . 78000 , then the share of a is ?
Options: a ) s . 42028 , b ) s . 42000 , c ) s . 42003 , d ) s . 42029 , e ) s . 24029
Rationale: "ratio of investments of a and b is ( 70000 * 12 ) : ( 120000 * 6 ) = 7 : 6 total profit = rs . 78000 share of b = 7 / 13 ( 78000 ) = rs . 42000 answer : b"
Answer: b
Python program:
a = const_60 * 100
b = 78000 - a
Problem: what is the minimum value of | x - 4 | + | x + 7 | + | x - 5 | ?
Options: a ) - 3 , b ) 3 , c ) 5 , d ) - 12 , e ) 12
Rationale: "a can not be the answer as all the three terms are in modulus and hence the answer will be non negative . | x - 4 | > = 0 - - > minimum occurs at x = 4 | x + 7 | > = 0 - - > minimum occurs at x = - 7 | x - 5 | > = 0 - - > minimum occurs at x = 5 x = - 7 - - > result = 11 + 0 + 12 = 23 . also any negative value will push the combined value of | x - 4 | + | x - 5 | to a value > 9 . x = 4 - - > result = 0 + 11 + 1 = 12 x = 5 - - > result = 1 + 12 + 0 = 13 x = 7 - - > result = 3 + 14 + 2 = 19 so minimum value of the expression occurs at x = 4 and the resultant value = 12 answer : e"
Answer: e
Python program:
a = 7 + 5
Problem: the average of 1 st 3 of 4 numbers is 16 and of the last 3 are 15 . if the sum of the first and the last number is 13 . what is the last numbers ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 5 , e ) 7
Rationale: "a + b + c = 48 b + c + d = 45 a + d = 13 a – d = 3 a + d = 13 2 d = 10 d = 5"
Answer: d
Python program:
a = 3 * 16
b = 13 - 16
c = b + 3 
d = a - c
e = d - 16
Problem: mahesh marks an article 15 % above the cost price of rs . 540 . what must be his discount percentage if he sells it at rs . 456 ?
Options: a ) 18 % , b ) 26.57 % , c ) 20 % , d ) 19 % , e ) none of these
Rationale: "cp = rs . 540 , mp = 540 + 15 % of 540 = rs . 621 sp = rs . 456 , discount = 621 - 456 = 165 discount % = 165 / 621 * 100 = 26.57 % answer : b"
Answer: b
Python program:
a = 100 + 15 
b = a / 100
c = 540 * b
d = c - 456
e = d * 100
f = 100 + 15 
g = f / 100
h = 540 * g
i = e / h
Problem: the h . c . f . of two numbers is 11 and their l . c . m . is 693 . if one of the numbers is 77 , find the other .
Options: a ) 99 , b ) 97 , c ) 95 , d ) 91 , e ) 96
Rationale: "other number = 11 x 693 / 77 = 99 answer is a ."
Answer: a
Python program:
a = 11 * 77
Problem: kate and danny each have $ 10 . together , they flip a fair coin 5 times . every time the coin lands on heads , kate gives danny $ 1 . every time the coin lands on tails , danny gives kate $ 1 . after the 5 coin flips , what is the probability that kate has more than $ 10 but less than $ 15 ?
Options: a ) 5 / 16 , b ) 1 / 2 , c ) 12 / 30 , d ) 15 / 32 , e ) 3 / 8
Rationale: the probability of the coin landing tails up either 3 or 4 times = p ( 3 t ) + p ( 4 t ) binomial distribution formula : nck p ^ k ( 1 - p ) ^ ( n - k ) p ( 3 t ) = 5 c 3 ( 1 / 2 ) ^ 3 ( 1 / 2 ) ^ 2 = 10 ( 1 / 2 ) ^ 5 p ( 4 t ) = 5 c 4 ( 1 / 2 ) ^ 4 ( 1 / 2 ) ^ 1 = 5 ( 1 / 2 ) ^ 5 = > p ( 3 t ) + p ( 4 t ) = 15 / 32 answer : d
Answer: d
Python program:
a = math.factorial(5)
b = math.factorial(4)
c = math.factorial(1)
d = b * c
e = a / d
f = math.factorial(5)
g = math.factorial(3)
h = math.factorial(2)
i = g * h
j = f / i
k = e + j 
l = 2 ** 5
m = k / l
Problem: there are two groups of students in the sixth grade . there are 30 students in group a , and 50 students in group b . if , on a particular day , 20 % of the students in group a forget their homework , and 12 % of the students in group b forget their homework , then what percentage of the sixth graders forgot their homework ?
Options: a ) 13 % , b ) 14 % , c ) 15 % , d ) 16 % , e ) 17 %
Rationale: total students = 30 + 50 = 80 20 % of 30 = 6 12 & of 50 = 6 total students who forget homework = 6 + 6 = 12 percentage = 1280 ∗ 100 = 15 = 12 / 80 ∗ 100 = 15 ; answer = c = 15 %
Answer: c
Python program:
a = 30 * 20
b = a / 100
c = 50 * 12
d = c / 100
e = b + d 
f = 30 + 50 
g = e / f
h = g * 100
Problem: a rectangle having length 100 cm and width 40 cm . if the length of the rectangle is increased by fifty percent then how much percent the breadth should be decreased so as to maintain the same area .
Options: a ) 25 % , b ) 33.33 % , c ) 40 % , d ) 75 % , e ) none of these
Rationale: "explanation : solution : ( 50 / ( 100 + 50 ) * 100 ) % = 33.33 % answer : b"
Answer: b
Python program:
a = 100 * 40
b = 3 * 10
c = b * 100
d = c / 100
e = 100 + d 
f = a / e
g = f / 40
h = 1 + g 
i = h * 10
Problem: a fair coin is tossed 13 times . what is the probability of getting more heads than tails in 13 tosses ?
Options: a ) 1 / 2 , b ) 63 / 128 , c ) 4 / 7 , d ) 61 / 256 , e ) 63 / 64
Rationale: "on each toss , the probability of getting a head is 1 / 2 and the probability of getting a tail is 1 / 2 . there is no way to get the same number of heads and tails on an odd number of tosses . there will either be more heads or more tails . then there must be more heads on half of the possible outcomes and more tails on half of the possible outcomes . p ( more heads ) = 1 / 2 the answer is a ."
Answer: a
Python program:
a = math.comb(13, 2)
b = math.comb(13, 3)
c = a + b 
d = math.comb(13, 4)
e = c + d 
f = math.comb(13, 13)
g = e + f 
h = 2 ** 13
i = g / h
Problem: raman mixed 34 kg of butter at rs . 150 per kg with 36 kg butter at the rate of rs . 125 per kg . at what price per kg should he sell the mixture to make a profit of 40 % in the transaction ?
Options: a ) 129 , b ) 287 , c ) 192 , d ) 188 , e ) 112
Rationale: "explanation : cp per kg of mixture = [ 34 ( 150 ) + 36 ( 125 ) ] / ( 34 + 36 ) = rs . 137.14 sp = cp [ ( 100 + profit % ) / 100 ] = 137.14 * [ ( 100 + 40 ) / 100 ] = rs . 192 . answer : c"
Answer: c
Python program:
a = 34 * 150
b = 36 * 125
c = a + b 
d = 36 + 34 
e = c / d
f = 34 * 150
g = 36 * 125
h = f + g 
i = 36 + 34 
j = h / i
k = 40 / 100
l = j * k
m = e + l
Problem: in a simultaneous throw of a pair of dice , find the probability of getting a total more than 5
Options: a ) 1 / 2 , b ) 7 / 12 , c ) 5 / 13 , d ) 5 / 12 , e ) 3 / 8
Rationale: "total number of cases = 4 * 4 = 16 favourable cases = [ ( 2,4 ) , ( 3,3 ) , ( 3,4 ) , ( 4,2 ) , ( 4,3 ) , ( 4,4 ) ] = 6 so probability = 6 / 16 = 3 / 8 answer is e"
Answer: e
Python program:
a = 2 * 3
b = 5 - a
c = b / 5
Problem: in a simultaneous throw of a pair of dice , find the probability of getting a total more than 9
Options: a ) 1 / 2 , b ) 7 / 18 , c ) 5 / 13 , d ) 5 / 12 , e ) 6 / 17
Rationale: "total number of cases = 8 * 8 = 64 favourable cases = [ ( 2,8 ) , ( 3,6 ) , ( 3,7 ) , ( 4,6 ) , ( 4,7 ) , ( 4,8 ) , ( 5,5 ) , ( 5,6 ) , ( 5,7 ) , ( 5,8 ) , ( 6,4 ) , ( 6,5 ) , ( 6,6 ) , ( 6,7 ) , ( 6,8 ) , ( 7,3 ) , ( 7,4 ) , ( 7,5 ) , ( 7,6 ) , ( 7,7 ) , ( 7,8 ) , ( 8,2 ) , ( 8,3 ) , ( 8,4 ) , ( 8,5 ) , ( 8,6 ) , ( 8,7 ) , ( 8,8 ) ] = 28 so probability = 28 / 64 = 7 / 18 answer is b"
Answer: b
Python program:
a = 2 * 3
b = 9 - a
c = b / 9
Problem: a cubical tank is filled with water to a level of 2 feet . if the water in the tank occupies 32 cubic feet , to what fraction of its capacity is the tank filled with water ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 2 / 3 , d ) 1 / 4 , e ) 3 / 4
Rationale: "the volume of water in the tank is h * l * b = 32 cubic feet . since h = 2 , then l * b = 16 and l = b = 4 . since the tank is cubical , the capacity of the tank is 4 * 4 * 4 = 64 . the ratio of the water in the tank to the capacity is 32 / 64 = 1 / 2 the answer is a ."
Answer: a
Python program:
a = 32 / 10
b = 2 / a
Problem: a lent rs . 5000 to b for 2 years and rs . 3000 to c for 4 years on simple interest at the same rate of interest and received rs . 2200 in all from both of them as interest . the rate of interest per annum is ?
Options: a ) 16 % , b ) 12 % , c ) 74 % , d ) 10 % , e ) 45 %
Rationale: "let the rate be r % p . a . then , ( 5000 * r * 2 ) / 100 + ( 3000 * r * 4 ) / 100 = 2200 100 r + 120 r = 2200 r = 10 % answer : d"
Answer: d
Python program:
a = 5000 * 2
b = 3000 * 4
c = a + b 
d = 2200 / c
e = d * 100
Problem: when 1 / 10 percent of 7000 is subtracted from 1 / 10 of 7000 , the difference is
Options: a ) 0 , b ) 50 , c ) 450 , d ) 693 , e ) 500
Rationale: we can break this problem into two parts : 1 ) what is 1 / 10 percent of 7,000 ? 2 ) what is 1 / 10 of 7,000 ? to calculate 1 / 10 percent of 7,000 we must first remember to divide 1 / 10 by 100 . so we have : ( 1 / 10 ) / ( 100 ) to divide a number by 100 means to multiply it by 1 / 100 , so we have : 1 / 10 x 1 / 100 = 1 / 1,000 thus , 1 / 10 percent of 7,000 = 1 / 1,000 x 7,000 = 7 . now let ' s concentrate on part 2 . we need to calculate 1 / 10 of 7,000 . to do this we simply multiply 1 / 10 by 7,000 . 1 / 10 x 7,000 = 700 the answer to part 1 is 7 , and the answer to part 2 is 700 . their difference is 700 – 7 = 693 . answer d .
Answer: d
Python program:
a = 10 * 7000
b = a / 100
Problem: a train running at the speed of 60 km / hr crosses a pole in 9 sec . what is the length of the train ?
Options: a ) 288 , b ) 279 , c ) 277 , d ) 272 , e ) 150
Rationale: "speed = 60 * 5 / 18 = 50 / 3 m / sec length of the train = speed * time = 50 / 3 * 9 = 150 m answer : e"
Answer: e
Python program:
a = 60 * 1000
b = a / 3600
c = b * 9
Problem: if 3 x = 9 y = z , what is x + y , in terms of z ?
Options: a ) z / 2 , b ) 2 z , c ) z / 3 , d ) 3 z / 5 , e ) 4 z / 9
Rationale: "3 x = 9 y = z x = z / 3 and y = z / 9 x + y = z / 3 + z / 9 = 4 z / 9 answer is e"
Answer: e
Python program:
a = 3 * 100
b = a / 2
c = b - 2
d = 3 * 100
e = d / 2
f = e + 2 
g = c / f
Problem: into a bag there are 20 honey and 5 cherry candies . if a boy pick only two candies simultaneous and randomly , what is the probability that he picks one candy of each flavor ?
Options: a ) 2 / 25 , b ) 1 / 50 , c ) 1 / 12 , d ) 1 / 6 , e ) 1 / 3
Rationale: we are told that we have 25 candies , 20 honey and 5 cherry candies . the candies are picked simultaneous and randomly , c 1 and c 2 , in different flavors . there are two acceptable outcomes : 1 ) c 1 is honey and c 2 is cherry ; 2 ) c 1 is cherry and c 2 is honey . let ' s go : 1 ) c 1 = ( 20 / 25 ) ( 5 / 24 ) = 1 / 6 chance of this happening . 2 ) c 2 = ( 5 / 25 ) ( 20 / 24 ) = 1 / 6 chance of this happening . then : ( 1 / 6 ) + ( 1 / 6 ) = 1 / 3 , chance of getting the result that you wanted . answer e .
Answer: e
Python program:
a = 20 + 5 
b = 20 / a
c = 20 + 5 
d = 5 / c
e = b * d
f = e * 2
Problem: if x = 1 + √ 2 , then what is the value of x 4 - 4 x 3 + 4 x 2 + 2 ?
Options: a ) - 1 , b ) 0 , c ) 1 , d ) 2 , e ) 3
Rationale: "answer x = 1 + √ 2 ∴ x 4 - 4 x 3 + 4 x 2 + 5 = x 2 ( x 2 - 4 x + 4 ) + 2 = x 2 ( x - 2 ) 2 + 2 = ( 1 + √ 2 ) 2 ( 1 + √ 2 - 2 ) 2 + 2 = ( √ 2 + 1 ) 2 ( √ 2 - 1 ) 2 + 2 = [ ( √ 2 ) 2 - ( 1 ) 2 ] 2 + 2 = ( 2 - 1 ) 2 = 1 + 2 = 3 correct option : e"
Answer: e
Python program:
a = math.sqrt(2)
b = 1 + a 
c = b ** 2
d = math.sqrt(2)
e = 1 + d 
f = e - 2
g = f ** 2
h = c * g
i = h + 4
Problem: a line has a slope of 3 / 4 and intersects the point ( - 12 , - 39 ) . at which point e does this line intersect the x - axis ?
Options: a ) ( 400 ) , b ) ( 300 ) , c ) ( 040 ) , d ) ( 4030 ) , e ) ( 030 )
Rationale: assume that the equation of the line is y = mx + c , where m and c are the slope and y - intercept . you are also given that the line crosses the point ( - 12 , - 39 ) , this means that this point will also lie on the line above . thus you get - 39 = m * ( - 12 ) + c , with m = 3 / 4 as the slope is given to be 3 / 4 . after substituting the above values , you get c = - 30 . thus the equation of the line is y = 0.75 * x - 30 and the point where it will intersect the x - axis will be with y coordinate = 0 . put y = 0 in the above equation of the line and you will get , x = 40 . thus , the point e of intersection is ( 400 ) . a is the correct answer .
Answer: a
Python program:
a = negate - (
b = negate * (
c = 3 / 4
d = a / b
e = negate * (
Problem: the salary of a person was reduced by 35 % . by what percent should his reduced salary be raised so as to bring it at par with his original salary ?
Options: a ) 50 % , b ) 32 % , c ) 25 % , d ) 54 % , e ) 29 %
Rationale: "let the original salary be $ 100 new salary = $ 65 increase on 65 = 35 increase on 100 = 35 / 65 * 100 = 54 % ( approximately ) answer is d"
Answer: d
Python program:
a = 35 / 100
b = 100 * a
c = 35 / 100
d = 100 * c
e = 100 - d
f = b / e
g = f * 100
Problem: if v and d are both integers , v > d , and - 3 v > 19 , then the largest value of d would be ?
Options: a ) - 5 , b ) - 6 , c ) - 7 , d ) - 8 , e ) - 10
Rationale: no , your thinking is incorrect . when we know that v > d and v < - 6.33 , the largest value of v can be - 7 while if v = - 7 , then largest value of d < - 7 will be - 8 . for negative numbers , - 7 > - 8 and - 8 > - 10 . you are right in saying that d can take any value less than - 7 - - - > d could be - 8 , - 9 , - 10 . . . . and out of all these values , - 8 is the greatest . look at the numbers on the number line . for any 2 numbers , the ones on the right are greater than the ones on the left : . . . . . . . - 11 - 10 - 9 - 8 - 7 - 6 - 5 . . . . . 0 1 2 3 4 5 6 . . . ( - 11 < - 10 , - 10 < - 8 , 4 < 5 etc ) . so , as per the question if d < v and v = - 7 , then d ' s largest ' possible ' value has to be - 8 . - 10 is smaller than - 8 = d
Answer: d
Python program:
a = 19 / 3
Problem: if ( 18 ^ a ) * 9 ^ ( 3 a – 1 ) = ( 2 ^ 5 ) ( 3 ^ b ) and a and b are positive integers , what is the value of a ?
Options: a ) 22 , b ) 11 , c ) 9 , d ) 6 , e ) 5
Rationale: "( 18 ^ a ) * 9 ^ ( 3 a – 1 ) = ( 2 ^ 5 ) ( 3 ^ b ) = 2 ^ a . 9 ^ a . 9 ^ ( 3 a – 1 ) = ( 2 ^ 5 ) ( 3 ^ b ) just compare powers of 2 from both sides answer = 5 = e"
Answer: e
Python program:
a = 3 * 1
Problem: a , b and c invest in the ratio of 3 : 4 : 5 . the percentage of return on their investments are in the ratio of 6 : 5 : 4 . find the total earnings , if b earns rs . 100 more than a :
Options: a ) 2900 , b ) 7250 , c ) 2767 , d ) 1998 , e ) 2771
Rationale: "explanation : a b c investment 3 x 4 x 5 x rate of return 6 y % 5 y % 4 y % return \ inline \ frac { 18 xy } { 100 } \ inline \ frac { 20 xy } { 100 } \ inline \ frac { 20 xy } { 100 } total = ( 18 + 20 + 20 ) = \ inline \ frac { 58 xy } { 100 } b ' s earnings - a ' s earnings = \ inline \ frac { 2 xy } { 100 } = 100 total earning = \ inline \ frac { 58 xy } { 100 } = 2900 answer : a ) rs . 2900"
Answer: a
Python program:
a = 3 * 6
b = 4 * 5
c = a + b 
d = 5 * 4
e = c + d 
f = 4 * 5
g = 3 * 6
h = f - g
i = 100 / h
j = e * i
Problem: a paint store mixes 3 / 4 pint of red paint and 2 / 3 pint of white paint to make a new paint color called perfect pink . how many pints of red paint would be needed to make 35 pints of perfect pink paint ?
Options: a ) 9 , b ) 16 , c ) 19 , d ) 25 1 / 3 , e ) 28 1 / 2
Rationale: "3 / 4 pint is required to make 3 / 4 + 2 / 3 = 17 / 12 pint of perfect pink so 17 / 12 pint requires 3 / 4 pint of red . . 1 pint will require 3 / 4 * 12 / 17 = 9 / 17 . . 35 pints will require 9 / 17 * 35 = 19 pints . . c"
Answer: c
Python program:
a = 3 * 2
b = 4 * 3
c = a / b
d = 35 * c
Problem: a can build a wall in the same time in which b and c together can do it . if a and b together could do it in 25 days and c alone in 35 days , in what time could b alone do it ?
Options: a ) 275 days , b ) 178 days , c ) 185 days , d ) 175 days , e ) 675 days
Rationale: explanation : no explanation is available for this question ! answer : d
Answer: d
Python program:
a = 25 * 35
b = 35 - 25
c = a / b
d = c * 2
Problem: if 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days , the time taken by 15 men and 20 boys in doing the same type of work will be ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "let 1 men ' s 1 day work = x and 1 boy ' s 1 day work = y . then , 6 x + 8 y = 1 / 10 and 26 x + 48 y = 1 / 2 solving these two equations , we get : x = 1 / 100 and y = 1 / 200 ( 15 men + 20 boys ) ' s 1 day work = ( 15 / 100 + 20 / 200 ) = 1 / 4 15 men and 20 boys can do the work in 4 days . answer : a"
Answer: a
Python program:
a = 6 + 4 
b = a * 10
c = 15 + 10 
d = b / c
Problem: a man goes downstream at 11 kmph , and upstream 8 kmph . the speed of the stream is
Options: a ) 1.5 kmph , b ) 4 kmph , c ) 16 kmph , d ) 2.5 kmph , e ) 26 kmph
Rationale: "speed of the stream = 1 / 2 ( 11 - 8 ) kmph = 1.5 kmph . correct option : a"
Answer: a
Python program:
a = 11 - 8
b = a / 2
Problem: in a 1000 m race , a beats b by 70 m and b beats c by 100 m . in the same race , by how many meters does a beat c ?
Options: a ) 145 m , b ) 176 m , c ) 168 m , d ) 163 m , e ) 218 m
Rationale: by the time a covers 1000 m , b covers ( 1000 - 70 ) = 930 m . by the time b covers 1000 m , c covers ( 1000 - 100 ) = 900 m . so , the ratio of speeds of a and c = 1000 / 930 * 1000 / 900 = 1000 / 837 so , by the time a covers 1000 m , c covers 837 m . so in 1000 m race a beats c by 1000 - 837 = 163 m . answer : d
Answer: d
Python program:
a = 1000 - 70
b = 1000 - 100
c = a * b
d = c / 1000
e = 1000 - d
Problem: what is the sum of the multiples of 4 from 40 to 80 , inclusive ?
Options: a ) 560 , b ) 660 , c ) 800 , d ) 760 , e ) 480
Rationale: "the formula we want to use in this type of problem is this : average * total numbers = sum first , find the average by taking the sum of the f + l number and divide it by 2 : a = ( f + l ) / 2 second , find the total numbers in our range by dividing our f and l numbers by 4 and add 1 . ( 80 / 4 ) - ( 40 / 4 ) + 1 multiply these together so what we show average * total numbers = sum ( 80 + 40 ) / 2 * ( 80 / 4 ) - ( 40 / 4 ) + 1 = sum 60 * 11 = 660 b"
Answer: b
Python program:
a = 80 - 3
b = 40 + 2 
c = a + b 
d = c / 2
e = 80 - 3
f = 40 + 2 
g = e - f
h = g / 4
i = h + 1 
j = d * i
Problem: what number times ( 1 ⁄ 2 ) ^ 2 will give the value of 2 ^ 3 ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 16 , e ) 32
Rationale: x * ( 1 / 2 ) ^ 2 = 2 ^ 3 x = 2 ^ 2 * 2 ^ 3 = 2 ^ 5 = 32 the answer is e .
Answer: e
Python program:
a = 2 ** 2
b = 2 ** 3
c = a * b
Problem: a bowl was filled with 10 ounces of water , and 0.00008 ounce of the water evaporated each day during a 50 - day period . what percent of the original amount of water evaporated during this period ?
Options: a ) 0.004 % , b ) 0.04 % , c ) 0.40 % , d ) 4 % , e ) 40 %
Rationale: "total amount of water evaporated each day during a 50 - day period = . 00008 * 50 = . 00008 * 100 / 2 = . 008 / 2 = . 004 percent of the original amount of water evaporated during this period = ( . 004 / 10 ) * 100 % = 0.04 % answer b"
Answer: b
Python program:
a = 50 * 0
b = a / 10
c = b * 100
Problem: a car travelling with 2 / 3 km of its actual speed covers 12 km in 2 hr 14 min 28 sec find the actual speed of the car ?
Options: a ) 8.9 kmph , b ) 2.96 kmph , c ) 1.09 kmph , d ) 45.9 kmph , e ) 4.8 kmph
Rationale: "time taken = 2 hr 14 min 28 sec = 823 / 50 hrs let the actual speed be x kmph then 2 / 3 x * 823 / 50 = 12 x = = 1.09 kmph answer ( c )"
Answer: c
Python program:
a = 14 * const_60
b = a + 28 
c = b / 3600
d = 2 + c 
e = 12 / d
f = e * 3
g = f / 2
Problem: if teena is driving at 55 miles per hour and is currently 7.5 miles behind joe , who is driving at 40 miles per hour in the same direction then in how many minutes will teena be 30 miles ahead of joe ?
Options: a ) 150 , b ) 60 , c ) 75 , d ) 90 , e ) 105
Rationale: "this type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30 - 40 seconds for a difficult one . teena covers 55 miles in 60 mins . joe covers 40 miles in 60 mins so teena gains 15 miles every 60 mins teena need to cover 7.5 + 30 miles . teena can cover 7.5 miles in 30 mins teena will cover 30 miles in 120 mins so answer 30 + 120 = 150 mins . ( answer a )"
Answer: a
Python program:
a = 55 - 40
b = a + 7 
c = 55 - 40
d = b / c
e = d * const_60
Problem: the least number which when increased by 4 each divisible by each one of 22 , 32 , 36 and 54 is :
Options: a ) 427 , b ) 859 , c ) 860 , d ) 4320 , e ) none of these
Rationale: "solution required number = ( l . c . m . of 24 , 32 , 36 , 54 ) - 4 = 864 - 4 = 860 . answer c"
Answer: c
Python program:
a = math.lcm(22, 32)
b = math.lcm(a, 36)
c = math.lcm(b, 54)
d = c - 4
Problem: a trader sells 30 meters of cloth for rs . 4500 at the profit of rs . 10 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) rs . 80 , b ) rs . 185 , c ) rs . 140 , d ) rs . 295 , e ) none of these
Rationale: "sp of 1 m of cloth = 4500 / 30 = rs . 150 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 150 - rs . 10 = rs . 140 . answer : c"
Answer: c
Python program:
a = 4500 / 30
b = a - 10
Problem: if 35 percent of 400 is 20 percent of x , then what is 70 percent of x ?
Options: a ) 200 , b ) 490 , c ) 700 , d ) 900 , e ) 1,400
Rationale: "35 / 100 ( 400 ) = 2 / 10 ( x ) x = 700 . . 70 percent of x = 70 / 100 ( 700 ) = 490 option b ."
Answer: b
Python program:
a = 35 * 400
b = a / 20
Problem: for any even integer p , 300 multiplied by p is square of an integer . what is the least value of p ?
Options: a ) 3 , b ) 4 , c ) 10 , d ) 12 , e ) 14
Rationale: p ∗ 3 ∗ 10 ^ 2 = s ^ 2 so , s = √ p ∗ 3 ∗ 10 ^ 2 so , if p = 3 we get a perfect square number ! ! hence answer will be ( a ) 3
Answer: a
Python program:
a = 300 / 100
Problem: if the selling price of 50 articles is equal to the cost price of 45 articles , then the loss or gain percent is :
Options: a ) 45 % , b ) 10 % , c ) 20 % , d ) 60 % , e ) 56 %
Rationale: "c . p . of each article be re . 1 . then , c . p . of 50 articles = rs . 50 ; s . p . of 50 articles = rs . 45 . loss % = 5 / 50 * 100 = 10 % answer b"
Answer: b
Python program:
a = 50 - 45
Problem: the average marks of a class of 20 students is 40 and that of another class of 50 students is 60 . find the average marks of all the students ?
Options: a ) 44.28 , b ) 54.28 , c ) 34.28 , d ) 64.28 , e ) 74.28
Rationale: "sum of the marks for the class of 20 students = 20 * 40 = 800 sum of the marks for the class of 50 students = 50 * 60 = 3000 sum of the marks for the class of 70 students = 800 + 3000 = 3800 average marks of all the students = 3800 / 70 = 54.28 answer : b"
Answer: b
Python program:
a = 20 * 40
b = 50 * 60
c = a + b 
d = 20 + 50 
e = c / d