euclaise/mathqa_programs huggingface dataset:
Problem: on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.48 per glass on the first day , what was the price per glass on the second day ?
Options: a ) $ 015 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.32 , e ) $ 0.45
Rationale: "on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.48 = 3 * x - - > x = $ 0.32 . answer : d ."
Answer: d
Python program:
a = 1 + 1 
b = a * 0
c = 1 + 2 
d = b / c
Problem: if sharon ' s weekly salary increased by 16 percent , she would earn $ 406 per week . if instead , her weekly salary were to decreased by 10 percent , how much would she earn per week ?
Options: a ) rs . 415 , b ) rs . 325 , c ) rs . 352 , d ) rs . 315 , e ) rs . 425
Rationale: "soln : - ( 406 / 116 ) 90 = 315 in this case long division does not take much time . ( 406 / 116 ) = 3.5 3.5 * 90 = rs . 315 answer : d"
Answer: d
Python program:
a = 16 / 100
b = 1 + a 
c = 406 / b
d = 10 / 100
e = 16 / 100
f = 1 + e 
g = 406 / f
h = d * g
i = c + h
Problem: amit , sumit and pramit go to a seaside town to spend a vacation there and on the first day everybody decides to visit different tourist locations . after breakfast , each of them boards a different tourist vehicle from the nearest bus - depot . after 3 hours , sumit who had gone to a famous beach , calls on the mobile of pramit and claims that he has observed a shark in the waters . pramit learns from the local guide that at that time of the year , only 8 sea - creatures ( including a shark ) are observable and the probability of observing any creature is equal . however , amit and pramit later recall during their discussion that sumit has a reputation for not telling the truth 5 out of 6 times . what is the probability that sumit actually observed a shark in the waters ?
Options: a ) 1 / 36 , b ) 1 / 30 , c ) 5 / 36 , d ) 1 / 24 , e ) 1 / 28
Rationale: explanation : the probability that sumit actually sees a shark , given that he claimed to have seen one . = > p ( he actually sees the shark and reports truth ) / p ( he claims of seeing a shark ) . = > p ( sees the shark ) p ( reports truth ) / ( p ( he sees a shark ) p ( reports truth ) + p ( does n ' t see ) p ( reports false ) . = > ( 1 / 8 × 1 / 6 ) / ( 1 / 8 × 1.6 + 7 / 8 × 5 / 6 ) = > 1 / 36 . answer : a
Answer: a
Python program:
a = 1 / 8
b = 1 / 6
c = a * b
d = 1 / 8
e = 1 / 6
f = d * e
g = 5 / 6
h = 6 + 1 
i = h / 8
j = g * i
k = f + j 
l = c / k
Problem: a certain sum is invested at simple interest at 15 % p . a . for two years instead of investing at 10 % p . a . for the same time period . therefore the interest received is more by rs . 840 . find the sum ?
Options: a ) s . 8400 , b ) s . 9000 , c ) s . 14000 , d ) s . 17000 , e ) s . 27000
Rationale: "let the sum be rs . x . ( x * 15 * 2 ) / 100 - ( x * 10 * 2 ) / 100 = 840 = > 30 x / 100 - 20 x / 100 = 840 = > 10 x / 100 = 840 = > x = 8400 . answer : a"
Answer: a
Python program:
a = 15 - 10
b = a * 2
c = b / 100
d = 840 / c
Problem: a dishonest shopkeeper professes to sell pulses at the cost price , but he uses a false weight of 950 gm . for a kg . his gain is … % .
Options: a ) 5.3 % , b ) 8.2 % , c ) 4.3 % , d ) 8.3 % , e ) 8.0 %
Rationale: he sells 950 grams of pulses and gains 50 grams . if he sells 100 grams of pulses then he will gain ( 50 / 950 ) * 100 = 5.26 4 . a software engineer has the capability of thinking 100 lines of code in five minutes and can type 100 lines of code in 10 minutes . he takes a break for five minutes after every ten minutes . how many lines of codes will he complete typing after an hour ? answer : a
Answer: a
Python program:
a = 4 + 1 
b = a * 2
c = b * 100
d = 950 / c
e = 1/(d)
f = e - 1
g = f * 100
Problem: there are 7 players in a bowling team with an average weight of 121 kg . if two new players join the team , one weighs 110 kg and the second weighs 60 kg , what will be the new average weight ?
Options: a ) 115 kg . , b ) 118 kg . , c ) 113 kg . , d ) 110 kg . , e ) 112 kg .
Rationale: the new average will be = ( 121 * 7 + 110 + 60 ) / 9 = 113 kgs c is the answer
Answer: c
Python program:
a = 7 * 121
b = 110 + 60 
c = a + b 
d = 7 + 2 
e = c / d
Problem: a student scored an average of 70 marks in 3 subjects : physics , chemistry and mathematics . if the average marks in physics and mathematics is 90 and that in physics and chemistry is 70 , what are the marks in physics ?
Options: a ) 130 , b ) 120 , c ) 110 , d ) 180 , e ) 150
Rationale: "given m + p + c = 70 * 3 = 210 - - - ( 1 ) m + p = 90 * 2 = 180 - - - ( 2 ) p + c = 70 * 2 = 140 - - - ( 3 ) where m , p and c are marks obtained by the student in mathematics , physics and chemistry . p = ( 2 ) + ( 3 ) - ( 1 ) = 180 + 140 - 210 = 110 answer : c"
Answer: c
Python program:
a = 90 * 2
b = 70 * 2
c = a + b 
d = 70 * 3
e = c - d
Problem: a box contains 3 pairs of blue gloves and two pairs of green gloves . each pair consists of a left - hand glove and a right - hand glove . each of the gloves is separate from its mate and thoroughly mixed together with the others in the box . if 3 gloves are randomly selected from the box , what is the probability that a matched set ( i . e . , a left - and right - hand glove of the same color ) will be among the 3 gloves selected ?
Options: a ) 3 / 10 , b ) 23 / 60 , c ) 7 / 12 , d ) 41 / 60 , e ) 5 / 6
Rationale: you can use the ' calculating the reverse ' method used by bunuel above or if you would like to calculate the probability of getting a matched set in the usual way , you can think of it in this way : bleft ( 3 ) , bright ( 3 ) , gleft ( 2 ) , gright ( 2 ) bleft , bright , g get a bleft and bright in ( 3 / 10 ) * ( 3 / 9 ) ways . then get any green in 4 / 8 ways . probability of getting b pair and a g = ( 3 / 10 ) * ( 3 / 9 ) * ( 4 / 8 ) * 3 ! ( you multiply by 3 ! here because you could pick in some other order e . g . bright , bleft , g or bleft , g , bright etc ) bleft , bright , b get a bleft and bright in ( 3 / 10 ) * ( 3 / 9 ) ways . then get any blue in 4 / 8 ways . probability of getting b pair and another b = ( 3 / 10 ) * ( 3 / 9 ) * ( 4 / 8 ) * 3 ! / 2 ! ( you multiply by 3 ! here to account for the order e . g . bright , bleft , bleft or bleft , bright , bright etc but two gloves will be identical so you divide by 2 ! ) gleft , gright , b get a gleft and gright in ( 2 / 10 ) * ( 2 / 9 ) ways . then get any blue in 6 / 8 ways . probability of getting g pair and a b = ( 2 / 10 ) * ( 2 / 9 ) * ( 6 / 8 ) * 3 ! gleft , gright , g get a gleft and gright in ( 2 / 10 ) * ( 2 / 9 ) ways . then get any other g in 2 / 8 ways . probability of getting g pair and a g = ( 2 / 10 ) * ( 2 / 9 ) * ( 2 / 8 ) * 3 ! / 2 ! adding them all up , you get 41 / 60 . answer : d
Answer: d
Python program:
a = 3 + 3 
b = 3 + 3 
c = b * 10
d = a / c
e = 10 + 2 
f = 3 + 3 
g = f * 10
h = e / g
i = d + h 
j = 1 - i
Problem: the output of a factory is increased by 10 % to keep up with rising demand . to handle the holiday rush , this new output is increased by 30 % . by approximately what percent would the output of the factory now have to be decreased in order to restore the original output ?
Options: a ) 20 % , b ) 24 % , c ) 30 % , d ) 32 % , e ) 79 %
Rationale: take it as original output = 100 . to meet demand increase by 10 % , then output = 110 . to meet holiday demand , new output increase by 30 % then output equals 143 to restore new holidy demand output to original 100 . final - initial / final * 100 = 43 / 143 * 100 = 30 % approxiamately . option c is correct .
Answer: c
Python program:
a = 100 + 10 
b = a / 100
c = 100 + 30 
d = c / 100
e = b * d
f = e - 1
g = 100 + 10 
h = g / 100
i = 100 + 30 
j = i / 100
k = h * j
l = f / k
m = l * 100
Problem: a 300 meter long train crosses a platform in 54 seconds while it crosses a signal pole in 18 seconds . what is the length of the platform ?
Options: a ) 99 , b ) 289 , c ) 350 , d ) 882 , e ) 600
Rationale: speed = [ 300 / 18 ] m / sec = 50 / 3 m / sec . let the length of the platform be x meters . then , x + 300 / 54 = 50 / 3 3 ( x + 300 ) = 2700 è x = 350 m . answer : e
Answer: e
Python program:
a = 300 / 18
b = a * 54
c = b - 300
Problem: 150 ml of 30 % sulphuric acid was added to approximate 400 ml of 12 % sulphuric acid solution . find the approximate concentration e of the acid in the mixture ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 6 , e ) 1 / 5
Rationale: "do not need any computation 30 % - - - - - - - - - - - 21 % - - - - - - - - - 12 % if volume of both sol . were equal the concentration e would be 21 % = 1 / 5 , but 12 % is more than 3 times only possibility is 1 / 6 d"
Answer: d
Python program:
a = 150 * 30
b = a / 100
c = 400 * 12
d = c / 100
e = b + d 
f = 150 + 400 
g = e / f
Problem: what is the smallest integer k for which 64 ^ k > 4 ^ 19 ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: 64 ^ k > 4 ^ 19 4 ^ ( 3 k ) > 4 ^ 19 3 k > 19 k = 7 the answer is d .
Answer: d
Python program:
a = 19 / 3
b = math.floor(a)
c = b + 1
Problem: a cistern 6 m long and 5 m wide contains water up to a depth of 1 m 25 cm . the total area of the wet surface is :
Options: a ) 49 m 2 , b ) 50 m 2 , c ) 53.5 m 2 , d ) 55 m 2 , e ) 57.5 m 2
Rationale: "area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 5 x 1.25 + 6 x 1.25 ) + 6 x 5 ] m 2 = 57.5 m 2 . answer : option e"
Answer: e
Python program:
a = 25 / 100
b = a + 1 
c = b * 5
d = 25 / 100
e = d + 1 
f = e * 6
g = c + f 
h = 2 * g
i = 5 * 6
j = h + i
Problem: there are 6 equally spaced points a , b , c , d , e and f marked on a circle with radius r . how many convex pentagons of distinctly different areas can be drawn using these points as vertices ?
Options: a ) 6 p 5
b ) 1
c ) 5
d ) none of these
e ) can not be determined
Rationale: solution : since , all the points are equally spaced ; hence the area of all the convex pentagons will be same . answer : option d
Answer: d
Python program:
a = math.factorial(6)
b = 6 - 2
c = math.factorial(b)
d = math.factorial(2)
e = c * d
f = a / e
Problem: a train 1600 m long can cross a pole in 40 sec and then find the speed of the train ?
Options: a ) 140 , b ) 142 , c ) 144 , d ) 146 , e ) 148
Rationale: "length = speed * time speed = l / t s = 1600 / 40 s = 40 m / sec speed = 40 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 144 kmph answer : c"
Answer: c
Python program:
a = 1600 / 1000
b = 40 / 3600
c = a / b
Problem: if 4 log ( 4 * 5 ^ 2 ) = x , find x
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "4 ( log 2 ^ 2 * 5 ^ 2 ) = x 4 log ( 5 * 2 ) ^ 2 = x 4 * 2 log ( 5 * 2 ) = x 8 log 10 = x log 10 base 10 = 1 so 8 * 1 = x x = 8 answer : d"
Answer: d
Python program:
a = 5 ** 2
b = 4 * a
c = b ** 4
Problem: if x is real , find the maximum value of the expression - 2 x ^ 2 + 9 x + 11 .
Options: a ) 12.125 , b ) 15.125 , c ) 18.125 , d ) 21.125 , e ) 24.125
Rationale: "this is an equation of a downward facing parabola . the maximum value is the top point of the parabola . - 2 x ^ 2 + 9 x + 11 = ( - 2 x + 11 ) ( x + 1 ) the roots are 11 / 2 and - 1 . the maximum value must be when x is halfway between these two points . x = 2.25 the maximum value is - 2 ( 2.25 ) ^ 2 + 9 ( 2.25 ) + 11 = 21.125 the answer is d ."
Answer: d
Python program:
a = 2 * 2
b = a / 9
c = 9 * b
d = c + 11 
e = 2 * 2
f = e / 9
g = f ** 2
h = 2 * g
i = d - h
Problem: find the l . c . m of 12 , 8 , 24 and 16 .
Options: a ) 48 , b ) 96 , c ) 80 , d ) 44 , e ) 140
Rationale: "explanation : 2 x 3 x 2 x 2 x 2 = 48 answer : option a"
Answer: a
Python program:
a = 3 ** 3
b = 2 ** 3
c = 4 + 1 
d = c ** 2
e = b * d
f = a * e
g = 24 / 2
h = g / 2
i = h / 3
j = 4 + 1 
k = i / j
l = 4 + 1 
m = k / l
n = f * m
Problem: if [ x ] is the greatest integer less than or equal to x , what is the value of [ - 11.6 ] + [ 13.4 ] + [ 12.7 ] ?
Options: a ) 3 , b ) 10 , c ) 13 , d ) 16 , e ) 17
Rationale: "you are asked what the closest lesser integer value to [ x ] is . [ - 11.6 ] = - 12.0 [ 13.4 ] = 13.0 [ 12.7 ] = 12.0 therefore , answer is : - 12.0 + 13.0 + 12.0 = 13.0 option a ."
Answer: c
Python program:
a = 13 + 4 
b = a - 11
Problem: ( 12345679 x 72 ) = ?
Options: a ) 88888888 , b ) 888888888 , c ) 898989898 , d ) 9999999998 , e ) none
Rationale: "explanation : 12345679 x 72 = 12345679 x ( 70 + 2 ) = 12345679 x 70 + 12345679 x 2 = 864197530 + 24691358 = 888888888 answer : option b"
Answer: b
Python program:
a = 4 + 1 
b = a ** 4
c = 12345679 * b
Problem: a jar contains only red , yellow , and orange marbles . if there are 3 red , 5 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ?
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
Rationale: 5 c 2 * 3 c 1 = 10 * 3 = 30 12 c 3 = 220 3 / 22 answer : d
Answer: d
Python program:
a = math.comb(5, 2)
b = math.comb(3, 1)
c = a * b
d = 5 + 4 
e = d + 3 
f = math.comb(e, 3)
g = c / f
Problem: if 10 ! - 2 * ( 5 ! ) ^ 2 is divisible by 10 ^ n , what is the greatest value of n ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: = 10 ∗ 9 ∗ 8 ∗ 7 ∗ 6 ∗ 5 ! − 2 ∗ 5 ! ∗ 5 ∗ 4 ∗ 3 ∗ 2 ∗ 1 = 5 ! ∗ 10 ∗ 3 ∗ 8 ( 125 ) = 5 ∗ ( 2 ∗ 2 ) ∗ 3 ∗ 2 ∗ ( 5 ∗ 2 ) ∗ 24 ∗ 5 ∗ 5 ∗ 5 = 5 ∗ 2 ∗ 5 ∗ 2 ∗ 5 ∗ 2 ∗ 5 ∗ 2 ∗ 24 ∗ 5 ∗ 3 = 10 ^ 4 ∗ 2 ^ 4 ∗ 5 ∗ 3 = 10 ^ 4 ∗ 5 ∗ 2 ∗ 12 ∗ 3 = 10 ^ 5 ∗ 36 answer : e
Answer: e
Python program:
a = 1 * 5
Problem: in a 3 digit number , the 100 digit is 2 more than the tens digit and the units digit is 2 less than the tens digit . if the sum of the digits is 27 , find the number ?
Options: a ) 867 , b ) 1179 , c ) 1196 , d ) 1098 , e ) 1197
Rationale: e 1197 let the three digit numbers be 100 a + 10 b + c a = b + 2 c = b - 2 a + b + c = 3 b = 27 = > b = 9 so a = 11 and b = 7 hence the three digit number is : 1197
Answer: e
Python program:
a = 27 / 3
b = a + 2 
c = b * 100
d = 27 / 3
e = d * 10
f = c + e 
g = 27 / 3
h = g - 2
i = f + h
Problem: a man sold 20 articles for $ 60 and gained 20 % . how many articles should he sell for $ 90 to incur a loss 10 % ?
Options: a ) 45 , b ) 41.2 , c ) 40 , d ) 50 , e ) 48
Rationale: "production cost per article : $ 60 * ( 100 % - 20 % ) / 20 = $ 2.40 required production costs for a loss of 20 % : $ 90 * ( 100 % + 10 % ) = $ 99 number of articles to be sold for $ 108 to incur a 20 % loss : $ 99 / $ 2.40 = 41.2 thus , solution b is correct ."
Answer: b
Python program:
a = original_price_before_loss / (
Problem: at what rate percent on simple interest will rs . 750 amount to rs . 900 in 2 years ?
Options: a ) 10 % , b ) 2 % , c ) 4 % , d ) 5 % , e ) 3 %
Rationale: "150 = ( 750 * 2 * r ) / 100 r = 10 % answer : a"
Answer: a
Python program:
a = 900 - 750
b = a / 750
c = b / 2
d = c * 100
Problem: what least number must be added to 686 , so that the sum is completely divisible by 5 ?
Options: a ) 2 , b ) 3 , c ) 5 , d ) 4 , e ) 6
Rationale: "if we divide 686 by 5 remainder is 1 5 - 1 = 4 answer : d"
Answer: d
Python program:
a = 4 * 10
b = a + 2 
c = b * 5
d = c - 686
Problem: 45 men took a dip in a water tank 40 m long and 20 m broad on a religious day . if the average displacement of water by a man is 4 m 3 , then the rise in the water level in the tank will be :
Options: a ) 20 cm , b ) 25 cm , c ) 35 cm , d ) 50 cm , e ) none of these
Rationale: explanation : total volume of water displaced = ( 4 x 45 ) m 3 = 180 m 3 rise in water level = 180 / 40 ã — 20 = 0.225 m = 22.5 cm answer : e
Answer: e
Python program:
a = 4 * 45
b = 40 * 20
c = a / b
Problem: square of 99 = ?
Options: a ) 9001
b ) 9621
c ) 9431
d ) 9801
e ) 9601
Rationale: square of ( 100 - 1 ) = 10000 + 1 - 200 9801 answer d
Answer: d
Python program:
a = 99 * 99
Problem: if 36 men can do a piece of work in 25 hours , in how many hours will 15 men do it ?
Options: a ) 10 hours , b ) 40 hours , c ) 20 hours , d ) 60 hours , e ) none of them
Rationale: "let the required number of hours be x . then , less men , more hours ( indirect proportion ) 15 : 36 : : 25 : x = ( 15 x x ) = ( 36 x 25 ) = ( 36 x 25 ) / 15 = 60 hence , 15 men can do it in 60 hours . answer is d ."
Answer: d
Python program:
a = 36 * 25
b = a / 15
Problem: a train 420 m long is running at a speed of 48 km / hr . in what time will it pass a bridge 60 m long ?
Options: a ) 40 sec , b ) 36 sec , c ) 60 sec , d ) 48 sec , e ) 18 sec
Rationale: "total length = 420 + 60 = 480 speed = 48 km / h = ( 48 * 5 ) / 18 = 40 / 3 m / s time = ( 480 * 3 ) / 40 = 36 sec . answer : b"
Answer: b
Python program:
a = 48 - 60
b = a * const_0_2778
c = 420 / b
Problem: nina has exactly enough money to purchase 6 widgets . if the cost of each widget were reduced by $ 1 , then nina would have exactly enough money to purchase 8 widgets . how much money does nina have ?
Options: a ) $ 22 , b ) $ 24 , c ) $ 30 , d ) $ 36 , e ) $ 40
Rationale: "b its is . let price = x ( x - 1 ) 8 = 6 x x = 4 hence total money = 6 * 4 = 24"
Answer: b
Python program:
a = 1 * 8
b = 8 - 6
c = a / b
d = c * 6
Problem: a bag contains 10 black and 20 white balls . one ball is drawn at random . what is the probability that the ball drawn is white ?
Options: a ) 1 / 2 , b ) 3 / 4 , c ) 2 / 3 , d ) 1 / 5 , e ) 3 / 7
Rationale: "total number of balls = 10 + 20 = 30 number of white balls = 20 probability of drawing a white ball = 20 / 30 = 2 / 3 answer is c"
Answer: c
Python program:
a = math.factorial(20)
b = 20 - 2
c = math.factorial(b)
d = a / c
e = math.factorial(2)
f = d / e
g = math.factorial(10)
h = 10 - 2
i = math.factorial(h)
j = g / i
k = math.factorial(2)
l = j / k
m = f + l 
n = 10 + 20 
o = math.factorial(n)
p = 10 + 20 
q = p - 2
r = math.factorial(q)
s = o / r
t = math.factorial(2)
u = s / t
v = m / u
Problem: a man invests rs . 7,000 at the rate of 5 % per annum . how much more should he invest at the rate of 8 % , so that he can earn a total of 6 % per annum ?
Options: a ) rs . 1200 , b ) rs . 1300 , c ) rs . 3500 , d ) rs . 2000 , e ) none of these
Rationale: "explanation : interest on rs . 7000 at 5 % per annum = ( 7000 × 5 × 1 ) / 100 = rs . 350 let his additional investment at 8 % = x interest on rs . x at 8 % per annum = ( x × 8 × 1 ) / 100 = 2 x / 25 . to earn 6 % per annum for the total , interest = ( 7000 + x ) × 6 × 1 / 100 . = > 350 + 2 x / 25 = ( 7000 + x ) × 6 × 1 / 100 . = > 35000 + 8 x = ( 7000 + x ) × 6 . = > 35000 + 8 x = 42000 + 6 x . = > 2 x = 7000 . = > x = 3500 . answer : c"
Answer: c
Python program:
a = 8 * 1000
b = 6 - 5
c = 8 - 6
d = b / c
e = a * d
Problem: if 16 ^ 5 * 15 ^ 4 * 14 ^ 3 * 13 ^ 2 = x , what is the units digit of x ?
Options: a ) 2 , b ) 3 , c ) 6 , d ) 5 , e ) 0
Rationale: 16 ^ 5 * 15 ^ 4 * 14 ^ 3 * 13 ^ 2 = x units digit of x will be 6 ^ 5 * 5 ^ 4 * 4 ^ 3 * 3 ^ 2 = 6 * 5 * 4 * 9 = 1080 therefore , units digit of x = 0 answer e
Answer: e
Python program:
a = 5 * 2
b = a / 10
Problem: a , b and c rent a pasture . if a puts 10 oxen for 7 months , b puts 12 oxen for 5 months and c puts 15 oxen for 3 months for grazing and the rent of the pasture is rs . 210 , then how much amount should c pay as his share of rent ?
Options: a ) 54 , b ) 45 , c ) 25 , d ) 15 , e ) 55
Rationale: "a : b : c = 10 × 7 : 12 × 5 : 15 × 3 = 2 × 7 : 12 × 1 : 3 × 3 = 14 : 12 : 9 amount that c should pay = 210 × 9 / 35 = 6 × 9 = 54 answer is a"
Answer: a
Python program:
a = 15 * 3
b = 10 * 7
c = 12 * 5
d = b + c 
e = 15 * 3
f = d + e 
g = a / f
h = 210 * g
Problem: if 50 honey bees make 50 grams of honey in 50 days , then 1 honey bee will make 1 gram of honey in how many days ?
Options: a ) 1 , b ) 3.5 , c ) 20 , d ) 49 , e ) 50
Rationale: "explanation : let the required number days be x . less honey bees , more days ( indirect proportion ) less honey , less days ( direct proportion ) honey bees 1 : 50 : : 50 : x honey 50 : 1 = > 1 x 50 x x = 50 x 1 x 50 = > x = 50 . answer : e"
Answer: e
Python program:
a = 1 / 50
b = 1 / a
Problem: the charge for a single room at hotel p is 55 percent less than the charge for a single room at hotel r and 10 percent less than the charge for a single room at hotel g . the charge for a single room at hotel r is what percent greater than the charge for a single room at hotel g ?
Options: a ) 50 % , b ) 60 % , c ) 75 % , d ) 80 % , e ) 100 %
Rationale: "p = 0.45 r = 0.9 g r = 0.9 g / 0.45 = 2 g thus r is 100 % greater than g . the answer is e ."
Answer: e
Python program:
a = 100 - 55
b = 100 - 10
c = a / b
d = c * 100
e = 100 - d
f = 100 - 55
g = 100 - 10
h = f / g
i = h * 100
j = e / i
k = j * 100
Problem: 69 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 ) 20 , b ) 23 , c ) 24 , d ) 25 , e ) 26
Rationale: "according to the chain rule , m 1 x t 1 = m 2 x t 2 therefore , 69 x 12 x 5 = 30 x 6 x x x = 23 hence , the number of days = 23 . answer : b"
Answer: b
Python program:
a = 69 * 12
b = a * 5
c = 30 * 6
d = b / c
Problem: a certain college ' s enrollment at the beginning of 1992 was 40 percent greater than it was at the beginning of 1991 , and its enrollment at the beginning of 1993 was 15 percent greater than it was at the beginning of 1992 . the college ' s enrollment at the beginning of 1993 was what percent greater than its enrollment at the beginning of 1991 ?
Options: a ) 63 % , b ) 24 % , c ) 50 % , d ) 55 % , e ) 61 %
Rationale: "suppose enrollment in 1991 was 100 then enrollment in 1992 will be 140 and enrollment in 1993 will be 140 * 1.15 = 161 increase in 1993 from 1991 = 161 - 100 = 61 answer : e"
Answer: e
Python program:
a = 100 + 40 
b = 100 + 15 
c = b / 100
d = a * c
e = d - 100
Problem: if the cost price is 75 % of the selling price , then what is the profit percent ?
Options: a ) 5 % , b ) 11 % , c ) 13 % , d ) 21 % , e ) 33 %
Rationale: "let s . p . = $ 100 c . p . = $ 75 profit = $ 25 profit % = 25 / 75 * 100 = 25 / 6 = 33 % approximately answer is e"
Answer: e
Python program:
a = 100 - 75
b = a / 75
c = b * 100
Problem: double of quarter of 3 percent written as a decimal is :
Options: a ) 0.003 , b ) 0.015 , c ) 0.25 , d ) 0.005 , e ) none of these
Rationale: "explanation : solution : ( 2 ) * ( 1 / 4 ) * 3 % = 2 * ( 1 / 4 * 3 / 100 ) = 0.015 . answer : b"
Answer: b
Python program:
a = 3 / 100
b = a / 3
c = b * 2
Problem: two brothers ram and ravi appeared for an exam . the probability of selection of ram is 5 / 7 and that of ravi is 1 / 5 . find the probability that both of them are selected .
Options: a ) 2 / 35 , b ) 2 / 3 , c ) 7 / 35 , d ) 1 / 7 , e ) 7 / 5
Rationale: "let a be the event that ram is selected and b is the event that ravi is selected . p ( a ) = 5 / 7 p ( b ) = 1 / 5 let c be the event that both are selected . p ( c ) = p ( a ) x p ( b ) as a and b are independent events : = 5 / 7 x 1 / 5 = 1 / 7 answer : d"
Answer: d
Python program:
a = 5 / 7
b = 1 / 5
c = a * b
Problem: find the least number must be subtracted from 11070 so that remaining number is divisible by 22 .
Options: a ) 2 , b ) 3 , c ) 4 , d ) 7 , e ) 8
Rationale: on dividing 11070 by 22 we get the remainder 4 , so 4 should be subtracted . answer is a .
Answer: a
Python program:
a = 11070 / 22
b = math.floor(a)
c = b * 22
d = 11070 - c