euclaise/mathqa_programs huggingface dataset:
Problem: in what ratio should a variety of wheat costing rs . 3 per kg be mixed with another variety of wheat costing rs . 6.25 per kg to obtain a mixture costing rs . 4.50 per kg ?
Options: a ) 8 : 6 , b ) 7 : 6 , c ) 5 : 6 , d ) 7 : 5 , e ) 6 : 7
Rationale: let us say the ratio of the quantities of cheaper and dearer varieties = x : y by the rule of allegation , x / y = ( 6.25 - 4.50 ) / ( 4.50 - 3 ) = 7 / 6 answer : b
Answer: b
Python program:
a = 4 / 5
b = a / 2
c = 6 + 25 
d = 4 / 5
e = 4 + 5 
f = c / e
Problem: in a rectangular axis system , what is the area of a parallelogram with the coordinates : ( 5,3 ) , ( 8,3 ) , ( 4,5 ) , ( 7,5 ) ?
Options: a ) 21 . , b ) 28 . , c ) 35 . , d ) 49 . , e ) 6 .
Rationale: "delta x will give us the dimension of one side of the parallelogram = 8 - 5 = 3 unit delta y will give us the dimension of the other side of parallelogram = 5 - 3 = 2 unit area of parallelogram = 3 * 2 = 6 answer is e"
Answer: e
Python program:
a = 3 + 2
Problem: the captain of a cricket team of 11 members is 27 years old and the wicket keeper is 3 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average age of the team ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: let the average age of the whole team be x years . 11 x - ( 27 + 30 ) = 9 ( x - 1 ) 11 x - 9 x = 48 2 x = 48 x = 24 . the average age of the team is 24 years . the answer is d .
Answer: d
Python program:
a = 27 + 3 
b = 27 + a 
c = 3 * 3
d = b - c
e = d / 2
Problem: angelina walked 180 meters from her home to the grocery at a constant speed . she then walked 240 meters to the gym at double the speed . she spent 40 seconds less on her way from the grocery to the gym than on her way from home to the grocery . what was angelina ' s speed , in meters per second , from the grocery to the gym ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 12
Rationale: "let the speed be x . . . so time taken from home to grocery = 180 / x . . the speed to gym = 2 x . . so time taken = 240 / 2 x = 120 / x . . its given 180 / x - 120 / x = 40 . . 60 / x = 40 = > 40 x = 60 = > x = 60 / 40 x = 1.5 m / secs . . so grocery to gym = 2 * 1.5 = 3 m / s . . . answer : b"
Answer: b
Python program:
a = 240 / 2
b = 180 - a
c = b / 40
d = c * 2
Problem: i have 150 pieces of cake . there are 50 friends in my house . i would like to give each friend the same amount of cake , how much should i give to each friend ?
Options: a ) 12 , b ) 7 , c ) 9 , d ) 15 , e ) 3
Rationale: 150 / 50 = 3 the answer is e .
Answer: e
Python program:
a = 150 / 50
Problem: there is food for 760 men for 22 days . how many more men should join after two days so that the same food may last for 4 days more ?
Options: a ) 3022 , b ) 3040 , c ) 3099 , d ) 3088 , e ) 3066
Rationale: "760 - - - - 22 760 - - - - 20 x - - - - - 4 x * 4 = 760 * 20 x = 3800 760 - - - - - - - 3040 answer : b"
Answer: b
Python program:
a = 22 - 2
b = 760 * a
c = b / 4
d = c - 760
Problem: sandy buys an old scooter for $ 900 and spends $ 300 on its repairs . if sandy sells the scooter for $ 1260 , what is the gain percent ?
Options: a ) 3 % , b ) 5 % , c ) 7 % , d ) 9 % , e ) 11 %
Rationale: "selling price / total cost = 1260 / 1200 = 1.05 the gain percent is 5 % . the answer is b ."
Answer: b
Python program:
a = 300 + 900 
b = 1260 - a
c = 300 + 900 
d = b / c
e = d * 100
Problem: find the amount on rs . 8000 in 2 years , the rate of interest being 4 % per first year and 5 % for the second year ?
Options: a ) 5568 , b ) 6369 , c ) 8736 , d ) 5635 , e ) 6734
Rationale: "8000 * 104 / 100 * 105 / 100 = > 8736 answer : c"
Answer: c
Python program:
a = 100 + 4 
b = 8000 * a
c = b / 100
d = 100 + 5 
e = c * d
f = e / 100
Problem: of the 1000 inhabitants of a town , 60 % are males of whom 20 % are literate . if , of all the inhabitants , 25 % are literate , then what percent of the females of the town are literate ?
Options: a ) 22.5 , b ) 27.5 , c ) 32.5 , d ) 37.5 , e ) none
Rationale: sol . number of males = 60 % of 1000 = 600 . number of females = ( 1000 - 600 ) = 400 . number of literates = 25 % of 1000 = 250 . number of literate males = 20 % of 600 = 120 . number of literate females = ( 250 - 120 ) = 130 . ∴ required percentage = ( 130 / 400 x 100 ) % = 32.5 % answer c
Answer: c
Python program:
a = 25 / 100
b = a * 1000
c = 20 / 100
d = 60 / 100
e = 1000 * d
f = c * e
g = b - f
h = 60 / 100
i = 1000 * h
j = 1000 - i
k = g / j
l = k * 100
Problem: how much water must be added to 68 litres of milk at 1 1 ⁄ 2 litres for 20 so as to have a mixture worth 10 2 ⁄ 3 a litre ?
Options: a ) 10 litres , b ) 17 litres , c ) 15 litres , d ) 18 litres , e ) none of these
Rationale: "c . p . of 1 litre of milk = ( 20 × 2 ⁄ 3 ) = 40 ⁄ 3 ∴ ratio of water and milk = 8 ⁄ 3 : 32 ⁄ 3 = 8 : 32 = 1 : 4 ∴ quantity of water to be added to 68 litres of milk = ( 1 ⁄ 4 × 68 ) litres = 17 litres . answer b"
Answer: b
Python program:
a = 1 / 2
b = 1 + a 
c = 20 / b
Problem: i bought two books ; for rs . 600 . i sold one at a loss of 15 % and other at a gain of 19 % and then i found each book was sold at the same price . find the cost of the book sold at a loss ?
Options: a ) 197 , b ) 280 , c ) 189 , d ) 278 , e ) 350
Rationale: "x * ( 85 / 100 ) = ( 600 - x ) 119 / 100 x = 350 answer : e"
Answer: e
Python program:
a = 100 + 19 
b = 600 * a
c = 100 - 15
d = 100 + 19 
e = c + d 
f = b / e
Problem: if x is to be chosen at random from the set { 1 , 2 , 3 , 4 } and y is to be chosen at random from the set { 5 , 6 , 7 , 8 } , what is the probability that xy will be even ?
Options: a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6
Rationale: "probably the best way to solve would be to use 1 - p ( opposite event ) = 1 - p ( odd ) = 1 - p ( odd ) * p ( odd ) = 1 - 2 / 4 * 2 / 3 = 8 / 12 = 1 / 2 . answer : c ."
Answer: c
Python program:
a = 2 ** 2
b = math.comb(4, 2)
c = math.comb(2, 1)
d = b * c
e = a / d
Problem: in how many ways can the integer 84 be expressed as a product of two different positive integers ?
Options: a ) 10 , b ) 8 , c ) 5 , d ) 4 , e ) 2
Rationale: "84 = ( 2 ^ 2 ) * 3 * 7 since 84 is not a perfect square , no of ways = 4 answer d"
Answer: d
Python program:
a = 84 / 1
b = a / 3
c = b - 3
Problem: find the value of y from ( 12 ) ^ 3 x 6 ^ 2 ÷ 432 = y ?
Options: a ) 2134 , b ) 2234 , c ) 2540 , d ) 2560 , e ) 144
Rationale: "144 e"
Answer: e
Python program:
a = 12 ** 3
b = 6 ** 2
c = a * b
d = c / 432
Problem: a man buys an article for $ 20 . and sells it for $ 35 . find the gain percent ?
Options: a ) 25 % , b ) 50 % , c ) 20 % , d ) 75 % , e ) 30 %
Rationale: "c . p . = $ 20 s . p . = $ 35 gain = $ 15 gain % = 15 / 20 * 100 = 75 % answer is d"
Answer: d
Python program:
a = 20 / 100
b = 35 / a
c = b - 100
Problem: a ball dropped from h height and moves 80 % of height each time . total distance covered is
Options: a ) 4 h , b ) 5 h , c ) 7 h , d ) 9 h , e ) 8 h
Rationale: first time distance is h second time 80 h / 100 = 4 h / 5 similarly third time 80 % of 4 h / 5 = h ( 4 ^ 2 ) / ( 5 ^ 2 ) and so on . . . this will lead to infinite terms of geometric progression i . e h + 2 * 4 h / 5 + 2 * 16 h / 25 . . . . . . . . . . . . sum = h + 2 * 4 h / ( 5 ( 1 - 4 / 5 ) ) = 9 h answer : d
Answer: d
Python program:
a = 80 / 10
b = a + 1
Problem: calculate 73196 ÷ ? = 631
Options: a ) 101 , b ) 116 , c ) 119 , d ) 116 , e ) 32
Rationale: "answer let 62976 / x = 631 then x = 62976 / 631 = 116 option : d"
Answer: d
Python program:
a = 73196 * 631
Problem: two trains of equal length , running with the speeds of 60 and 20 kmph , take 50 seconds to cross each other while they are running in the same direction . what time will they take to cross each other if they are running in opposite directions ?
Options: a ) 12.5 , b ) 8.01 , c ) 7.5 , d ) 26 , e ) 22
Rationale: "rs = 60 - 40 = 20 * 5 / 18 = 100 / 18 t = 50 d = 50 * 100 / 18 = 2500 / 9 rs = 60 + 20 = 80 * 5 / 18 t = 2500 / 9 * 18 / 400 = 12.5 sec . answer : a"
Answer: a
Python program:
a = 60 - 20
b = const_0_2778 * a
c = b * 50
d = 60 + 20 
e = const_0_2778 * d
f = 1/(e)
g = c * f
Problem: on the number line , the number p is twice as many units from - 2 as - 2 is from 7 . if p is less than – 2 , what is the value of p ?
Options: a ) – 20 , b ) – 10 , c ) – 6 , d ) 10 , e ) 14
Rationale: "distance between - 2 and 7 = 9 since number p is twice as many units from - 2 as - 2 is from 7 , therefore p can be - 20 since , p is less than - 2 , the value of p = - 20 answer a"
Answer: a
Python program:
a = negate - (
Problem: find value for x from below equation ? x + 1 = 4
Options: a ) - 5 , b ) - 4 , c ) 4 , d ) 3 , e ) 2
Rationale: "1 . subtract 1 from both sides : x + 1 - 1 = 4 - 1 2 . simplify both sides : x = 3 d"
Answer: d
Python program:
a = 4 - 1
Problem: find large number from below question the difference of two numbers is 1325 . on dividing the larger number by the smaller , we get 5 as quotient and the 5 as remainder
Options: a ) 1650 , b ) 1324 , c ) 1245 , d ) 1300 , e ) 1635
Rationale: "let the smaller number be x . then larger number = ( x + 1325 ) . x + 1325 = 5 x + 5 4 x = 1320 x = 330 large number = 330 + 1320 = 1650 answer : a"
Answer: a
Python program:
a = 1325 - 5
b = 5 - 1
c = a / b
d = c * 5
Problem: jo ' s collection contains us , indian and british stamps . if the ratio of us to indian stamps is 4 to 2 and the ratio of indian to british stamps is 5 to 1 , what is the ratio of us to british stamps ?
Options: a ) 5 : 1 , b ) 10 : 5 , c ) 15 : 2 , d ) 20 : 2 , e ) 25 : 2
Rationale: "u / i = 4 / 2 i / b = 5 / 1 since i is multiple of both 2 ( as per first ratio ) and 5 ( as per second ratio ) so let ' s assume that i = 10 i . e . multiplying teh first ratio by 5 and second ration by 2 in each numerator and denominator then , u : i : b = 20 : 10 : 2 i . e . u : b = 20 : 2 answer : option d"
Answer: d
Python program:
a = 4 * 5
b = 1 * 2
c = a / b
Problem: if 11 boys meet at a reunion and each boy shakes hands exactly once with each of the others , then what is the total number of handshakes
Options: a ) 55 , b ) 42 , c ) 43 , d ) 44 , e ) 45
Rationale: "n ( n - 1 ) / 2 = 11 * 10 / 2 = 55 answer : a"
Answer: a
Python program:
a = math.factorial(11)
b = 11 - 2
c = math.factorial(b)
d = math.factorial(2)
e = c * d
f = a / e
Problem: 0.0005215 / 0.000305 x 6.2 = ?
Options: a ) 10.6 , b ) 11.3 , c ) 12.7 , d ) 13.4 , e ) 14.5
Rationale: "explanation : ? = 0.0005215 / 0.000305 x 6.2 = 10.6 answer : option a"
Answer: a
Python program:
a = 0 / 5215
Problem: the output of a factory was increased by 10 % to keep up with rising demand . to handle the holiday rush , this new output was increased by 25 % . by approximately what percent would the output now have to be decreased in order to restore the original output ?
Options: a ) 20 % , b ) 24 % , c ) 30 % , d ) 27 % , e ) 79 %
Rationale: "the original output increases by 10 % and then 25 % . total % change = a + b + ab / 100 total % change = 10 + 25 + 10 * 25 / 100 = 37.5 % now , you want to change it to 0 , so , 0 = 37.5 + x + 37.5 x / 100 x = - 37.5 ( 100 ) / 137.5 = 27 % approximately answer is d"
Answer: d
Python program:
a = 100 + 10 
b = 100 + 10 
c = 25 / 100
d = b * c
e = a + d 
f = e - 100
g = f * 100
h = 100 + 10 
i = 100 + 10 
j = 25 / 100
k = i * j
l = h + k 
m = g / l
Problem: a and b started a business investing rs . 24,000 and rs 18,000 respectively . in what ratio the profit earned after 2 years be divided between a and b respectively ?
Options: a ) 4 : 3 , b ) 9 : 2 , c ) 18 : 20 , d ) 1 : 4 , e ) 18 : 4
Rationale: "a : b = 24000 : 18000 = 8 : 6 = 4 : 3 answer : a"
Answer: a
Python program:
a = 3 * 3
b = 3 * 3
c = b + 1 
d = a * c
e = d + 2 
f = 3 * 3
g = f + 1 
h = 2 * g
i = e / h
Problem: find 283 / 1983 × 100
Options: a ) 14.29 , b ) 14.21 , c ) 14.22 , d ) 14.27 , e ) 14.23
Rationale: "never start finding common factors . adjust the denominator to 2000 . so we are introducing an error of 17 which is 171983 = 1117171983 = 1117 th of the denominator . 283002000 = 14.15283002000 = 14.15 but this answer is slightly less than actual answer . now 14 . 1511714.15117 = 0.12 approximately . adding 0.12 to 14.25 gives 14.27 . option b is correct ."
Answer: b
Python program:
a = 283 / 1983
Problem: compound x contains elements a and b at an approximate ratio , by weight , of 2 : 10 . approximately how many grams of element b are there in 342 grams of compound x ?
Options: a ) 54 , b ) 162 , c ) 250 , d ) 270 , e ) 280
Rationale: "total number of fractions = 2 + 10 = 12 element b constitutes = 10 out of 12 parts of x so in 342 gms of x have 342 * 10 / 12 = 280 gms of b and 342 - 280 = 62 gms of a . cross check : - a / b = 62 / 280 = 2 / 10 ( as given ) ans e"
Answer: e
Python program:
a = 342 * 10
b = 2 + 10 
c = a / b
Problem: a certain article of clothing was discounted during a special sale to 4 / 5 of its original retail price . when the clothing did n ' t sell , it was discounted even further to 1 / 2 of its original retail price during a second sale . by what percent did the price of this article of clothing decrease from the first sale to the second sale ?
Options: a ) 50 % , b ) 33.33 % , c ) 40 % , d ) 16.66 % , e ) 12.5 %
Rationale: "say the original retail price of the item was $ 200 . the price after the first sale = 4 / 5 * $ 200 = $ 160 . the price after the second sale = 1 / 2 * $ 200 = $ 100 . the percent change from the first sale to the second = ( 160 - 100 ) / 150 = 1 / 3 = 40 % . answer : c ."
Answer: c
Python program:
a = 4 / 5
b = 4 / 5
c = 1 / 2
d = b * c
e = a - d
f = e * 100
Problem: income and expenditure of a person are in the ratio 8 : 7 . if the income of the person is rs . 40000 , then find his savings ?
Options: a ) 5000 , b ) 6000 , c ) 7000 , d ) 8000 , e ) 9000
Rationale: "let the income and the expenditure of the person be rs . 8 x and rs . 7 x respectively . income , 8 x = 40000 = > x = 5000 savings = income - expenditure = 8 x - 7 x = x so , savings = rs . 5000 . answer : a"
Answer: a
Python program:
a = 7 / 8
b = a * 40000
c = 40000 - b
Problem: workers decided to raise rs . 3 lacs by equal contribution from each . had they contributed rs . 50 eachextra , the contribution would have been rs . 3.50 lacs . how many workers were they ?
Options: a ) 220 , b ) 230 , c ) 500 , d ) 560 , e ) 1000
Rationale: "n * 50 = ( 350000 - 300000 ) = 50000 n = 50000 / 50 = 1000 e"
Answer: e
Python program:
a = 3 - 50
b = a * 1000
c = b * 100
d = c / 50
Problem: how many positive integers less than 60 have a reminder 01 when divided by 4 ?
Options: a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17
Rationale: "1 also gives the remainder of 1 when divided by 4 . so , there are total of 15 numbers . answer : c ."
Answer: c
Python program:
a = 4 + 1 
b = a - 1
c = math.factorial(b)
d = math.factorial(1)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: a boat goes 100 km downstream in 10 hours , and 200 km upstream in 25 hours . the speed of the stream is ?
Options: a ) 1 , b ) 22 1 / 7 , c ) 2 , d ) 22 1 / 2 , e ) 3
Rationale: "100 - - - 10 ds = 10 ? - - - - 1 200 - - - - 30 us = 8 ? - - - - - 1 s = ( 10 - 8 ) / 2 = 1 kmph . answer : a"
Answer: a
Python program:
a = 100 / 10
b = 200 / 25
c = a - b
d = c / 2
Problem: if 25 % of x is 30 less than 20 % of 1000 , then x is ?
Options: a ) 188 , b ) 216 , c ) 156 , d ) 680 , e ) 121
Rationale: "25 % of x = x / 4 ; 20 % of 1000 = 20 / 100 * 1000 = 200 given that , x / 4 = 200 - 30 = > x / 4 = 170 = > x = 680 . answer : d"
Answer: d
Python program:
a = 20 / 100
b = 1000 * a
c = b - 30
d = 25 / 100
e = c / d
Problem: mr . bhaskar is on tour and he has rs . 360 for his expenses . if he exceeds his tour by 4 days , he must cut down his daily expenses by rs . 3 . for how many days is mr . bhaskar on tour ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: if his tour is for x days and he is spending rs y per day , then xy = 360 x = 360 / y or y = 360 / x ( x + 4 ) * ( y - 3 ) = 360 or xy + 4 y - 3 x - 12 = 360 or 4 y - 3 x - 12 = 0 4 * 360 / x - 3 x - 12 = 0 solving it , we get x = 20 answer : b
Answer: b
Python program:
a = 3 * 3
b = a * 2
c = 360 / b
Problem: a bag contains 3 blue and 5 white marbles . one by one , marbles are drawn out randomly until only two are left in the bag . what is the probability z that out of the two , one is white and one is blue ?
Options: a ) 15 / 56 , b ) 41 / 56 , c ) 13 / 28 , d ) 15 / 28 , e ) 5 / 14
Rationale: "the required probability z = probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls . ways to select 6 out of total 8 = 8 c 6 ways to select 4 out of 5 white balls = 5 c 4 ways to select 2 out of 3 blue balls = 3 c 2 thus the required probability = ( 5 c 4 * 3 c 2 ) / 8 c 6 = 15 / 28 . d is thus the correct answer ."
Answer: d
Python program:
a = 3 * 5
b = 3 + 5 
c = 5 + 2 
d = b * c
e = d / 2
f = a / e
Problem: a boat having a length 5 m and breadth 3 m is floating on a lake . the boat sinks by 1 cm when a man gets on it . the mass of man is
Options: a ) 12 kg , b ) 60 kg , c ) 72 kg , d ) 96 kg , e ) none
Rationale: "solution volume of water displaced = ( 5 x 3 x 0.01 ) m 3 = 0.15 m 3 . mass of man = volume of water displaced × density of water = ( 0.15 × 1000 ) kg = 150 kg . answer e"
Answer: e
Python program:
a = 5 * 3
b = 1 / 100
c = a * b
d = c * 1000
Problem: a batsman in his 15 th inning makes a score of 75 and their by increasing his average by 3 . what is his average after the 15 th inning ?
Options: a ) 31 , b ) 32 , c ) 33 , d ) 34 , e ) 35
Rationale: "14 x + 75 = 15 ( x + 3 ) x = 30 + 3 = 33 answer : c"
Answer: c
Python program:
a = 3 * 15
b = 75 - a
c = b + 3
Problem: a man purchased 3 blankets @ rs . 100 each , 1 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 150 . find the unknown rate of two blankets ?
Options: a ) 1050 , b ) 2770 , c ) 1550 , d ) 5102 , e ) 5000
Rationale: "10 * 150 = 1500 3 * 100 + 1 * 150 = 450 1500 – 450 = 1050 answer : a"
Answer: a
Python program:
a = 10 * 150
b = 3 * 100
c = 1 * 150
d = b + c 
e = a - d
Problem: five bells commence tolling together and toll at intervals of 2 , 4 , 6 , 8,10 seconds respectively . in 60 minutes , how many times do they toll together ?
Options: a ) 41 , b ) 10 , c ) 31 , d ) 16 , e ) 17
Rationale: l . c . m of 2 , 4,6 , 8,10 is 240 . i . e after each 2 min they will toll together . so in 60 min they will toll 30 times . as they have initially tolled once , the answer will be 30 + 1 = 31 . answer : c
Answer: c
Python program:
a = 2 + 3 
b = a * 2
c = b * 3
d = 2 * c
e = d * 2
f = e / const_60
g = 60 / f
Problem: a cube of side 4 meter length is cut into small cubes of side 25 cm each . how many such small cubes can be obtained ?
Options: a ) 4069 , b ) 6048 , c ) 1000 , d ) 4096 , e ) 4060
Rationale: "along one edge , the number of small cubes that can be cut = 400 / 25 = 16 along each edge 16 cubes can be cut . ( along length , breadth and height ) . total number of small cubes that can be cut = 16 * 16 * 16 = 4096 answer : d"
Answer: d
Python program:
a = 4 ** 2
b = a ** 3
c = 4 ** 3
d = b / c
Problem: on a certain date , pat invested $ 6,000 at x percent annual interest , compounded annually . if the total value of the investment plus interest at the end of 10 years will be $ 24,000 , in how many years total will the total value of the investment plus interest increase to $ 48,000 ?
Options: a ) 15 , b ) 16 , c ) 18 , d ) 20 , e ) 24
Rationale: "24,000 = 6,000 ( 1 + x ) ^ 10 4 = ( 1 + x ) ^ 10 = 2 ^ 2 ( 1 + x ) ^ 10 = ( ( 1 + x ) ^ 5 ) ^ 2 = 2 ^ 2 therefore , ( 1 + x ) ^ 5 = 2 48,000 = 6000 ( 1 + x ) ^ n ( 1 + x ) ^ n = 8 ( 1 + x ) ^ n = 2 ^ 3 ( 1 + x ) ^ n = ( ( 1 + x ) ^ 5 ) ^ 3 = ( 1 + x ) ^ 15 therefore , n = 15 . the answer is a ."
Answer: a
Python program:
a = 3 * 10
b = 4 + 1 
c = a / b
d = math.log(c)
e = 2 * 10
f = 4 + 1 
g = e / f
h = 1 / 10
i = g ** h
j = math.log(i)
k = d / j
Problem: if | y + 7 | = 12 , what is the sum of all the possible values of y ?
Options: a ) - 14 , b ) - 12 , c ) - 8 , d ) 8 , e ) 12
Rationale: there will be two cases y + 7 = 12 or y + 7 = - 12 = > y = 5 or y = - 19 sum of both the values will be - 19 + 5 = - 14 answer : a
Answer: a
Python program:
a = 12 - 7
b = negate - (
c = a + b
Problem: the tax on a commodity is diminished by 15 % and its consumption increased by 10 % . the effect on revenue is ?
Options: a ) 8.5 , b ) 6.5 , c ) 5.5 , d ) 5.6 , e ) 4.4
Rationale: "100 * 100 = 10000 85 * 110 = 9350 - - - - - - - - - - - 10000 - - - - - - - - - - - 650 100 - - - - - - - - - - - ? = > 6.5 % decrease answer : b"
Answer: b
Python program:
a = 10 / 100
b = 1 + a 
c = 15 / 100
d = 1 - c
e = b * d
f = e * 100
g = 100 - f
Problem: positive integer y is 50 percent of 50 percent of positive integer x , and y percent of x equals 25 . what is the value of x ?
Options: a ) 25 , b ) 50 , c ) 75 , d ) 100 , e ) 125
Rationale: "y = 0.5 * 0.5 * x = x / 4 y % * x = 25 ( y / 100 ) * x = 25 ( x / 400 ) * x = 25 x ^ 2 = 25 * 400 x = 100 the answer is d ."
Answer: d
Python program:
a = 50 / 25
b = 50 / 25
c = a * b
d = c * 1000
Problem: cindy has her eye on a sundress but thinks it is too expensive . it goes on sale for 15 % less than the original price . before cindy can buy the dress , however , the store raises the new price by 25 % . if the dress cost $ 78.2 after it went on sale for 15 % off , what is the difference between the original price and the final price ?
Options: a ) $ 0.00 , b ) $ 5.75 , c ) $ 3.40 , d ) $ 5.00 , e ) $ 6.80
Rationale: "0.85 * { original price } = $ 78.2 - - > { original price } = $ 92 . { final price } = $ 78.2 * 1.25 = $ 97.75 . the difference = $ 97.75 - $ 92 = $ 5.75 answer : b ."
Answer: b
Python program:
a = 100 + 25 
b = a / 100
c = 78 * 2
d = 100 - 15
e = d / 100
f = 78 / 2
g = c - f
Problem: evaluate 20 % of 450 + 45 % of 200
Options: a ) 232 , b ) 242 , c ) 252 , d ) 262 , e ) 180
Rationale: "explanation : = ( 20 / 100 ) * 450 + ( 45 / 100 ) * 200 = 180 option e"
Answer: e
Python program:
a = 450 / 20
b = 20 / a
Problem: which greatest possible length can be used to measure exactly 12 meter 34 cm , 8 meter 98 cm and 6 meter 65 cm
Options: a ) 1 cm , b ) 2 cm , c ) 24 cm , d ) 55 cm , e ) 50 cm
Rationale: explanation : convert first all terms into cm . i . e . 1234 cm , 898 cm , 665 cm . now whenever we need to calculate this type of question , we need to find the hcf . hcf of above terms is 1 . option a
Answer: a
Python program:
a = 12 * 100
b = a + 34 
c = 8 * 100
d = c + 98 
e = b / d
f = math.floor(e)
Problem: working together , printer a and printer b would finish the task in 20 minutes . printer a alone would finish the task in 60 minutes . how many pages does the task contain if printer b prints 4 pages a minute more than printer a ?
Options: a ) 120 , b ) 180 , c ) 240 , d ) 280 , e ) 340
Rationale: "20 * a + 20 * b = x pages in 20 mins printer a will print = 20 / 60 * x pages = 1 / 3 * x pages thus in 20 mins printer printer b will print x - 1 / 3 * x = 2 / 3 * x pages also it is given that printer b prints 4 more pages per min that printer a . in 20 mins printer b will print 80 more pages than printer a thus 2 / 3 * x - 1 / 3 * x = 80 = > x = 240 pages answer : c"
Answer: c
Python program:
a = 60 / 20
b = a - 1
c = 4 / b
d = c * 60
Problem: a perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer . how many positive integers n are there such that n is less than 20,000 and at the same time n is a perfect square and a perfect cube ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "if n is a perfect square and a perfect cube , then n = a ^ 6 for some integer a . the numbers are 1 ^ 6 = 1 , 2 ^ 6 = 64 , 3 ^ 6 = 729 , 4 ^ 6 = 4096 , 5 ^ 6 = 15,625 . the answer is c ."
Answer: c
Python program:
a = 4 + 2 
b = a / 1