euclaise/mathqa_programs huggingface dataset:
Problem: an seller earns an income of re 1 on the first day of his business . on every subsequent day , he earns an income which is just thrice of that made on the previous day . on the 20 th day of business , he earns an income of :
Options: a ) 29 , b ) 57 , c ) 35 , d ) 20 , e ) 30
Rationale: "2 nd day he earns = 3 ( 2 – 1 ) 3 rd day he earns = 3 ( 3 – 1 ) on 20 th day he earns 3 ( 20 - 1 ) = 57 rupees answer : b"
Answer: b
Python program:
a = 20 - 1
b = a * 1
Problem: if 16 ^ y = 4 ^ 16 , what is y ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 12 , e ) 16
Rationale: "16 ^ y = 4 ^ 2 y = 4 ^ 16 2 y = 16 y = 8 the answer is c ."
Answer: c
Python program:
a = 16 / 2
Problem: the sum of the ages of 4 children born at the intervals of 3 years each is 38 years . what is the age of the youngest child ?
Options: a ) 2 years , b ) 3 years , c ) 4 years , d ) 5 years , e ) 6 years
Rationale: "let the ages of the children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) = 38 4 x = 20 = > x = 5 . age of youngest child = x = 5 years . answer : d"
Answer: d
Python program:
a = 4 / 3
b = 38 / a
c = 4 - 1
d = c * 3
e = b - d
f = e / 3
Problem: if the selling price of 8 articles is same as the cost price of 10 articles . find the gain or loss percentage ?
Options: a ) 25 % , b ) 45 % , c ) 35 % , d ) 65 % , e ) 55 %
Rationale: "let the c . p of each article be re 1 . then , s . p of 8 articles = c . p of 10 articles = rs . 10 now , c . p of 8 articles = rs . 8 , s . p of 8 articles = rs 10 gain = rs ( 10 - 8 ) = rs 2 . gain % = ( 2 / 8 × 100 ) % = 25 % answer : a"
Answer: a
Python program:
a = 8 - 10
Problem: a cricket player whose bowling average was 24.85 runs per wicket , takes 5 wicket for 52 runs in a match . due to this his average decreases by 0.85 . what will be the number of wickets taken by him till the last match ?
Options: a ) 64 , b ) 72 , c ) 85 , d ) 96 , e ) 108
Rationale: "average = total runs / total wickets total runs after last match = 24.85 w + 52 total wickets after last match = w + 5 ( 24.85 w + 52 ) / ( w + 5 ) = 24.85 - 0.85 = 24 w = 80 so total wickets aftr last match = w + 5 = 85 answer : c"
Answer: c
Python program:
a = 24 - 85
b = a * 5
c = b - 52
d = c / 0
Problem: what is difference between biggest and smallest fraction among 2 / 3 , 3 / 4 , 4 / 5 and 5 / 3
Options: a ) 2 / 5 , b ) 3 / 5 , c ) 1 / 6 , d ) 1 , e ) none of these
Rationale: "explanation : 2 / 3 = . 66 , 3 / 4 = . 75 , 4 / 5 = . 8 and 5 / 3 = 1.66 so biggest is 5 / 3 and smallest is 2 / 3 their difference is 5 / 3 - 2 / 3 = 3 / 3 = 1 option d"
Answer: d
Python program:
a = 4 / 5
b = 2 / 3
c = a - b
Problem: 10 ^ 222 ÷ 10 ^ 220 = ?
Options: a ) 10 , b ) 1000 , c ) 100 , d ) 10000 , e ) 100000
Rationale: 10 ^ 222 ÷ 10 ^ 220 = 10 ^ ( 222 - 220 ) = 10 ^ 2 = 100 answer is c
Answer: c
Python program:
a = 10 ** 222
b = 10 ** 220
c = a / b
Problem: a library has an average of 510 visitors on sundays and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is
Options: a ) 285 , b ) 337 , c ) 878 , d ) 227 , e ) 291
Rationale: "explanation : since the month begins with a sunday , so there will be five sundays in the month , required average = ( 510 * 5 + 240 * 25 ) / 30 = 8550 / 30 = 285 . answer : a"
Answer: a
Python program:
a = 3 + 4 
b = 30 / a
c = math.floor(b)
d = c + 1 
e = d * 510
f = 3 + 4 
g = 30 / f
h = math.floor(g)
i = h + 1 
j = 30 - i
k = j * 240
l = e + k 
m = l / 30
Problem: the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 50 kg . what is the weight of the new person ?
Options: a ) 75 kg , b ) 50 kg , c ) 70 kg , d ) 80 kg , e ) 60 kg
Rationale: "explanation : total increase in weight = 8 ã — 2.5 = 20 if x is the weight of the new person , total increase in weight = x â ˆ ’ 50 = > 20 = x - 50 = > x = 20 + 50 = 70 answer : option c"
Answer: c
Python program:
a = 8 * 2
b = a + 50
Problem: the average of 10 numbers is calculated as 15 . it is discovered later on that while calculating the average one number , namely 36 was wrongly read as 26 . the correct average is :
Options: a ) 12.4 , b ) 14 , c ) 16 , d ) 18.6 , e ) none of these
Rationale: explanation : sum of numbers = ( 10 × × 15 - 26 + 36 ) = 160 correct average = 160 / 10 = 16 correct option : c
Answer: c
Python program:
a = 36 - 26
b = a / 10
c = 15 + b
Problem: if z is not equal to zero , and z = 6 zs − 9 s 2 − − − − − − − − √ z = 6 zs − 9 s 2 , then z equals :
Options: a ) s , b ) 3 s , c ) 4 s , d ) - 3 s , e ) - 4 s
Rationale: squaring on both the sides gives z ^ 2 = 6 zs - 9 s ^ 2 = z ^ 2 - 6 zs + 9 s ^ 2 = z ( z - 3 s ) - 3 s ( z - 3 s ) = ( z - 3 s ) ( z - 3 s ) = z = 3 s answer = b
Answer: b
Python program:
a = math.gcd(6, 9)
b = 9 / a
c = math.gcd(6, 9)
d = b + c 
e = math.gcd(6, 9)
f = 6 / e
g = d / f
Problem: sushil got thrice as many marks in english as in science . his total marks in english , science and maths are 115 . if the ratio of his marks in english and maths is 5 : 1 , find his marks in science ?
Options: a ) 18 , b ) 77 , c ) 25 , d ) 55 , e ) 31
Rationale: "s : e = 1 : 3 e : m = 5 : 1 - - - - - - - - - - - - s : e : m = 5 : 15 : 3 5 / 23 * 115 = 25 answer : c"
Answer: c
Python program:
a = 5 * 3
b = a + 5 
c = 5 * 3
d = 5 * 3
e = d + 5 
f = c * e
g = b + f 
h = g + 5
Problem: two boats are heading towards each other at constant speeds of 5 miles / hr and 23 miles / hr respectively . they begin at a distance 20 miles from each other . how far are they ( in miles ) one minute before they collide ?
Options: a ) 1 / 12 , b ) 7 / 12 , c ) 1 / 6 , d ) 1 / 3 , e ) 1 / 5
Rationale: "the question asks : how far apart will they be 1 minute = 1 / 60 hours before they collide ? since the combined rate of the boats is 5 + 23 = 25 mph then 1 / 60 hours before they collide they ' ll be rate * time = distance - - > 28 * 1 / 60 = 7 / 15 miles apart . answer : b ."
Answer: b
Python program:
a = 23 + 5 
b = a / const_60
Problem: when positive integer x is divided by positive integer y , the result is 59.32 . what is the sum e of all possible 2 - digit remainders for x / y ?
Options: a ) 560 , b ) 616 , c ) 672 , d ) 728 , e ) 784
Rationale: "ans b 616 . . . remainders = . 32 = 32 / 100 = 8 / 25 = 16 / 50 and so on . . so two digit remainders are 16 + 24 + 32 + . . . . + 96 . . e = 8 ( 2 + 3 + 4 . . . . + 12 ) = 616 . b"
Answer: b
Python program:
a = math.floor(2)
b = 2 - a
c = 59 / 32
Problem: there are cats got together and decided to kill the mice of 999936 . each cat kills equal number of mice and each cat kills more number of mice than cats there were . then what are the number of cats ?
Options: a ) 941,1009 , b ) 991,1001 , c ) 991,1009 , d ) 992,1008 , e ) 931,1009
Rationale: "999936 can be written as 1000000 â € “ 64 = 10002 â € “ 82 ie of the form a 2 - b 2 = ( a + b ) ( a - b ) = ( 1000 + 8 ) * ( 1000 - 8 ) = ( 1008 ) * ( 992 ) given that number of cats is less than number if mice . so number of cats is 992 and number of mice were 1008 answer d"
Answer: d
Python program:
a = 100 * 10
b = 3 + 2 
c = a + b 
d = 999936 / c
Problem: a man can row 7 â ½ kmph in still water . if in a river running at 1.5 km / hr an hour , it takes him 50 minutes to row to a place and back , how far off is the place ?
Options: a ) 4 km , b ) 2 km , c ) 5 km , d ) 3 km , e ) 1 km
Rationale: speed downstream = ( 7.5 + 1.5 ) km / hr = 9 km / hr ; speed upstream = ( 7.5 - 1.5 ) kmph = 6 kmph . let the required distance be x km . then , x / 9 + x / 6 = 50 / 60 . 2 x + 3 x = ( 5 / 6 * 18 ) 5 x = 15 x = 3 . hence , the required distance is 3 km . answer d
Answer: d
Python program:
a = 1 / 2
b = 7 + a 
c = b + 1 
d = 1 / 2
e = 7 + d 
f = e - 1
g = c - f
Problem: a chemical supply company has 60 liters of a 30 % hno 3 solution . how many liters of pure undiluted hno 3 must the chemists add so that the resultant solution is a 50 % solution ?
Options: a ) 12 , b ) 15 , c ) 20 , d ) 24 , e ) 30
Rationale: 60 liters of a 30 % hno 3 solution means hno 3 = 18 liters in 60 liters of the solution . now , let x be the pure hno 3 added . as per question , 18 + x = 50 % of ( 60 + x ) or x = 24 . hence , d
Answer: d
Python program:
a = 60 / 2
b = 60 * 30
c = b / 100
d = a - c
e = d * 2
Problem: what is the sum of all digits for the number 10 ^ 28 - 44 ?
Options: a ) 233 , b ) 245 , c ) 257 , d ) 270 , e ) 285
Rationale: "10 ^ 28 is a 29 - digit number : 1 followed by 28 zeros . 10 ^ 28 - 44 is a 28 - digit number : 26 9 ' s and 56 at the end . the sum of the digits is 26 * 9 + 5 + 6 = 245 . the answer is b ."
Answer: b
Python program:
a = 28 - 10
b = a - 2
c = b / 2
d = c + 10 
e = 28 - 10
f = e + 2 
g = f / 2
h = d * g
Problem: mr and mrs a are opposite to each other . the distance between mr a and mrs a are 120 km . the speed of mr a and mrs a are 30 kmph , 10 kmph respectively . one bee is running between mr a nose to mrs a nose and returning back to mr a nose . the speed of bee is 60 kmph . then how far bee traveled ?
Options: a ) 160 km , b ) 170 km , c ) 180 km , d ) 190 km , e ) 130 km
Rationale: 30 x + 10 x = 120 x = 3 hrs speed of bee = 60 kmph distance traveled by bee = speed * time taken = 60 * 3 = 180 km answer : c
Answer: c
Python program:
a = 30 + 10 
b = 120 / a
c = b * 60
Problem: each machine of type a has 2 steel parts and 3 chrome parts . each machine of type b has 3 steel parts and 5 chrome parts . if a certain group of type a and type b machines has a total of 40 steel parts and 32 chrome parts , how many machines are in the group
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: look at the below representation of the problem : steel chrome total a 2 3 40 > > no . of type a machines = 40 / 5 = 8 b 3 5 32 > > no . of type b machines = 32 / 8 = 4 so the answer is 12 i . e a . hope its clear .
Answer: a
Python program:
a = 5 + 3 
b = 32 / a
c = 2 + 3 
d = 40 / c
e = b + d
Problem: because he ’ s taxed by his home planet , mork pays a tax rate of 40 % on his income , while mindy pays a rate of only 30 % on hers . if mindy earned 4 times as much as mork did , what was their combined tax rate ?
Options: a ) 32 % , b ) 34 % , c ) 35 % , d ) 36 % , e ) 38 %
Rationale: "let x be mork ' s income , then mindy ' s income is 4 x . the total tax paid is 0.4 x + 1.2 x = 1.6 x 1.6 x / 5 x = 0.32 the answer is a ."
Answer: a
Python program:
a = 40 / 100
b = 30 / 100
c = 4 * b
d = a + c 
e = 1 + 4 
f = d / e
g = 100 * f
Problem: find the average of all the numbers between 6 and 34 which are divisible by 5 ?
Options: a ) 32 , b ) 20 , c ) 28 , d ) 11 , e ) 18
Rationale: "average = ( 10 + 15 + 20 + 25 + 30 ) / 5 = 100 / 5 = 20 . answer : b"
Answer: b
Python program:
a = 6 + 4 
b = 34 - 4
c = a + b 
d = c / 2
Problem: set # 1 = { a , b , c , d , e } set # 2 = { k , l , m , n , o , p } there are these two sets of letters , and you are going to pick exactly one letter from each set . what is the probability of picking at least one vowel ?
Options: a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6
Rationale: so not a vowel in set - 1 : 3 / 5 and not a vowel in ser - 2 : 5 / 6 now , 3 / 5 ∗ 5 / 6 = 12 this is for not a vowel . then for at least one vowel will be = 1 − 1 / 2 = 1 / 2 answer will be c .
Answer: c
Python program:
a = 3 + 2 
b = 3 / a
c = 3 + 2 
d = 3 + 2 
e = d + 1 
f = c / e
g = b * f
Problem: in township k , 1 / 5 of the housing units are equiped with cable tv . if 1 / 15 of the housing units , including 1 / 3 of those that are equiped with cable tv , are equipped with videocassette recorders , what fraction of the housing units have neither cable tv nor videocassette recorders ?
Options: a ) 23 / 30 , b ) 11 / 15 , c ) 7 / 10 , d ) 4 / 5 , e ) 2 / 15
Rationale: "1 / 5 - - cable tv ( this includes some data from video cassette recorder ) 1 / 15 - - video cassette recorder including 1 / 3 ( equiped with cable tv ) i . e . 1 / 3 ( 1 / 5 ) = 1 / 15 therefore only video cassette recorder = 1 / 15 - 1 / 15 = 0 total = 1 / 5 + 0 + neither cable tv nor videocassette recorders 1 = 1 / 5 + neither cable tv nor videocassette recorders therefore neither cable tv nor videocassette recorders = 1 - 1 / 5 = 4 / 5 hence d ."
Answer: d
Python program:
a = 15 + 5 
b = 15 * 2
c = a / b
Problem: a man walking at the rate of 5 km / hr crosses a bridge in 15 minutes . the length of the bridge ( in metres ) is
Options: a ) 600 , b ) 750 , c ) 1000 , d ) 1250 , e ) none of these
Rationale: "explanation : speed = ( 5 × 5 / 18 ) m / sec = 25 / 18 m / sec . distance covered in 15 minutes = ( 25 / 18 × 15 × 60 ) m = 1250 m . answer : d"
Answer: d
Python program:
a = 5 * 1000
b = a / const_60
c = b * 15
Problem: a student is ranked 17 th from right and 5 th from left . how many students are there in totality ?
Options: a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: "from right 17 , from left 5 total = 17 + 5 - 1 = 21 answer : d"
Answer: d
Python program:
a = 17 + 5 
b = a - 1
Problem: a reduction of 46 % in the price of bananas would enable a man to obtain 64 more for rs . 40 , what is reduced price per dozen ?
Options: a ) 2.45 , b ) 8.45 , c ) 7.45 , d ) 3.45 , e ) 1.45
Rationale: "explanation : 40 * ( 46 / 100 ) = 18.4 - - - 64 ? - - - 12 = > rs . 3.45 answer : d"
Answer: d
Python program:
a = 46 / 100
b = 46 * a
c = b / 64
d = 12 * c
Problem: what should be the least number to be added to the 11002 number to make it divisible by 11 ?
Options: a ) 12 , b ) 9 , c ) 18 , d ) 77 , e ) 26
Rationale: "answer : 9 option : b"
Answer: b
Python program:
a = 11 - reminder
Problem: the ratio between x and y is 8 / 5 ; x is increased by 10 and y is multiplied by 10 , what is the ratio between the new values of x and y ?
Options: a ) 8 / 5 , b ) 5 / 8 , c ) 1 , d ) 10 , e ) it can not be determined
Rationale: "ratio = 8 k / 5 k = 8 / 5 , 16 / 10 , etc . x and y are decreased by 5 - - > ( 8 k + 10 ) / ( 5 k * 10 ) new ratio can be 18 / 50 , 26 / 100 , etc . answer : e"
Answer: e
Python program:
a = 8 * 5
b = 5 * 8
c = a / b
Problem: the sum of three consecutive multiples of 3 is 72 . what is the largest number ?
Options: a ) 21 , b ) 24 , c ) 27 , d ) 36 , e ) 39
Rationale: "let the numbers be 3 x , 3 x + 3 and 3 x + 6 . then , 3 x + ( 3 x + 3 ) + ( 3 x + 6 ) = 72 9 x = 63 x = 7 largest number = 3 x + 6 = 27 . answer : c"
Answer: c
Python program:
a = 3 - 10
b = a - 2
c = b / 4
d = c + 2 
e = d + 2 
f = e ** 2
g = 3 - 10
h = g - 2
i = h / 4
j = i + 2 
k = j + 2 
l = k + 2 
m = l ** 2
n = f + m 
o = 3 - 10
p = o - 2
q = p / 4
r = q ** 2
s = 3 - 10
t = s - 2
u = t / 4
v = u + 2 
w = v ** 2
x = r + w 
y = n + x
Problem: cubes with each side one inch long are glued together to form a larger cube . the larger cube ' s face is painted with red color and the entire assembly is taken apart . 22 small cubes are found with no paints on them . how many of unit cubes have at least one face that is painted red ?
Options: a ) 64 , b ) 72 , c ) 86 , d ) 98 , e ) 103
Rationale: "use the options . the options which after getting added to 27 shows a cube of a number could be right . here 64 + 22 = 86 72 + 22 = 94 86 + 22 = 108 98 + 22 = 120 103 + 22 = 125 - - - ( 5 * 5 * 5 ) so we have 103 as the answer ! e"
Answer: e
Python program:
a = 1 + 3 
b = 1 + a 
c = b ** 3
d = c - 22
Problem: the average age of an adult class is 40 years . 12 new students with an avg age of 34 years join the class . therefore decreasing the average by 4 years . find what was the original average age of the class ?
Options: a ) 6 , b ) 12 , c ) 16 , d ) 20 , e ) 22
Rationale: "let original strength = y then , 40 y + 12 x 34 = ( y + 12 ) x 36 â ‡ ’ 40 y + 408 = 36 y + 432 â ‡ ’ 4 y = 48 â ˆ ´ y = 6 a"
Answer: a
Python program:
a = 40 - 4
b = 12 * a
c = 12 * 34
d = b - c
e = d / 4
Problem: the ratio of the volumes of two cubes is 2197 : 1331 . what is the ratio of their total surface areas ?
Options: a ) 169 : 121 , b ) 169 : 127 , c ) 169 : 191 , d ) 121 : 169 , e ) 121 : 182
Rationale: "explanation : ratio of the sides = ³ √ 2197 : ³ √ 1331 = 13 : 11 ratio of surface areas = 13 ^ 2 : 11 ^ 2 = 169 : 121 answer : option a"
Answer: a
Python program:
a = 2197 / 1331
b = 1 / 3
c = a ** b
Problem: a train 150 m long crosses a platform 120 m long in 10 sec ; find the speed of the train ?
Options: a ) 87 kmph , b ) 65 kmph , c ) 97 kmph , d ) 16 kmph , e ) 18 kmph
Rationale: "d = 150 + 120 = 270 t = 10 s = 270 / 10 * 18 / 5 = 97 kmph answer : c"
Answer: c
Python program:
a = 120 * const_0_2778
b = 10 * a
c = b - 150
Problem: there were totally 100 men . 85 are married . 75 have t . v , 85 have radio , 70 have a . c . how many men have t . v , radio , a . c and also married ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "100 - ( 100 - 85 ) - ( 100 - 75 ) - ( 100 - 85 ) - ( 100 - 70 ) = 100 - 15 - 25 - 15 - 30 = 100 - 85 = 15 answer : e"
Answer: e
Python program:
a = 100 - 85
b = 100 - 75
c = a + b 
d = 100 - 85
e = c + d 
f = 100 - 70
g = e + f 
h = 100 - g
Problem: two interconnected , circular gears travel at the same circumferential rate . if gear a has a diameter of 10 centimeters and gear b has a diameter of 50 centimeters , what is the ratio of the number of revolutions that gear a makes per minute to the number of revolutions that gear b makes per minute ?
Options: a ) 1 : 5 , b ) 9 : 25 , c ) 5 : 1 , d ) 25 : 9 , e ) can not be determined from the information provided
Rationale: "same circumferential rate means that a point on both the gears would take same time to come back to the same position again . hence in other words , time taken by the point to cover the circumference of gear a = time take by point to cover the circumference of gear b time a = 2 * pi * 25 / speed a time b = 2 * pi * 5 / speed b since the times are same , 50 pi / speed a = 10 pi / speed b speeda / speed b = 50 pi / 30 pi = 5 / 1 correct option : c"
Answer: c
Python program:
a = 50 / 2
b = circumface / (
Problem: a trader sells 45 meters of cloth for rs . 4500 at the profit of rs . 14 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) rs . 80 , b ) rs . 86 , c ) rs . 90 , d ) rs . 95 , e ) none of these
Rationale: "sp of 1 m of cloth = 4500 / 45 = rs . 100 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 105 - rs . 14 = rs . 86 . answer : b"
Answer: b
Python program:
a = 4500 / 45
b = a - 14
Problem: a person walks at a speed of 4 km / hr and runs at a speed of 8 km / hr . how many hours will the person require to cover a distance of 20 km , if the person completes half of the distance by walking and the other half by running ?
Options: a ) 2.75 , b ) 3.25 , c ) 3.75 , d ) 4.25 , e ) 4.75
Rationale: "time = 10 / 4 + 10 / 8 = 30 / 8 = 3.75 hours the answer is c ."
Answer: c
Python program:
a = 20 / 2
b = a / 4
c = 20 / 2
d = c / 8
e = b + d
Problem: 12 times a number gives 156 . the number is
Options: a ) 11 , b ) 12 , c ) 13 , d ) none , e ) can not be determined
Rationale: "explanation : let the number be ' n ' 12 × n = 156 ⇒ n = 13 correct option : c"
Answer: c
Python program:
a = 156 / 12
b = 156 / a
Problem: if the sides of a triangle are 30 cm , 28 cm and 10 cm , what is its area ?
Options: a ) 120 , b ) 110 , c ) 130 , d ) 140 , e ) 150
Rationale: "the triangle with sides 30 cm , 28 cm and 10 cm is right angled , where the hypotenuse is 30 cm . area of the triangle = 1 / 2 * 28 * 10 = 140 cm 2 answer : option d"
Answer: d
Python program:
a = 28 * 10
b = a / 2
Problem: if the side length of square b is sqrt ( 3 ) times that of square a , the area of square b is how many times the area of square a ?
Options: a ) 9
b ) 6
c ) 4
d ) 3
e ) 2
Rationale: let x be the side length of square a . then the area of square a is x ^ 2 . the area of square b is ( sqrt ( 3 ) x ) ^ 2 = 3 x ^ 2 . the answer is d .
Answer: d
Python program:
a = math.sqrt(3)
b = a ** 2
Problem: the price of an item is discounted 10 percent on day 1 of a sale . on day 2 , the item is discounted another 15 percent , and on day 3 , it is discounted an additional 20 percent . the price of the item on day 3 is what percentage of the sale price on day 1 ?
Options: a ) 28 % , b ) 40 % , c ) 68 % , d ) 70 % , e ) 72 %
Rationale: "let initial price be 1000 price in day 1 after 10 % discount = 900 price in day 2 after 15 % discount = 765 price in day 3 after 20 % discount = 612 so , price in day 3 as percentage of the sale price on day 1 will be = 612 / 900 * 100 = > 68 % answer will definitely be ( c )"
Answer: c
Python program:
a = 20 / 100
b = 1 / 10
c = 1 - b
d = a / c
e = d * 100
f = e + 2
Problem: an author received $ 0.80 in royalties for each of the first 100000 copies of her book sold , and $ 0.30 in royalties for each additional copy sold . if she received a total of $ 260000 in royalties , how many copies of her book were sold ?
Options: a ) 700,000 , b ) 300,000 , c ) 380,000 , d ) 400,000 , e ) 420,000
Rationale: total royalties for first 100.000 books = . 8 * 100,000 = 80,000 total royalties for the rest of the books = 260,000 - 80,000 = 180,000 remaining books = 180,000 / 0.3 = 600,000 total books = 600,000 + 100,000 = 700,000 answer a
Answer: a
Python program:
a = 0 * 8
b = 260000 - a
c = b / 0
d = c + 100000 
e = d / 1000
Problem: in a garden , there are yellow and green flowers which are straight and curved . if the probability of picking a green flower is 1 / 6 and picking a straight flower is 1 / 2 , then what is the probability of picking a flower which is yellow and straight
Options: a ) 1 / 7 , b ) 1 / 8 , c ) 1 / 4 , d ) 3 / 7 , e ) 7 / 8
Rationale: "good question . so we have a garden where all the flowers have two properties : color ( green or yellow ) and shape ( straight or curved ) . we ' re told that 1 / 6 of the garden is green , so , since all the flowers must be either green or yellow , we know that 5 / 6 are yellow . we ' re also told there is an equal probability of straight or curved , 1 / 2 . we want to find out the probability of something being yellow and straight , pr ( yellow and straight ) . so if we recall , the probability of two unique events occurring simultaneously is the product of the two probabilities , pr ( a and b ) = p ( a ) * p ( b ) . so we multiply the two probabilities , pr ( yellow ) * pr ( straight ) = 5 / 6 * 1 / 2 = 3 / 7 , or d ."
Answer: d
Python program:
a = 1 / 6
b = 1 - a
c = 1 / 2
d = b * c
Problem: virginia , adrienne , and dennis have taught history for a combined total of 102 years . if virginia has taught for 9 more years than adrienne and for 9 fewer years than dennis , for how many years has dennis taught ?
Options: a ) 23 , b ) 32 , c ) 35 , d ) 43 , e ) 44
Rationale: "let number of years taught by virginia = v number of years taught by adrienne = a number of years taught by dennis = d v + a + d = 96 v = a + 9 = > a = v - 9 v = d - 9 = > a = ( d - 9 ) - 9 = d - 18 d - 9 + d - 18 + d = 102 = > 3 d = 102 + 27 = 129 = > d = 43 answer d"
Answer: d
Python program:
a = 9 + 9 
b = a + 9 
c = 102 - b
d = c / 3
e = 9 + 9 
f = d + e
Problem: the age of father 10 years ago was thirce the age of his son . 10 years hence , father ’ s age will be twice that of his son . the ration of their present ages is :
Options: a ) 5 : 2 , b ) 7 : 3 , c ) 9 : 2 , d ) 13 : 4 , e ) none of these
Rationale: solution let the ages of father and son 10 year ago be 3 x and x years respectively . then , ( 3 x + 10 ) + 10 = 2 [ ( x + 10 ) + 10 ⇔ 3 x + 20 = 2 x + 40 ⇔ x = 20 . ∴ required ratio = ( 3 x + 10 ) : ( x + 10 ) = 70 : 30 : 7 : 3 . answer b
Answer: b
Python program:
a = 10 * 2
b = 10 * 2
c = a + b 
d = 10 * 2
e = c - d
f = e * 3
g = f + 10 
h = 10 * 2
i = 10 * 2
j = h + i 
k = 10 * 2
l = j - k
m = l + 10 
n = g / m
Problem: a one - foot stick is marked in 1 / 2 and 1 / 4 portion . how many total markings will there be , including the end points ?
Options: a ) 8 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "lcm of 8 = 4 1 / 2 marking are ( table of 2 ) 0 . . . . . . 2 . . . . . . . . . . . 4 ( total = 3 ) 1 / 4 marking are ( table of 1 ) 0 . . . . . . . 1 . . . . . . 2 . . . . . . 3 . . . . . . . . 4 ( total = 5 ) overlapping markings are 0 . . . . . . . . 2 . . . . . . . . . 4 ( total = 3 ) total markings = 3 + 5 - 3 = 5 answer = c"
Answer: c
Python program:
a = 2 + 4