euclaise/mathqa_programs huggingface dataset:
Problem: pat , kate , and mark charged a total of 153 hours to a certain project . if pat charged twice as much time to the project as kate and 1 / 3 as much time as mark , how many more hours did mark charge to the project than kate ?
Options: a ) 85 , b ) 36 , c ) 72 , d ) 90 , e ) 108
Rationale: "85 all u do is do 2 : 1 : 6 = > 2 x + x + 6 x = 153 = > x = 17 34 : 17 : 102 102 - 17 = 85 answer a"
Answer: a
Python program:
a = 1 / 3
b = 1 + a 
c = 3 * 2
d = 1 / c
e = b + d 
f = 153 / e
g = 1 / 3
h = 1 + g 
i = 3 * 2
j = 1 / i
k = h + j 
l = 153 / k
m = 3 * 2
n = l / m
o = f - n
Problem: if d = 1 / ( 2 ^ 3 * 5 ^ 8 ) is expressed as a terminating decimal , how many nonzero digits will d have ?
Options: a ) one , b ) two , c ) three , d ) seven , e ) ten
Rationale: "another way to do it is : we know x ^ a * y ^ a = ( x * y ) ^ a given = 1 / ( 2 ^ 3 * 5 ^ 8 ) = multiply and divide by 2 ^ 5 = 2 ^ 5 / ( 2 ^ 3 * 2 ^ 5 * 5 ^ 8 ) = 2 ^ 5 / 10 ^ 8 = > non zero digits are 32 = > ans b"
Answer: b
Python program:
a = 1 + 2
Problem: the arithmetic mean of 5 negative integers is - 100 . if the average of 3 of these integers is - 90 , what is the least possible value that one of the other 2 integers can have ?
Options: a ) 229 , b ) - 1 , c ) - 229 , d ) 90 , e ) - 90
Rationale: the arithmetic mean of 5 negative integers is ( a + b + c + d + e ) / 5 = - 100 so , the sum of 5 negative integers would be a + b + c + d + e = - 100 * 5 = - 500 similarly , the sum of 3 negative integers would be a + b + c = - 90 * 3 = - 270 thus , the sum of the other 2 integers is - 500 + 270 = - 230 . since we know that the integers are negative then the least one from these two can be - 229 , the other one being - 1 . hence , the correct ans is c
Answer: c
Python program:
a = 5 * 90
b = a - 100
c = 90 - b
d = 90 / 3
e = c + d 
f = e + 1
Problem: rs . 3150 is divided so that 5 times the first share , thrice the 2 nd share and six times the third share amount to the same . what is the value of the third share ?
Options: a ) s 529 , b ) s 527 , c ) s 570 , d ) s 750 , e ) s 507
Rationale: "a + b + c = 3150 5 a = 2 b = 6 c = x a : b : c = 1 / 5 : 1 / 2 : 1 / 6 = 6 : 15 : 5 5 / 21 * 3150 = rs 750 answer : d"
Answer: d
Python program:
a = 5 + 2 
b = a + 3 
c = 3150 / b
d = 5 * c
Problem: maxwell leaves his home and walks toward brad ' s house . one hour later , brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 94 kilometers , maxwell ' s walking speed is 4 km / h , and brad ' s running speed is 6 km / h . what is the total time it takes maxwell before he meets up with brad ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 10
Rationale: "total distance = 94 kms maxwell speed = 4 kms / hr maxwell travelled for 1 hour before brad started , therefore maxwell traveled for 4 kms in 1 hour . time taken = total distance / relative speed total distance after brad started = 90 kms relative speed ( opposite side ) ( as they are moving towards each other speed would be added ) = 6 + 4 = 10 kms / hr time taken to meet brad after brad started = 90 / 10 = 9 hrs distance traveled by maxwell = maxwell ' s speed * time taken = 4 * 9 = 36 + 4 = 40 kms . . . therefore total time taken by maxwell to meet brad = distance travelled by maxwell / maxwell ' s speed = 40 / 4 = 10 hrs . . . answer e"
Answer: e
Python program:
a = 94 + 6 
b = 4 + 6 
c = a / b
Problem: excluding stoppages , the speed of a train is 48 kmph and including stoppages it is 40 kmph . of how many minutes does the train stop per hour ?
Options: a ) 16 , b ) 17 , c ) 15 , d ) 10 , e ) 12
Rationale: "t = 8 / 48 * 60 = 10 answer : d"
Answer: d
Python program:
a = 40 / 48
b = const_60 * a
c = const_60 - b
Problem: if a child walks at the rate of 5 m / min from his home , he is 6 minutes late for school , if he walks at the rate of 7 m / min he reaches half an hour earlier . how far is his school from his home ?
Options: a ) 450 min , b ) 540 min , c ) 630 min , d ) 360 min , e ) none of these
Rationale: let the distance between home and school is x . let actual time to reach be t . thus , x / 5 = t + 6 - - - - ( 1 ) and x / 7 = t - 30 - - - - - ( 2 ) solving equation 1 and 2 x = 630 min answer : c
Answer: c
Python program:
a = 1 / 2
b = const_60 * a
c = b + 6 
d = 1 / 5
e = 1 / 7
f = d - e
g = c / f
Problem: evaluate : | 9 - 8 ( 3 - 12 ) | - | 5 - 11 | = ?
Options: a ) 75 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: according to order of operations , inner brackets first . hence | 9 - 8 ( 3 - 12 ) | - | 5 - 11 | = | 9 - 8 * ( - 9 ) | - | 5 - 11 | according to order of operations , multiplication within absolute value signs ( which may be considered as brackets when it comes to order of operations ) next . hence = | 9 + 72 | - | 5 - 11 | = | 81 | - | - 6 | = 81 - 6 = 75 correct answer a ) 75
Answer: a
Python program:
a = 3 - 12
b = 8 * a
c = 9 - b
d = 5 - 11
e = c - negate
Problem: in town x , 64 percent of the population are employed , and 50 percent of the population are employed males . what percent of the employed people in town x are females ?
Options: a ) 16 % , b ) 22 % , c ) 32 % , d ) 40 % , e ) 52 %
Rationale: "we are asked to find the percentage of females in employed people . total employed people 64 % , out of which 50 are employed males , hence 14 % are employed females . ( employed females ) / ( total employed people ) = 14 / 64 = 22 % answer : b ."
Answer: b
Python program:
a = 64 - 50
b = a / 64
c = b * 100
Problem: a train passes a station platform in 35 sec and a man standing on the platform in 20 sec . if the speed of the train is 54 km / hr . what is the length of the platform ?
Options: a ) 228 , b ) 240 , c ) 225 , d ) 166 , e ) 1811
Rationale: "speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 20 = 300 m . let the length of the platform be x m . then , ( x + 300 ) / 35 = 15 = > x = 225 m . answer : c"
Answer: c
Python program:
a = 54 * const_0_2778
b = 20 * a
Problem: the cash difference between the selling prices of an book at a profit of 5 % and 10 % is $ 3 . the ratio of the two selling prices is :
Options: a ) 21 : 22 , b ) 52 : 33 , c ) 52 : 53 , d ) 45 : 53 , e ) 51 : 34
Rationale: "let c . p . of the book be $ x . then , required ratio = 105 % of x / 110 % of x = 105 / 110 = 21 / 22 = 21 : 22 a"
Answer: a
Python program:
a = 100 + 5 
b = 100 + 10 
c = a / b
Problem: what is the greatest prime factor of 3 ^ 6 - 1 ?
Options: a ) 2 , b ) 3 , c ) 7 , d ) 13 , e ) 17
Rationale: "3 ^ 6 - 1 = ( 3 ^ 3 ) ^ 2 - 1 = ( 27 ^ 2 ) - 1 dividing ( 27 ^ 2 ) - 1 by 13 will give us a reminder of 0 ( hint : ( 2 * 13 + 1 ) ^ 2 - 1 / 13 = ( reminder 1 ) - 1 = 0 hence the greatest prime factor must be 13 . answer : d"
Answer: d
Python program:
a = 6 / 2
b = 3 / a
c = math.floor(b)
Problem: village p ’ s population is 1200 greater than village q ' s population . if village q ’ s population were reduced by 800 people , then village p ’ s population would be 6 times as large as village q ' s population . what is village q ' s current population ?
Options: a ) 1050 , b ) 1100 , c ) 1150 , d ) 1200 , e ) 1250
Rationale: "p = q + 1200 . p = 6 ( q - 800 ) . 6 ( q - 800 ) = q + 1200 . 5 q = 6000 . q = 1200 . the answer is d ."
Answer: d
Python program:
a = 800 * 6
b = 1200 + a 
c = b / 3
Problem: a person buys an article at rs . 800 . at what price should he sell the article so as to make a profit of 35 % ?
Options: a ) 600 , b ) 277 , c ) 269 , d ) 261 , e ) 1080
Rationale: "cost price = rs . 800 profit = 35 % of 800 = rs . 280 selling price = cost price + profit = 800 + 280 = 1080 answer : e"
Answer: e
Python program:
a = 35 / 100
b = 800 * a
c = 800 + b
Problem: how many liters of water must be added to 18 liters of milk and water containing 10 % water to make it 40 % water ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "by rule of alligation : 40 % - 10 % = 30 % 100 % - 40 % = 60 % quantity of pure water : quantity of the mixture = 1 : 2 there are 18 liters of mixture , so we need to add 9 liters of pure water . the answer is d ."
Answer: d
Python program:
a = 18 / 10
b = 40 / 10
c = a * b
Problem: dacid obtained 96 , 95 , 82 , 97 and 95 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 79 , b ) 93 , c ) 88 , d ) 88 , e ) 75
Rationale: "average = ( 96 + 95 + 82 + 97 + 95 ) / 5 = 465 / 5 = 93 . answer : b"
Answer: b
Python program:
a = 96 + 95 
b = a + 82 
c = b + 97 
d = c + 95 
e = 10 / 2
f = d / e
Problem: the number 0.5 is how much greater than 1 / 6 ?
Options: a ) 1 / 3 , b ) 2 / 10 , c ) 1 / 50 , d ) 1 / 500 , e ) 2 / 500
Rationale: "let x be the difference then . 5 - 1 / 3 = x 5 / 10 - 1 / 3 = x x = 1 / 3 ans a"
Answer: a
Python program:
a = 1 / 6
b = 0 - 5
Problem: there are 22 students in a class . in how many different ways can a committee of 3 students be formed ?
Options: a ) 1180 , b ) 1320 , c ) 1540 , d ) 1760 , e ) 1920
Rationale: "22 c 3 = 22 * 21 * 20 / 6 = 1540 the answer is c ."
Answer: c
Python program:
a = 3 / 22
b = 1 - a
c = b * 22
Problem: a 70 cm long wire is to be cut into two pieces so that one piece will be 2 / 5 th of the other , how many centimeters will the shorter piece be ?
Options: a ) 12 , b ) 20 , c ) 88 , d ) 77 , e ) 14
Rationale: "1 : 2 / 5 = 5 : 2 2 / 7 * 70 = 20 answer : b"
Answer: b
Python program:
a = 2 / 5
b = a + 1 
c = 70 / b
d = 70 - c
Problem: the slant height of a cone is 20 cm and radius of the base is 10 cm , find the curved surface of the cone .
Options: a ) 330 , b ) 159 , c ) 150 , d ) 200 , e ) 628
Rationale: "π * 10 * 20 = 628 answer : e"
Answer: e
Python program:
a = math.pi * 10
b = a * 20
Problem: evaluate : 6602.5 + 660.25 + 66.025 + 6.6025 + 0.66025
Options: a ) 6819.59775 , b ) 7336.03775 , c ) 6918.59775 , d ) 6198.59775 , e ) 6891.59775
Rationale: "6602.5 660.25 66.025 6.6025 + 0.66025 - - - - - - - - - - - - - - - 7336.03775 answer is b ."
Answer: b
Python program:
a = 660 * 25
b = a * 6
c = 6602 - 5
Problem: the least number which when divided by 3 , 4 , 5 and 6 leaves a remainder 6 , but when divided by 9 leaves no remainder , is
Options: a ) 117 , b ) 126 , c ) 252 , d ) 336 , e ) none of these
Rationale: "explanation : l . c . m of 3 , 4 , 5 , 6 = 60 therefore required number is of the form 60 k + 6 . least value of k for which ( 60 k + 6 ) is divisible by 9 is k = 2 therefore required number = ( 60 x 2 + 6 ) = 126 . answer : b"
Answer: b
Python program:
a = math.lcm(3, 4)
b = math.lcm(a, 5)
c = math.lcm(b, 6)
d = c * 2
Problem: the temperature of a certain cup of coffee 10 minutes after it was poured was 120 degrees fahrenheit . if the temperature f of the coffee t minutes after it was poured can be determined by the formula f = 120 ( 2 ^ - at ) + 60 , where f is in degrees fahrenheit and a is a constant . then the temperature of the coffee 20 minutes after it was poured was how many degrees fahrenheit ?
Options: a ) 65 , b ) 75 , c ) 80 , d ) 85 , e ) 90
Rationale: "answer : b the temperature of coffee 10 minutes after it was poured ( 120 f ) will help in solving the constant “ a ” . 120 = 120 ( 2 ^ 10 a ) + 60 2 ^ - 1 = 2 ^ 10 a a = - 1 / 10 the temperature of coffee 20 minutes after it was poured is : f = 120 ( 2 ^ - 20 / 10 ) + 60 f = 120 * 1 / 4 + 60 f = 30 + 60 f = 90 e"
Answer: e
Python program:
a = 60 / 10
b = 1 - 2
c = a * b
d = 2 ** c
e = d * 120
f = e + 60
Problem: the ratio 10 : 20 expressed as percent equals to
Options: a ) 50 % , b ) 80 % , c ) 40 % , d ) 90 % , e ) 100 %
Rationale: "explanation : actually it means 10 is what percent of 20 , which can be calculated as , ( 10 / 20 ) * 100 = 10 * 5 = 50 answer : option a"
Answer: a
Python program:
a = 10 / 20
b = a * 100
Problem: the speed of a train is 120 kmph . what is the distance covered by it in 40 minutes ?
Options: a ) 50 kmph , b ) 60 kmph , c ) 70 kmph , d ) 80 kmph , e ) 85 kmph
Rationale: "120 * 40 / 60 = 80 kmph answer : d"
Answer: d
Python program:
a = 40 / const_60
b = a * 120
Problem: a right triangle aec has to be constructed in the xy - plane so that the right angle is at a and ae is parallel to x axis . the coordinates of a , e and c are integers and satisfy the inequalities - 1 ≤ x ≤ 7 and 1 ≤ y ≤ 7 . how many different triangles can be constructed with these properties ?
Options: a ) 63 , b ) 336 , c ) 567 , d ) 3024 , e ) 5040
Rationale: all the cordinates are integer hence , possible ae values are { - 10 } , { - 11 } . . . . { - 17 } : 8 ways . . . . { 7 , - 1 } , { 70 } . . . . . . { 76 } : 8 ways 9 * 8 ways = 72 for ac values can be { 12 } , { 13 } . . . . { 17 } : 6 ways . . . . . . { 71 } , { 72 } . . . . . { 76 } : 6 ways 7 * 6 = 42 total = 72 * 42 = 3024 hence d
Answer: d
Python program:
a = math.factorial(7)
b = 7 - 1
c = b * 4
d = 7 - 1
e = c * d
f = 7 * 2
g = e * f
h = a - g
Problem: if a ^ 2 + b ^ 2 = 25 and ab = 10 , what is the value of the expression ( a - b ) ^ 2 + ( a + b ) ^ 2 ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 50 , e ) 70
Rationale: "( a - b ) ^ 2 = a ^ 2 + b ^ 2 - 2 ab = 25 - 20 = 5 ( a + b ) ^ 2 = a ^ 2 + b ^ 2 + 2 ab = 25 + 20 = 45 so ( a + b ) ^ 2 + ( a - b ) ^ 2 = 45 + 5 = 50 d"
Answer: d
Python program:
a = math.sqrt(25)
b = a * 10
c = b + 3
Problem: if 25 typists can type 60 letters in 20 minutes , then how many letters will 75 typists working at the same rate complete in 1 hour ?
Options: a ) 270 , b ) 540 , c ) 610 , d ) 510 , e ) 500
Rationale: no . of letters typing by 25 typists in 20 minutes = 60 no . of letters typing by 25 typists in 60 minutes = 60 * 3 = 180 no . of letters typing by 75 typists in 60 minutes = 180 / 25 * 75 = 540 answer : b
Answer: b
Python program:
a = 60 * 3
b = a / 25
c = b * 75
Problem: a shopkeeper labeled the price of his articles so as to earn a profit of 20 % on the cost price . he then sold the articles by offering a discount of 10 % on the labeled price . what is the actual percent profit earned in the deal ?
Options: a ) 18 % , b ) 20 % , c ) 17 % , d ) 19 % , e ) none of these
Rationale: "explanation : let the cp of the article = rs . 100 . then labeled price = rs . 120 . sp = rs . 120 - 10 % of 120 = rs . 120 - 13 = rs . 118 . gain = rs . 118 â € “ rs . 100 = rs . 18 therefore , gain / profit percent = 18 % . answer : option d"
Answer: d
Python program:
a = 100 + 20 
b = 100 + 20 
c = 10 / 100
d = b * c
e = a - d
f = e - 100
Problem: a person can row at 9 kmph and still water . he takes 6 1 / 2 hours to row from a to b and back . what is the distance between a and b if the speed of the stream is 1 kmph ?
Options: a ) 32 , b ) 28 , c ) 29 , d ) 54 , e ) 20
Rationale: "let the distance between a and b be x km . total time = x / ( 9 + 1 ) + x / ( 9 - 1 ) = 6.5 = > x / 10 + x / 8 = 13 / 2 = > ( 4 x + 5 x ) / 40 = 13 / 2 = > x = 29 km . answer : c"
Answer: c
Python program:
a = 9 - 1
b = 9 + 1 
c = a * b
d = c * 6
e = 9 + 1 
f = 9 - 1
g = e + f 
h = d / g
Problem: in the junior basketball league there are 18 teams , 2 / 3 of them are bad and ½ are rich . what ca n ' t be the number of teams that are rich and bad
Options: a ) 4 . , b ) 6 . , c ) 7 . , d ) 10 . , e ) 8 .
Rationale: "total teams = 18 bad teams = ( 2 / 3 ) * 18 = 12 rich teams = 9 so maximum value that the both rich and bad can take will be 9 . so e = 10 can not be that value . ans d ."
Answer: d
Python program:
a = 1 / 2
b = 18 * a
c = b + 1
Problem: the sum of the present age of henry and jill is 43 . what is their present ages if 5 years ago henry was twice the age of jill ?
Options: a ) and 27 , b ) and 24 , c ) and 22 , d ) and 29 , e ) of these
Rationale: "let the age of jill 5 years ago be x , age of henry be 2 x x + 5 + 2 x + 5 = 43 x = 11 present ages will be 16 and 27 answer : a"
Answer: a
Python program:
a = 43 + 5 
b = a / 3
c = 43 - b
Problem: a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 84 percent of the distribution lies within one standard deviation d of the mean , what percent of the distribution is less than m + d ?
Options: a ) 16 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 %
Rationale: "this is easiest to solve with a bell - curve histogram . m here is equal to µ in the gaussian normal distribution and thus m = 50 % of the total population . so , if 84 % is one st . dev , then on either side of m we have 84 / 2 = 42 % . so , 84 % are to the right and left of m ( = 50 % ) . in other words , our value m + d = 50 + 42 = 92 % goingfrom the mean m , to the right of the distributionin the bell shaped histogram . . this means that 92 % of the values are below m + d . like i said , doing it on a bell - curve histogram is much easier to fullygethow this works , or you could apply gmat percentile jargon / theory to it e"
Answer: e
Python program:
a = 100 - 84
b = a / 2
c = 100 - b
Problem: the compound ratio of 5 : 8 , 3 : 2 and 4 : 5 ?
Options: a ) 1 : 1 , b ) 1 : 87 , c ) 3 : 4 , d ) 1 : 9 , e ) 1 : 2
Rationale: "5 / 8 * 3 / 2 * 4 / 5 = 3 / 4 1 : 1 answer : c"
Answer: c
Python program:
a = 5 * 3
b = 8 * 2
c = a / b
d = 3 * 4
e = 2 * 5
f = d / e
g = c / f
Problem: by selling 14 pencils for a rupee a man loses 22 % . how many for a rupee should he sell in order to gain 22 % ?
Options: a ) 10 , b ) 9 , c ) 7 , d ) 6 , e ) 4
Rationale: "88 % - - - 14 122 % - - - ? 88 / 122 * 14 = 10 answer : a"
Answer: a
Python program:
a = 100 + 22 
b = 100 - 22
c = 1 / b
d = a * c
e = 1 / d
f = e * 14
Problem: i travel the first part of my journey at 40 kmph and the second part at 60 kmph and cover the total distance of 240 km to my destination in 5 hours . how long did the first part of my journey last
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: the total time of journey = 5 hours . let ' x ' hours be the time that i travelled at 40 kmph therefore , 5 – x hours would be time that i travelled at 60 kmph . hence , i would have covered x × 40 + ( 5 − x ) 60 kms in the 5 hours = 240 kms . solving , for x in the equation 40 x + ( 5 – x ) × 60 = 240 , we get 40 x + 300 – 60 x = 240 ⇒ 20 x = 60 or x = 3 hours answer : c
Answer: c
Python program:
a = 60 * 5
b = a - 240
c = 60 - 40
d = b / c
Problem: if 4 cats can kill 4 rats in 4 minutes , how long will it take 100 cats to kill 100 rats ?
Options: a ) 1 minutes , b ) 2 minutes , c ) 3 minutes , d ) 4 minutes , e ) 5 minutes
Rationale: "it will take 4 minutes for 100 cats to kill 100 rats . 1 cat can kill 1 rat in 4 minutes , so 100 cats can kill 100 rats in 4 minutes answer d"
Answer: d
Python program:
a = 4 * 1
Problem: how many seconds will a 500 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 75 km / hr ?
Options: a ) 25 , b ) 30 , c ) 99 , d ) 88 , e ) 61
Rationale: "speed of train relative to man = 75 - 3 = 72 km / hr . = 72 * 5 / 18 = 20 m / sec . time taken to pass the man = 500 * 1 / 20 = 25 sec . answer : a"
Answer: a
Python program:
a = 75 - 3
b = a * const_0_2778
c = 500 / b
Problem: if the volume of the cube is 729 , then the surface area of the cube will be
Options: a ) 486
b ) 255
c ) 2866
d ) 265
e ) 872
Rationale: explanation : \ inline \ fn _ jvn a ^ 3 = 729 ; a = 9 surface area = ( 6 x 9 x 9 ) = 486 \ inline \ fn _ jvn cm ^ 2 answer : a ) 486 sq . cm
Answer: a
Python program:
a = 3 * 2
b = cube_edge_by_volume ** (
c = a * b
Problem: when the circumference and area of a circle are numerically equal , then the diameter is numerically equal to
Options: a ) area
b ) circumference
c ) 4
d ) 2 π
e ) none of these
Rationale: according to question , circumference of circle = area of circle or π d = π ( d ⁄ 2 ) 2 [ where d = diameter ] ∴ d = 4 answer c
Answer: c
Python program:
a = 2 * math.pi
b = a / math.pi
c = b * 2
Problem: if x and y are integers such that ( x + 1 ) ^ 2 is less than or equal to 49 and ( y - 1 ) ^ 2 is less than 64 , what is the sum of the maximum possible value of xy and the minimum possible value of xy ?
Options: a ) - 16 , b ) - 14 , c ) 0 , d ) 14 , e ) 16
Rationale: ( x + 1 ) ^ 2 < = 49 x < = 6 x > = - 8 ( y - 1 ) ^ 2 < 64 y < 9 y > - 7 max possible value of xy is - 8 × - 6 = 48 minimum possible value of xy is - 8 × 8 = - 64 - 64 + 48 = - 16 answer : a
Answer: a
Python program:
a = math.sqrt(49)
b = math.sqrt(64)
c = a + b
Problem: in an election between two candidates , one got 55 % of the total valid votes , 20 % of the votes were invalid . if the total number of votes was 7500 , the number of valid votes that the other candidate got , was
Options: a ) 2500 , b ) 2700 , c ) 3000 , d ) 3100 , e ) nobe
Rationale: solution number of valid votes = 80 % of 7500 = 6000 . valid votes polled by other candidates = 45 % of 6000 ( 45 / 100 × 6000 ) = 2700 . answer b
Answer: b
Python program:
a = 20 / 100
b = 1 - a
c = 55 / 100
d = 1 - c
e = b * d
f = e * 7500
Problem: cost is expressed by the formula tb ^ 4 . if b is doubled , the new cost r is what percent of the original cost ?
Options: a ) r = 200 , b ) r = 600 , c ) r = 800 , d ) r = 1600 , e ) r = 50
Rationale: original cost c 1 = t 1 * b 1 ^ 4 new cost c 2 = t 2 * b 2 ^ 4 . . . . only b is doubled so t 2 = t 1 and b 2 = 2 b 1 c 2 = t 2 * ( 2 b 1 ) ^ 4 = 16 ( t 1 * b 1 ^ 4 ) = 16 c 1 16 times c 1 = > 1600 % of c 1 ans d = 1600
Answer: d
Python program:
a = 2 ** 4
b = a * 100
Problem: the ratio of three numbers is 5 : 3 : 4 and their sum is 108 . the second number of the three numbers is ?
Options: a ) 23 , b ) 27 , c ) 30 , d ) 32 , e ) 34
Rationale: "5 : 3 : 4 total parts = 12 12 parts - - > 108 1 part - - - - > 9 the second number of the three numbers is = 3 3 parts - - - - > 27 b )"
Answer: b
Python program:
a = 4 ** 3
b = 5 ** 3
c = 3 ** 3
d = b + c 
e = a + d 
f = 108 / e
g = math.sqrt(f)
Problem: there are two concentric circles with radii 5 and 4 . if the radius of the outer circle is increased by 20 % and the radius of the inner circle decreased by 50 % , by what percent does the area between the circles increase ?
Options: a ) 56 , b ) 156 , c ) 256 , d ) 356 , e ) 456
Rationale: the area of a circle is pir ^ 2 , where r is the radius . the area of the big circle is 25 pi . the area of the small circle is 16 pi . the area a 1 between the circles is 9 pi . when the big circle ' s radius increases , the new area is 36 pi . when the small circle ' s radius decreases , the new area is 4 pi . the area a 2 between the circles is 32 pi . the ratio of a 2 / a 1 is 32 / 9 = 3.56 which is an increase of 256 % . the answer is c .
Answer: c
Python program:
a = 100 + 20 
b = a / 100
c = 5 * b
d = c ** 2
e = 100 - 50
f = e / 100
g = 4 * f
h = g ** 2
i = d - h
j = 5 ** 2
k = 4 ** 2
l = j - k
m = i - l
n = 5 ** 2
o = 4 ** 2
p = n - o
q = m / p
r = q * 100
Problem: a sum of money at simple interest amounts to rs . 815 in 2 years and to rs . 854 in 3 years . the sum is :
Options: a ) 500 , b ) 698 , c ) 780 , d ) 737 , e ) none
Rationale: "sol . s . i . for 1 year = rs . ( 854 - 815 ) = rs . 39 . s . i . for 2 years = rs . ( 39 * 2 ) = rs . 78 . â ˆ ´ principal = rs . ( 815 - 78 ) = rs . 737 . answer d"
Answer: d
Python program:
a = 854 - 815
b = a * 2
c = b / 3
d = 815 - c
Problem: the ratio of the area of a square to that of the square drawn on its diagonal is ?
Options: a ) 2 : 5
b ) 3 : 4
c ) 3 : 5
d ) 1 : 2
e ) 2 : 3
Rationale: explanation : a 2 : ( a â ˆ š 2 ) 2 a 2 : 2 a 2 - > 1 : 2 answer is d
Answer: d
Python program:
a = math.sqrt(2)
b = 1 / a
c = b ** 2
Problem: a rectangular floor that measures 8 meters by 10 meters is to be covered with carpet squares that each measure 2 meters by 2 meters . if the carpet squares cost $ 10 apiece , what is the total cost for the number of carpet squares needed to cover the floor ?
Options: a ) $ 200 , b ) $ 240 , c ) $ 480 , d ) $ 960 , e ) $ 1,920
Rationale: "the width of the rectangular floor ( 8 m ) is a multiple of one side of the square ( 2 m ) , and the length of the floor ( 10 m ) is also a multiple of the side of the square . so the number of carpets to cover the floor is ( 8 / 2 ) * ( 10 / 2 ) = 20 . the total cost is 20 * 10 = $ 200 . the answer is , therefore , a ."
Answer: a
Python program:
a = 8 * 8