euclaise/mathqa_programs huggingface dataset:
Problem: nd the area of trapezium whose parallel sides are 20 cm and 16 cm long , and the distance between them is 15 cm ?
Options: a ) 270 cm 2 , b ) 275 cm 2 , c ) 280 cm 2 , d ) 285 cm 2 , e ) 290 cm 2
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 16 ) * ( 15 ) = 270 cm 2 answer : a"
Answer: a
Python program:
a = 20 + 16 
b = 15 * a
c = b / 2
Problem: how many positive integer solutions does the equation 2 x + 1 y = 100 have ?
Options: a ) 44 , b ) 33 , c ) 50 , d ) 35 , e ) 14
Rationale: "formula : ( constant ) / ( lcm of two nos ) = 100 / ( 2 * 1 ) = 50 answer : c"
Answer: c
Python program:
a = 1 / 2
Problem: if all the 6 are replaced by 9 , then the algebraic sum of all the numbers from 1 to 100 ( both inclusive ) varies by how much ?
Options: a ) 330 , b ) 360 , c ) 380 , d ) 400 , e ) 420
Rationale: "unit place increased by 3 . so 6 , 16,26 , . . . . 96 . total 10 * 3 = 30 increased . ten ' s place increased by 30 . so 60,61 , . . . 69 . total 10 * 30 = 300 increased . so total varies = 300 + 30 = 330 . answer : a"
Answer: a
Python program:
a = 9 - 6
b = a * 10
c = b * 10
d = 9 - 6
e = d * 10
f = c + e
Problem: a train 130 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train . find the speed of the train .
Options: a ) 45 kmph , b ) 50 kmph , c ) 55 kmph , d ) 60 kmph , e ) 73 kmph
Rationale: "explanation : let the speed of the train be x kmph . speed of the train relative to man = ( x + 5 ) kmph = ( x + 5 ) × 5 / 18 m / sec . therefore 130 / ( ( x + 5 ) × 5 / 18 ) = 6 < = > 30 ( x + 5 ) = 2340 < = > x = 73 speed of the train is 73 kmph . answer : option e"
Answer: e
Python program:
a = 6 * const_0_2778
b = 130 / a
c = b - 5
Problem: sale of rs 6835 , rs . 9927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs , 6700 ?
Options: a ) 4966 , b ) 6191 , c ) 2877 , d ) 2676 , e ) 1881
Rationale: "total sale for 5 months = rs . ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs . 34009 . required sale = rs . [ ( 6700 x 6 ) - 34009 ] = rs . ( 40200 - 34009 ) = rs . 6191 answer : b"
Answer: b
Python program:
a = 6835 + 9927 
b = a + 6855 
c = b + 7230 
d = c + 6562 
e = d / 5
f = e - 6700
g = f * 5
Problem: find the average of all prime numbers between 10 and 40
Options: a ) 15.6 , b ) 22.5 , c ) 18.6 , d ) 32.2 , e ) 26.9
Rationale: "prime numbers between 10 and 40 are 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 required average = ( 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 ) / 8 = 180 / 8 = 22.5 answer is b"
Answer: b
Python program:
a = 10 + 1 
b = 10 + 1 
c = b + 2 
d = a + c 
e = 40 - 10
f = 40 - 2
g = e + f 
h = d + g 
i = h / 10
Problem: if y is 80 % greater than x , than x is what % less than y ?
Options: a ) 20 , b ) 25 , c ) 33 1 / 3 , d ) 44 4 / 9 , e ) 80
Rationale: "let x = 100 so y = 180 we want percentage change . so , ( 100 - 180 ) / 180 = - 44.44 % = 44 4 / 9 % lesser than y . hence option ( d ) ."
Answer: d
Python program:
a = 80 + 100 
b = 80 / a
c = b * 100
Problem: how many miles is 150 km ?
Options: a ) 91.5 miles , b ) 92.75 miles , c ) 93.75 miles , d ) 94.5 miles , e ) 95.75 miles
Rationale: "93.75 miles 150 / 1.6 answer : c"
Answer: c
Python program:
a = volume_cube / (
Problem: every disk in a bag is either blue , yellow or green . the ratio of blue disks to yellow disks to green disks in this bag is 3 : 7 : 8 . if the total number of disks in the bag is 108 , how many more green disks than blue disks are in the bag ?
Options: a ) 25 , b ) 28 , c ) 30 , d ) 35 , e ) 40
Rationale: "let b : y : g = 3 x : 7 x : 8 x . 3 x + 7 x + 8 x = 18 x = 108 - - > x = 6 . g - b = 8 x - 3 x = 5 x = 30 . the answer is c ."
Answer: c
Python program:
a = 3 + 7 
b = a + 8 
c = 108 / b
d = 8 - 3
e = c * d
Problem: a room is 7 meters 20 centimeters in length and 4 meters 32 centimeters in width . find the least number of square tiles of equal size required to cover the entire floor of the room .
Options: a ) 10 , b ) 15 , c ) 17 , d ) 19 , e ) 21
Rationale: "let us calculate both the length and width of the room in centimeters . length = 7 meters and 20 centimeters = 720 cm width = 4 meters and 32 centimeters = 432 cm as we want the least number of square tiles required , it means the length of each square tile should be as large as possible . further , the length of each square tile should be a factor of both the length and width of the room . hence , the length of each square tile will be equal to the hcf of the length and width of the room = hcf of 720 and 432 = 144 thus , the number of square tiles required = ( 720 x 432 ) / ( 144 x 144 ) = 5 x 3 = 15 answer : b"
Answer: b
Python program:
a = 7 * 100
b = a + 20 
c = 4 * 100
d = c + 32 
e = b * d
f = 7 * 100
g = f + 20 
h = 4 * 100
i = h + 32 
j = math.gcd(g, i)
k = 7 * 100
l = k + 20 
m = 4 * 100
n = m + 32 
o = math.gcd(l, n)
p = j * o
q = e / p
Problem: a number is greater than 3 but less than 8 . also the number is greater than 6 but less than 10 . what is the number ?
Options: a ) 5 , b ) 7 , c ) 6 , d ) 8 , e ) 9
Rationale: b 7
Answer: b
Python program:
a = 8 - 1
Problem: efrida and frazer who live 13 miles apart , meet at a restaurant that is directly north of efrida ' s home and directly east of frazer ' s home . if the restaurant is two miles closer to efrida ' s home , than to frazer ' s home , how many miles is the restaurant from frazer ' s home ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 10 , e ) 11
Rationale: "it ' s a simple geometry problem . look at the diagram below : answer : e ."
Answer: e
Python program:
a = 13 ** 2
b = 2 ** 2
c = a - b
d = c / 2
e = math.sqrt(d)
f = e + 2
Problem: a cistern is filled by a tap in 8 1 / 2 hours . due to leak in the bottom of the cistern , it takes half an hour longer to fill the cistern . if the cistern is full how many hours will it take the leak to empty it ?
Options: a ) 133 , b ) 143 , c ) 153 , d ) 163 , e ) 173
Rationale: "filling rate - leak rate = net rate 1 / 8.5 - leak rate = 1 / 9 leak rate = 2 / 17 - 1 / 9 = 1 / 153 the answer is c ."
Answer: c
Python program:
a = 1 / 2
b = 8 + a 
c = 1 / b
d = 1 / 4
e = c - d
f = 1 / e
Problem: nicky and cristina are running a race . since cristina is faster than nicky , she gives him a 54 meter head start . if cristina runs at a pace of 5 meters per second and nicky runs at a pace of only 3 meters per second , how many seconds will nicky have run before cristina catches up to him ?
Options: a ) 15 seconds , b ) 18 seconds , c ) 25 seconds , d ) 27 seconds , e ) 45 seconds
Rationale: "used pluging in method say t is the time for cristina to catch up with nicky , the equation will be as under : for nicky = n = 3 * t + 54 for cristina = c = 5 * t @ t = 27 , n = 135 c = 135 right answer ans : d"
Answer: d
Python program:
a = 5 - 3
b = 54 / a
Problem: susan can type 10 pages in 5 minutes . mary can type 5 pages in 10 minutes . working together , how many pages can they type in 30 minutes ?
Options: a ) 15 , b ) 20 , c ) 25 , d ) 65 , e ) 75
Rationale: susan can type 2 pages in 1 min mary can type 0.5 pages in 1 min so , both of them work together they type 2.5 pages in 1 min so , in 30 min they type ( 30 * 2.5 ) = 75 pages answer : e
Answer: e
Python program:
a = 30 / 10
b = a * 5
c = 30 / 5
d = 10 * c
e = b + d
Problem: ( 178 % of 1265 ) ÷ 5.96 = ?
Options: a ) 125 , b ) 175 , c ) 225 , d ) 375 , e ) 524
Rationale: explanation : ? = ( 178 x 1265 / 100 ) ÷ 6 = 2250 / 600 = 375 answer : option d
Answer: d
Python program:
a = 178 / 100
b = a * 1265
c = b / 5
Problem: at the faculty of aerospace engineering , 312 students study random - processing methods , 234 students study scramjet rocket engines and 112 students study them both . if every student in the faculty has to study one of the two subjects , how many students are there in the faculty of aerospace engineering ?
Options: a ) 430 , b ) 434 , c ) 438 , d ) 444 , e ) 446
Rationale: "312 + 234 - 112 ( since 112 is counted twice ) = 434 b is the answer"
Answer: b
Python program:
a = 112 / 2
b = 312 - a
c = 112 / 2
d = 234 - c
e = b + d
Problem: there are 399 doctors and nurses in a hospital . if the ratio of the doctors to the nurses is 8 : 11 , then how many nurses are there in the hospital ?
Options: a ) 152 , b ) 209 , c ) 57 , d ) 231 , e ) 181
Rationale: "given , the ratio of the doctors to the nurses is 8 : 11 number of nurses = 11 / 19 x 399 = 231 answer : d"
Answer: d
Python program:
a = 11 - 8
b = 8 * a
c = b * 11
Problem: after spending rs . 5000 on rent , rs . 1500 on milk , rs . 4500 on groceries , rs . 2500 on childrens education rs . 2000 on petrol and rs . 6100 on miscellaneous expenses , mr . kishore saved 10 % of his monthly salary . how much did he save in rs . ?
Options: a ) 2160 , b ) 2350 , c ) 2000 , d ) 2300 , e ) 2400
Rationale: "explanation : total exp = 5000 + 1500 + 4500 + 2500 + 2000 + 6100 = 21600 exp in % = 100 - 10 = 90 % , 21600 = 90 % saving = 10 % = 21600 x 10 / 90 = rs . 2400 answer : e"
Answer: e
Python program:
a = 5000 + 1500 
b = a + 4500 
c = b + 2500 
d = c + 2000 
e = d + 6100 
f = e * 100
g = 100 - 10
h = f / g
i = 5000 + 1500 
j = i + 4500 
k = j + 2500 
l = k + 2000 
m = l + 6100 
n = h - m
Problem: a train 825 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 90 seconds . the speed of the train is :
Options: a ) 33 , b ) 27 , c ) 27 , d ) 50 , e ) 81
Rationale: "speed of the train relative to man = ( 125 / 10 ) m / sec = ( 25 / 2 ) m / sec . [ ( 25 / 2 ) * ( 18 / 5 ) ] km / hr = 45 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 45 = = > x = 50 km / hr . answer : d"
Answer: d
Python program:
a = 5 * const_0_2778
b = a * 5
c = 825 - b
d = c / 5
e = d / const_0_2778
Problem: in a hostel , the number of students decreased by 10 % and the price of food increased by 20 % over the previous year . if each student consumes the same amount of food then by how much should the consumption of food be cut short by every student , so that the total cost of the food remains the same as that of the previous year ?
Options: a ) 19 % , b ) 15 % , c ) 25 % , d ) 40 % , e ) 7.4 %
Rationale: "cost of food ( c ) = food consumed per student ( f ) * number of students ( n ) * price of food ( p ) originally , c = fnp when number of students decrease by 8 % , and the price of food increases by 20 % , c = f ( new ) * ( 0.9 n ) * ( 1.2 p ) = > f ( new ) = f / ( 0.9 * 1.2 ) = > f ( new ) = 0.9259 f therefore the new cost of food must be 92.59 % of the old cost , or the cost of food must decrease by 7.4 % ( option e )"
Answer: e
Python program:
a = 100 * 100
b = 100 - 10
c = 100 + 20 
d = b * c
e = a / d
f = 1 - e
g = f * 100
Problem: the time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream . if the speed of the boat in still water is 63 kmph , find the speed of the stream ?
Options: a ) 15 , b ) 19 , c ) 14 , d ) 21 , e ) 16
Rationale: "the ratio of the times taken is 2 : 1 . the ratio of the speed of the boat in still water to the speed of the stream = ( 2 + 1 ) / ( 2 - 1 ) = 3 / 1 = 3 : 1 speed of the stream = 63 / 3 = 21 kmph . answer : d"
Answer: d
Python program:
a = 63 * 2
b = a / 3
c = 63 - b
Problem: if the sales tax reduced from 3 1 / 2 % to 3 1 / 3 % , then what difference does it make to a person who purchases an article with market price of rs . 6600 ?
Options: a ) 11 , b ) 13 , c ) 14 , d ) 18 , e ) 10
Rationale: "required difference = [ 3 ½ % of rs . 6600 ] – [ 3 1 / 3 % of rs . 6600 ] = [ ( 7 / 20 - ( 10 / 3 ) ] % of rs . 6600 = 1 / 6 % of rs . 6600 = rs . [ ( 1 / 6 ) 8 ( 1 / 100 ) * 6600 ] = rs . 11 . answer is a ."
Answer: a
Python program:
a = 1 / 2
b = a + 3 
c = 1 / 3
d = c + 3 
e = b - d
f = e * 6600
g = f / 100
Problem: working alone at its constant rate , machine a produces x boxes in 10 minutes and working alone at its constant rate , machine b produces 2 x boxes in 5 minutes . how many minutes does it take machines a and b , working simultaneously at their respective constant rates , to produce 7 x boxes ?
Options: a ) 3 minutes , b ) 4 minutes , c ) 5 minutes , d ) 14 minutes , e ) 12 minutes
Rationale: "rate = work / time given rate of machine a = x / 10 min machine b produces 2 x boxes in 5 min hence , machine b produces 4 x boxes in 10 min . rate of machine b = 4 x / 10 we need tofind the combined time that machines a and b , working simultaneouslytakeat their respective constant rates let ' s first find the combined rate of machine a and b rate of machine a = x / 10 min + rate of machine b = 4 x / 10 = 5 x / 10 now combine time = combine work needs to be done / combine rate = 7 x / 5 x * 10 = 14 min ans : d"
Answer: d
Python program:
a = 7 * 10
b = speed + ( 
c = 2 * 10
d = a / b
Problem: in a shop , the profit is 320 % of the cost . if the cost increases by 25 % but the selling price remains constant , approximately what percentage of the selling price is the profit ?
Options: a ) 70 % , b ) 50 % , c ) 100 % , d ) 60 % , e ) 55 %
Rationale: "cp . = rs . 100 . = > profit = rs . 320 , s . p . = rs . 420 . new c . p . = 125 % of rs . 100 = rs . 125 new s . p . = rs . 420 . profit = rs . ( 420 - 125 ) = rs . 295 . req = ( 295 / 420 * 100 ) = = > 70 % answer a"
Answer: a
Python program:
a = 320 + 100 
b = 25 + 100 
c = a - b
d = 320 + 100 
e = c / d
f = e * 100
Problem: 2 trains in same direction at 50 km / hr , 32 km / hr . a man in slower train observes 15 sec elapse before the faster train completely passed by him what is length of faster train ?
Options: a ) 65 meters , b ) 75 meters , c ) 85 meters , d ) 95 meters , e ) 55 meters
Rationale: relative speed = 18 k / hr = 5 m / sec distance covered = length of faster train = 5 * 15 = 75 meters answer : b
Answer: b
Python program:
a = 50 - 32
b = a * 1000
c = b / 3600
d = c * 15
Problem: lionel left his house and walked towards walt ' s house , 48 miles away . four hours later , walt left his house and ran towards lionel ' s house . if lionel ' s speed was 2 miles per hour and walt ' s 6 miles per hour , how many miles had lionel walked when he met walt ?
Options: a ) 12 , b ) 18 , c ) 20 , d ) 24 , e ) 28
Rationale: "in the first 4 hours lionel at the rate of 2 miles per hour covered distance = rate * time = 4 * 2 = 8 miles . so , the distance between him and walt was 48 - 8 = 40 miles when walt left his house . now , their combined rate to cover this distance was 2 + 6 = 8 miles per hour , hence they will meet ( they will cover that distance ) in time = distance / rate = 40 / 8 = 5 hours . total time that lionel was walking is 4 + 5 = 9 hours , which means that he covered in that time interval distance = rate * time = 2 * 9 = 18 miles . answer : b ."
Answer: b
Python program:
a = 2 * 2
b = 48 - a
c = 6 + 2 
d = b / c
e = d + 2 
f = 2 * e
Problem: x and y started a business by investing rs . 36000 and rs . 42000 respectively after 4 months z joined in the business with an investment of rs . 48000 , then find share of z in the profit of rs . 13860 ?
Options: a ) 4032 , b ) 4000 , c ) 3250 , d ) 3825 , e ) 3985
Rationale: "ratio of investment , as investments is for different time . investment x number of units of time . ratio of investments x : y : z = 36000 : 42000 : 48000 = > 6 : 7 : 8 . x = 6 x 12 months = 72 , y = 7 x 12 = 84 , z = 8 x 8 = 64 = > 18 : 21 : 16 . ratio of investments = > x : y : z = 18 : 21 : 16 . investment ratio = profit sharing ratio . z = 13860 ã — 16 / 55 = rs . 4032 . share of z in the profit is rs . 4032 . option a"
Answer: a
Python program:
a = 3 * 4
b = a - 4
c = 48000 * b
d = 3 * 4
e = 36000 * d
f = 3 * 4
g = 42000 * f
h = e + g 
i = 3 * 4
j = i - 4
k = 48000 * j
l = h + k 
m = 13860 / l
n = c * m
Problem: a cyclist traveled for two days . on the second day the cyclist traveled 3 hours longer and at an average speed 10 mile per hour slower than she traveled on the first day . if during the two days she traveled a total of 280 miles and spent a total of 12 hours traveling , what was her average speed on the second day ?
Options: a ) 5 mph , b ) 10 mph , c ) 20 mph , d ) 30 mph , e ) 40 mph
Rationale: "solution : d = 280 mi t = 12 hrs day 1 time = t 1 day 2 time = t 2 t 2 - t 1 = 4 hrs - - - - - ( i ) t 1 + t 2 = 12 hrs - - - - - ( ii ) adding i and ii , t 2 = 8 hrs and t 1 = 4 hrs day 1 rate = r 1 day 2 rate = r 2 r 1 - r 2 = 10 mph i . e . r 1 = 10 + r 2 280 = 8 r 2 + 4 r 1 i . e . 280 = 8 r 2 + 4 ( 10 + r 2 ) i . e . r 2 = 20 mph answer : b"
Answer: b
Python program:
a = 12 - 3
b = a / 2
c = b * 10
d = 280 - c
e = 12 - 3
f = e / 2
g = 12 - 3
h = g / 2
i = h + 3 
j = f + i 
k = d / j
Problem: from the digits 2 , 3 , 4 , 5 , 6 and 7 , how many 5 - digit numbers can be formed that have distinct digits and are multiples of 12 ?
Options: a ) 36 , b ) 60 , c ) 84 , d ) 72 , e ) 86
Rationale: detailed solution any multiple of 12 should be a multiple of 4 and 3 . first , let us look at the constraint for a number being a multiple of 3 . sum of the digits should be a multiple of 3 . sum of all numbers from 2 to 7 is 27 . so , if we have to drop a digit and still retain a multiple of 3 , we should drop either 3 or 6 . so , the possible 5 digits are 2 , 4 , 5 , 6 , 7 or 2 , 3 , 4 , 5 , 7 . when the digits are 2 , 4 , 5 , 6 , 7 . the last two digits possible for the number to be a multiple of 4 are 24 , 64 , 52 , 72 , 56 , 76 . for each of these combinations , there are 6 different numbers possible . so , with this set of 5 digits we can have 36 different numbers . when the digits are 2 , 3 , 4 , 5 , 7 . the last two digits possible for the number to be a multiple of 4 are 32 , 52 , 72 , 24 . for each of these combinations , there are 6 different numbers possible . so , with this set of 5 digits we can have 24 different numbers . overall , there are 60 different 5 - digit numbers possible . correct answer : b
Answer: b
Python program:
a = 5 - 2
b = math.factorial(a)
c = 2 * 3
d = b * c
e = 5 - 2
f = math.factorial(e)
g = 4 * f
h = d + g
Problem: what is the least common multiple of 8,12 , 32,14
Options: a ) 672 , b ) 682 , c ) 328 , d ) 964 , e ) 285
Rationale: "the given numbers are 8,12 , 32,14 thus the l . c . m is 2 * 2 * 2 * 1 * 3 * 4 * 7 = 672 the answer is a"
Answer: a
Python program:
a = 8 + 12 
b = a * 2
Problem: the difference between the local value and the face value of 8 in the numeral 96348621 is
Options: a ) 6992 , b ) 6982 , c ) 7982 , d ) 7972 , e ) 7992
Rationale: "explanation : ( local value of 8 ) - ( face value of 8 ) = ( 8000 - 8 ) = 7992 e )"
Answer: e
Python program:
a = 8 * 1000
b = a - 8
Problem: find the ratio in which rice at rs . 7.20 a kg be mixed with rice at rs . 5.80 a kg to produce a mixture worth rs . 6.30 a kg ?
Options: a ) 5 : 9 , b ) 2 : 3 , c ) 3 : 4 , d ) 4 : 5 , e ) none of these
Rationale: "solution required ratio = 50 : 90 = 5 : 9 answer a"
Answer: a
Python program:
a = 6 - 30
b = 7 - 20
c = a / b
Problem: three pipes , a , b , & c are attached to a tank . a & b can fill it in 20 & 30 minutes respectively while c can empty it in 15 minutes . if a , b & c are kept open successively for 4 minute each , how soon will the tank be filled ?
Options: a ) 2 hours , b ) 12 hours , c ) 3 hours , d ) 5 hours , e ) 6 hours
Rationale: in three minute 1 / 20 + 1 / 30 - 1 / 15 = 1 / 60 part is filled 12 min - - - - - - - - 1 / 60 parts x min - - - - - - - - - 1 part ( full ) x = 720 min = 12 hours answer : b
Answer: b
Python program:
a = 4 + 4 
b = a + 4
Problem: when positive integer x is divided by 8 , the quotient is y and the remainder is 2 . when 2 x is divided by 7 , the quotient is 2 y and the remainder is 4 . what is the value of 6 y – x ?
Options: a ) - 1 , b ) 1 , c ) - 2 , d ) 2 , e ) - 3
Rationale: "( 1 ) x = 8 y + 2 ( 2 ) 2 x = 14 y + 4 ( 2 ) - ( 1 ) : x = 6 y + 2 6 y - x = - 2 the answer is c ."
Answer: c
Python program:
a = 2 * 2
b = a - 4
c = 7 * 2
d = 2 * 8
e = c - d
f = b / e
g = 6 * f
h = 2 * 2
i = h - 4
j = 7 * 2
k = 2 * 8
l = j - k
m = i / l
n = 8 * m
o = n + 2 
p = g - o
Problem: if n = 2 ^ 0.15 and n ^ b = 32 , b must equal
Options: a ) 3 / 80 , b ) 3 / 5 , c ) 4 , d ) 100 / 3 , e ) 80 / 3
Rationale: "15 / 100 = 3 / 20 n = 2 ^ 3 / 20 n ^ b = 2 ^ 5 ( 2 ^ 3 / 20 ) ^ b = 2 ^ 5 b = 100 / 3 answer : d"
Answer: d
Python program:
a = math.log(32)
b = 2 ** 0
c = math.log(b)
d = a / c
Problem: a man is 25 years older than his son . in two years , his age will be twice the age of his son . the present age of his son is
Options: a ) 21 , b ) 22 , c ) 20 , d ) 18 , e ) 23
Rationale: "explanation : let the son ' s present age be x years . then , man ' s present age = ( x + 25 ) years = > ( x + 25 ) + 2 = 2 ( x + 2 ) = > x + 27 = 2 x + 4 so , x = 23 . answer : e"
Answer: e
Python program:
a = 2 * 2
b = a - 2
c = 25 - b
d = 2 - 1
e = c / d
Problem: during a special promotion , a certain filling station is offering a 10 percent discount on gas purchased after the first 5 gallons . if kim purchased 20 gallons of gas , and isabella purchased 25 gallons of gas , then isabella ‟ s total per - gallon discount is what percent of kim ‟ s total per - gallon discount ?
Options: a ) 80 % , b ) 107 % , c ) 116.7 % , d ) 120 % , e ) 140 %
Rationale: "kim purchased 20 gallons of gas . she paid for 5 + 0.9 * 15 = 18.5 gallons , so the overall discount she got was 1.5 / 20 = 7.5 % . isabella purchased 25 gallons of gas . she paid for 5 + 0.9 * 20 = 23 gallons , so the overall discount she got was . 5 / 25 = 8 % . 8 is 8 / 7.5 * 100 = 107 % of 7.5 . answer : b ."
Answer: b
Python program:
a = 10 - 1
b = 10 + a 
c = 100 - 10
d = b * c
e = d / 100
f = e + 5 
g = f / 25
h = 1 - g
i = h * 100
j = 10 + 4 
k = 100 - 10
l = j * k
m = l / 100
n = 5 + m 
o = n / 20
p = 1 - o
q = p * 100
r = i / q
s = r * 100
Problem: jerome anticipated that the webweb . com stock price would fall and sold all his webweb . com stocks for $ 5 per stock . he paid $ 10,000 tax on the revenue . a week later , jerome became convinced that the webweb . com stock price would rise , and he used the money that he had gotten from selling the webweb . com stocks to purchase them again , this time at $ 6 per stock . if jerome ended up having 2000 webweb . com stocks fewer than the number he had before selling them , how many webweb . com stocks did he have originally ?
Options: a ) 10,000 , b ) 11,600 , c ) 12,000 , d ) 14,000 , e ) 16,400
Rationale: let the number of shares be x . 5 * x - 10000 ( money paid in taxes ) = 6 ( x - 2000 ) solving for x , we get the shares as 12000 . ans : ( option c )
Answer: c
Python program:
a = 5 + 6
Problem: if m is a positive integer and m ^ 2 is divisible by 54 , then the largest positive integer that must divide m is ?
Options: a ) 3 , b ) 6 , c ) 18 , d ) 12 , e ) 16
Rationale: m ^ 2 is divisible by 48 so m ^ 2 must be multiple of 48 . if the value of m is multiples of 18 then it will satisfy the condition . if we if m is 12 or 24 or 36 then it ans is c but if m = 54 then answer should be 16 . is the question right ? or am i missing some thing ? c
Answer: c
Python program:
a = 54 / 3
b = a / 3
c = 3 * b
Problem: if 24 lines are drawn in a plane such that no two of them are parallel and no three are concurrent , then in how many points do they intersect ?
Options: a ) 276 , b ) 350 , c ) 425 , d ) 512 , e ) 648
Rationale: "if two lines are not parallel , then they will intersect in exactly one point . lines can be extended infinitely on both ends so somewhere they will intersect with each other if they are not parallel . we are also given that no three lines are concurrent . this means that no three lines intersect at the same point . so every pair of two lines we select will have a unique point of intersection which they will not share with any third line . the number of ways to select 2 lines from 24 lines is 24 c 2 = 276 the answer is a ."
Answer: a
Python program:
a = math.factorial(24)
b = 24 - 2
c = math.factorial(b)
d = math.factorial(2)
e = c * d
f = a / e