euclaise/mathqa_programs huggingface dataset:
Problem: you collect baseball cards . suppose you start out with 21 . maria takes half of one more than the number of baseball cards you have . since you ' re nice , you give peter 1 baseball card . since his father makes baseball cards , paul decides to triple your baseball cards . how many baseball cards do you have at the end ?
Options: a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 27
Rationale: "solution start with 21 baseball cards . maria takes half of one more than the number of baseball cards you have . so maria takes half of 21 + 1 which is 11 , so you ' re left with 21 - 11 = 10 . peter takes 1 baseball card from you : 10 - 1 = 9 baseball cards . paul triples the number of baseball cards you have : 9 ã — 3 = 27 baseball cards . so you have 27 at the end . correct answer : e"
Answer: e
Python program:
a = 21 - 4
b = a - 4
c = b - 1
d = c * 3
Problem: a man ' s speed with the current is 18 km / hr and the speed of the current is 3.4 km / hr . the man ' s speed against the current is
Options: a ) 9 , b ) 10.4 , c ) 11.2 , d ) 12.5 , e ) 13
Rationale: "man ' s rate in still water = ( 18 - 3.4 ) km / hr = 14.6 km / hr . man ' s rate against the current = ( 14.6 - 3.4 ) km / hr = 11.2 km / hr . answer : c"
Answer: c
Python program:
a = 18 - 3
b = a - 3
Problem: in town p , 60 percent of the population are employed , and 48 percent of the population are employed males . what percent of the employed people in town p are females ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 40 %
Rationale: "the percent of the population who are employed females is 60 - 48 = 12 % the percent of employed people who are female is 12 % / 60 % = 20 % . the answer is a ."
Answer: a
Python program:
a = 60 - 48
b = a / 60
c = b * 100
Problem: average monthly income of a family of 4 earning members was rs . 782 . one of the earning members died and therefore , the average income came down to rs 650 . the income of the deceased was ?
Options: a ) rs . 1178 , b ) rs . 820 , c ) rs . 990 , d ) rs . 1385 , e ) none
Rationale: "answer income of the deceased = total income of 4 members - total income of remaining 3 members . = 782 x 4 - 650 x 3 rs . = 1178 rs . correct option : a"
Answer: a
Python program:
a = 782 * 4
b = 4 - 1
c = 650 * b
d = a - c
Problem: how many words , with or without meaning , can be formed using all letters of the word equation using each letter exactly once ?
Options: a ) 38,320 , b ) 39,320 , c ) 40,320 , d ) 38,400 , e ) 39,400
Rationale: "the word equation has exactly 8 letters which are all different . therefore the number of words that can be formed = number of permutations of 8 letters taken all at a time . = p ( 8 , 8 ) = 8 ! = 8 × 7 x 6 × 5 x 4 x 3 x 2 × 1 = 40,320 answer : c"
Answer: c
Python program:
a = math.factorial(3)
Problem: a train 350 m long is running at a speed of 68 kmph . how long does it take to pass a man who is running at 8 kmph in the same direction as the train ?
Options: a ) 5 sec , b ) 9 sec , c ) 12 sec , d ) 21 sec , e ) 18 sec
Rationale: "speed of the train relative to man = ( 68 - 8 ) kmph = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec time taken by the train to cross the man = time taken by it to cover 350 m at 50 / 3 m / sec = 350 * 3 / 50 sec = 21 sec answer : d"
Answer: d
Python program:
a = 68 - 8
b = a * const_0_2778
c = 350 / b
Problem: what is remainder of the division ( 1125 * 1127 * 1129 ) / 12 ?
Options: a ) 0 , b ) 3 , c ) 1 , d ) 2 , e ) 4
Rationale: "remainder will be number / 100 here as the divisor is two digit number = 12 . hence checking for the last two digits = 5 * 7 * 9 = 15 thus remainder = 3 . answer : b"
Answer: b
Python program:
a = 1125 * 1127
b = a * 1129
c = 1125 * 1127
d = c * 1129
e = d - 3
f = b - e
Problem: the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 8000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is
Options: a ) 20 , b ) 21 , c ) 22 , d ) 7 , e ) 24
Rationale: "solution let the toatl number of workers be x . then 8000 x = ( 8000 x 7 ) + 6000 ( x - 7 ) x = 7 . answer d"
Answer: d
Python program:
a = 8000 - 8000
b = 7 * a
c = 8000 - 6000
d = b / c
e = 7 + d
Problem: 0.0005 ? = 0.01
Options: a ) 5 , b ) 0.05 , c ) 0.5 , d ) 50 , e ) none of these
Rationale: "explanation : required answer = 0.0005 / 0.01 = 0.05 / 1 = 0.05 . answer : option b"
Answer: b
Python program:
a = 0 / 5
b = a * 100
Problem: a library has an average of 140 visitors on sundays and 80 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is :
Options: a ) 90 , b ) 100 , c ) 105 , d ) 110 , e ) 125
Rationale: "explanation : since the month begins with a sunday , so there will be five sundays in the month , required average = ( 140 * 5 + 80 * 25 ) / 30 = 2700 / 30 = 90 answer : a ) 90"
Answer: a
Python program:
a = 3 + 4 
b = 30 / a
c = math.floor(b)
d = c + 1 
e = d * 140
f = 3 + 4 
g = 30 / f
h = math.floor(g)
i = h + 1 
j = 30 - i
k = j * 80
l = e + k 
m = l / 30
Problem: the distance from city a to city b is 180 miles . while driving from city a to city b , bob drives at a constant speed of 40 miles per hour . alice leaves city a 30 minutes after bob . what is the minimum constant speed in miles per hour that alice must exceed in order to arrive in city b before bob ?
Options: a ) 45 , b ) 48 , c ) 50 , d ) 52 , e ) 54
Rationale: "the time it takes bob to drive to city b is 180 / 40 = 4.5 hours . alice needs to take less than 4 hours for the trip . alice needs to exceed a constant speed of 180 / 4 = 45 miles per hour . the answer is a ."
Answer: a
Python program:
a = 180 / 40
b = 30 / const_60
c = a - b
d = 180 / c
Problem: a soccer store typically sells replica jerseys at a discount of 30 percent to 50 percent off list price . during the annual summer sale , everything in the store is an additional 20 percent off the original list price . if a replica jersey ' s list price is $ 80 , approximately what percent of the list price is the lowest possible sale price ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 40 , e ) 50
Rationale: "let the list price be 2 x for min sale price , the first discount given should be 50 % , 2 x becomes x here now , during summer sale additional 20 % off is given ie sale price becomes 0.8 x it is given lise price is $ 80 = > 2 x = 80 = > x = 40 and 0.8 x = 32 so lowest sale price is 32 , which is 40 % of 80 hence , d is the answer"
Answer: d
Python program:
a = 80 / 2
Problem: find the least number must be added to 228712 so that remaining no . is divisible by 9 ?
Options: a ) 5 , b ) 3 , c ) 1 , d ) 6 , e ) 2
Rationale: on dividing 228712 by 9 we get the remainder 4 , so 5 should be subtracted a
Answer: a
Python program:
a = 9 - reminder
Problem: how many revolutions will a circular wheel make to travel a distance of 3 km , given that the radius is 2.4 m ?
Options: a ) 11085.7 , b ) 15085.7 , c ) 35085.7 , d ) 15015.7 , e ) 15083.7
Rationale: 2 * 22 / 7 * 2.4 * x = 15085.7 x = 1000 answer : a
Answer: a
Python program:
a = 2 * 10
b = a + 2 
c = 4 + 3 
d = b / c
e = d * 2
f = e * 2
g = f * 1000
h = 3 * 1000
i = g - h
j = i - 1000
Problem: if 4 gallons of gasoline are added to a tank that is already filled to 3 / 4 of its capacity , the tank is then filled to 9 / 10 of its capacity . how many gallons does the tank hold ?
Options: a ) 20 , b ) 24 , c ) 36 , d ) 40 , e ) 60
Rationale: "let the capacity of the tank = c ( 3 / 4 ) c + 4 = ( 9 / 10 ) c = > ( 9 / 10 ) c - ( 3 / 4 ) c = 4 = > ( 3 / 20 ) c = 4 = > c = ( 4 * 20 ) / 3 = 26.66 number of gallons of gasoline that the tank currently holds = 3 / 4 * c + 4 = 19.99 + 4 = 23.99 = 24 answer b"
Answer: b
Python program:
a = 9 / 10
b = 3 / 4
c = a - b
d = 4 / c
e = 3 / 4
f = d * e
g = f + 4
Problem: a drink vendor has 50 liters of maaza , 144 liters of pepsi and 368 liters of sprite . he wants to pack them in cans , so that each can contains the same number of liters of a drink , and does n ' t want to mix any two drinks in a can . what is the least number of cans required ?
Options: a ) 135 , b ) 237 , c ) 281 , d ) 300 , e ) 380
Rationale: "the number of liters in each can = hcf of 50 , 144 and 368 = 2 liters . number of cans of maaza = 50 / 2 = 25 number of cans of pepsi = 144 / 2 = 72 number of cans of sprite = 368 / 2 = 184 the total number of cans required = 25 + 72 + 184 = 281 cans . answer : c"
Answer: c
Python program:
a = math.gcd(50, 144)
b = math.gcd(a, 368)
c = 368 / b
d = math.gcd(50, 144)
e = math.gcd(d, 368)
f = 50 / e
g = math.gcd(50, 144)
h = math.gcd(g, 368)
i = 144 / h
j = f + i 
k = c + j
Problem: express a speed of 36 kmph in meters per second ?
Options: a ) 10 mps , b ) 76 mps , c ) 26 mps , d ) 97 mps , e ) 16 mps
Rationale: "36 * 5 / 18 = 10 mps answer : a"
Answer: a
Python program:
a = const_0_2778 * 36
Problem: lily shop runs a sale on goldfish and platys . if one customer buys 13 goldfish and 12 platys for $ 5.60 , and another buys 14 goldfish and 21 platys for $ 8.05 , what is the ratio of the price of goldfish to platys ?
Options: a ) 0.8 , b ) 0.75 , c ) c ) 8 / 9 , d ) 5 / 7 , e ) 6 / 8
Rationale: the approach of plugging in the numbers is a fine approach . but , in this case , the answer was the first option and thus , by plugging in a number in the ration given , we arrived at the answer quickly ! however , what if the correct ratio was option d or c ? in any case , the algebraic solution is n ' t that complex if you realize a key concept : the number 7 can be factored out of the second equation ! here ' s the working : lily shop runs a sale on goldfish and platys . 13 x + 12 y = 5.60 < < < < < equation 1 14 x + 21 y = 8.05 < < < < < equation 2 2 x + 3 y = 1.15 [ factor out 7 from equation 2 ] < < < < < equation 3 8 x + 12 y = 4.6 [ multiply equation 3 with 4 ] 5 x = 1.0 [ equation 1 - equation 2 ] x = 0.2 3 y = 1.15 - 0.4 = 0.75 [ substitute for x in equation 1 ] y = 0.25 x / y = 0.2 / 0.25 = 20 / 25 = 4 / 5 = 0.8 [ answer a ] the whole thing must have taken me about 45 s : d
Answer: d
Python program:
a = 5 / 6
Problem: a woman invested $ 1,000 , part at 5 % and the rest at 6 % . her total investment with interest at the end of the year was $ 1,051 . how much did she invest at 5 % ?
Options: a ) $ 500 , b ) $ 600 , c ) $ 700 , d ) $ 900 , e ) $ 950
Rationale: "et x be the portion invested at 5 % and let ( 1 - x ) be the rest which is invested at 6 % the question states that the return after 1 year is ( 1051 / 1000 ) - 1 = 0.051 = 5.1 % we want to find the dollar amount invested in x using our defined variables , put together the equation and solve for x ( the percentage of 1000 invested at 5 % ) 0.05 x + 0.06 ( 1 - x ) = 0.051 ( 0.05 ) x + 0.06 - ( 0.06 ) x = 0.051 - 0.01 x = - 0.009 x = - 0.009 / - 0.01 = 9 / 10 = 90 % so x = 90 % of the 1000 which is 900 answer : d"
Answer: d
Python program:
a = 5 * 2
b = a * 100
c = 5 * 2
d = c * 100
e = 5 * 2
f = e * 5
g = f + 4 
h = d + g 
i = 5 * 2
j = i * 100
k = h - j
l = k * 100
m = 5 * 2
n = m * 100
o = 5 * n
p = l - o
q = b - p
Problem: in a class , 9 students like to play basketball and 8 like to play cricket . 6 students like to play on both basketball and cricket . how many students like to play basketball or cricket or both ?
Options: a ) 12 , b ) 11 , c ) 16 , d ) 18 , e ) 22
Rationale: "draw a venn diagram yourself ! b + c - bc = number of students that play either basketball or cricket 9 + 8 - 6 = 11 b )"
Answer: b
Python program:
a = 9 + 8 
b = a - 6
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 7000 , the number of valid votes that the other candidate got , was :
Options: a ) 2800 , b ) 2700 , c ) 2900 , d ) 2200 , e ) 2520
Rationale: "e number of valid votes = 80 % of 7000 = 5600 . valid votes polled by other candidate = 45 % of 6000 = ( 45 / 100 x 5600 ) = 2520 ."
Answer: e
Python program:
a = 20 / 100
b = 1 - a
c = 55 / 100
d = 1 - c
e = b * d
f = e * 7000
Problem: if daily wages of a man is double to that of a woman , how many men should work for 10 days to earn rs . 14400 ? given that wages for 40 women for 30 days are rs . 21600 .
Options: a ) 12 , b ) 14 , c ) 16 , d ) 20 , e ) 40
Rationale: "explanation : wages of 1 woman for 1 day = 21600 / 40 ã — 30 wages of 1 man for 1 day = 21600 ã — 2 / 40 ã — 30 wages of 1 man for 10 days = 21600 ã — 2 ã — 10 / 40 ã — 30 number of men = 14400 / ( 21600 ã — 2 ã — 10 / 40 ã — 30 ) = 144 / ( 216 ã — 20 / 40 ã — 30 ) = 40 answer : option e"
Answer: e
Python program:
a = 40 * 30
b = 21600 / a
c = 2 * b
d = 10 * c
e = 14400 / d
Problem: two assembly line inspectors , lauren and steven , inspect widgets as they come off the assembly line . if lauren inspects every fifth widget , starting with the fifth , and steven inspects every third , starting with the third , how many of the 98 widgets produced in the first hour of operation are not inspected by either inspector ?
Options: a ) 91 , b ) 59 , c ) 53 , d ) 47 , e ) 45
Rationale: "widgets inspected by lauren : ( ( 95 - 5 ) / 5 ) + 1 = 18 + 1 = 19 widgets inspected by steven : ( ( 96 - 3 ) / 3 ) + 1 = 31 + 1 = 32 widgets inspected by both : ( ( 90 - 15 ) + 1 = 6 total : 19 + 32 - 6 = 45 hence , widgets not inspected : 98 - 45 = 53 answer : c"
Answer: c
Python program:
a = 4 + 1 
b = 98 / a
c = math.floor(b)
d = 98 / 4
e = math.floor(d)
f = c + e 
g = 4 + 1 
h = 10 + g 
i = 98 / h
j = math.floor(i)
k = f - j
l = 98 - k
Problem: the rate of spin of a certain gyroscope doubled every 10 seconds from the moment a particular stopwatch started . if after a minute and a half the gyroscope reached a speed of 1600 meters per second , what was the speed , in meters per second , when the stopwatch was started ?
Options: a ) 25 / 3 , b ) 25 / 4 , c ) 25 / 8 , d ) 25 / 16 , e ) 25 / 32
Rationale: "let x be the original speed when the stopwatch was started . in 90 seconds , the speed doubled 9 times . 2 ^ 9 * x = 1600 x = ( 2 ^ 6 * 25 ) / 2 ^ 9 = 25 / 8 the answer is c ."
Answer: c
Python program:
a = const_60 / 2
b = a + const_60 
c = b / 10
d = c - 1
e = 2 ** d
f = 1600 / e
g = f / 2
Problem: last year manfred received 26 paychecks . each of his first 6 paychecks was $ 750 ; each of his remaining paychecks was $ 40 more than each of his first 6 paychecks . to the nearest dollar , what was the average ( arithmetic mean ) amount of his pay checks for the year ?
Options: a ) $ 781 , b ) $ 755 , c ) $ 765 , d ) $ 773 , e ) $ 775
Rationale: "= ( 750 * 6 + 790 * 20 ) / 26 = 781 answer is a . posted from my mobile device"
Answer: a
Python program:
a = 750 + 40 
b = a * 40
c = 6 * 750
d = b + c 
e = d / 26
Problem: if two different solutions of alcohol with a respective proportion of water to alcohol of 3 : 1 and 2 : 3 were combined , what is the concentration of alcohol in the new solution if the original solutions were mixed in equal amounts ?
Options: a ) 30.0 % , b ) 36.6 % , c ) 42.5 % , d ) 44.4 % , e ) 60.0 %
Rationale: alcohol : water first mixture - - 3 : 1 - - 15 : 5 second mixture - - 2 : 3 - - 8 : 12 equal amounts of the mixture were combined , hence the final mixture will be in the ratio - - ( 15 + 8 ) : ( 5 + 12 ) - - 23 : 17 % of alcohol - - 17 / ( 23 + 17 ) * 100 = ( 17 / 40 ) * 100 = 42.5 answer : c
Answer: c
Python program:
a = 1 + 3 
b = 1 + 3 
c = 3 + 2 
d = b + c 
e = a / d
f = e * 100
Problem: if the sum of 3 consecutive even numbers is 44 more than the average of these numbers , then the largest of these numbers is ?
Options: a ) 24 , b ) 66 , c ) 9 , d ) 7 , e ) 01
Rationale: answer : 24 explanation : let the smallest of these number be x . the other two numbers are ( x + 2 ) and ( x + 4 ) . x + ( x + 2 ) + ( x + 4 ) = ( x + ( x + 2 ) + ( x + 4 ) ) / 3 + 44 3 x + 3 * ( x + 2 ) + 3 * ( x + 4 ) = x + ( x + 2 ) + ( x + 4 ) + 132 9 x + 18 = 3 x + 138 6 x = 120 x = 20 therefore , the largest number is 24 . answer : a
Answer: a
Python program:
a = 44 - 4
b = a / 2
c = b + 3 
d = c + 1
Problem: a man swims downstream 72 km and upstream 45 km taking 9 hours each time ; what is the speed of the current ?
Options: a ) 3 kmph , b ) 1.5 kmph , c ) 13 kmph , d ) 6.5 kmph , e ) 7 : 3 kmph
Rationale: "explanation : 72 - - - 9 ds = 8 ? - - - - 1 45 - - - - 9 us = 5 ? - - - - 1 s = ? s = ( 8 - 5 ) / 2 = 1.5 answer : option b"
Answer: b
Python program:
a = 45 / 9
b = 72 / 9
c = a + b 
d = c / 2
Problem: solution y is 30 percent liquid x and 70 percent water . if 4 kilograms of water evaporate from 8 kilograms of solution y and 4 kilograms of solution y are added to the remaining 6 kilograms of liquid , what percent of this new solution is liquid x ?
Options: a ) 40 % , b ) 41 1 / 2 % , c ) 44 % , d ) 45 % , e ) 46 %
Rationale: "in 8 kilograms of solution y there are 0.3 * 8 = 2.4 kilograms of solution x ; after 4 kilograms of water are replaced by 4 kilograms of solution y , to the existing 2.4 kilograms of solution x , 0.3 * 4 = 1.2 kilograms of solution x are added , so in the new solution of 8 kilograms there are 2.4 + 1.2 = 3.6 kilograms of solution x , which is 3.6 / 8 * 100 = 45 % of this new solution . answer : d ."
Answer: d
Python program:
a = 30 / 100
b = 8 * a
c = 30 / 100
d = 4 * c
e = b + d 
f = 30 / 100
g = 8 * f
h = 30 / 100
i = 4 * h
j = g + i 
k = 70 / 100
l = 8 * k
m = l - 4
n = 70 / 100
o = 4 * n
p = m + o 
q = j + p 
r = e / q
s = 100 * r
Problem: a grocer has a sale of rs . 6435 , rs . 6927 , 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 . 6600 ?
Options: a ) s . 4991 , b ) s . 5591 , c ) s . 6001 , d ) s . 6991 , e ) s . 7991
Rationale: "total fr 5 mnths = ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs 34009 . reqd . sale = rs . [ ( 6600 * 6 ) - 34009 ] = rs . ( 39600 - 34009 ) = rs . 5591 . answer : b"
Answer: b
Python program:
a = 5 + 1 
b = a * 6600
c = 6435 + 6927 
d = c + 6855 
e = d + 7230 
f = e + 6562 
g = b - f
Problem: a can run 3 kms in 3 min 18 sec and b can run same distance in 3 min 40 sec , then by how much distance a can beat b ?
Options: a ) 300 m , b ) 220 m , c ) 280 m , d ) 195 m , e ) 295 m
Rationale: distance travelled = 3000 m time taken by a = 3 m 18 s time taken by b = 3 m 40 sec = 220 sec speed of b = 3000 m / 220 s = 150 / 11 m / s difference between time of a and b = 22 sec when time will be 3 m 18 s a will have travelled 3000 m but b need 22 sec more to finish . distance travelled by b in 22 sec = ( 150 / 11 ) * 22 = 300 m hence , a beat b by 300 m answer : a
Answer: a
Python program:
a = 3 * 1000
b = 3 * const_60
c = b + 40 
d = 3 * const_60
e = d + 18 
f = c - e
g = a * f
h = 3 * const_60
i = h + 40 
j = g / i
Problem: 22 cubic centimetres of silver is drawn into a wire 1 mm in diameter . the length of the wire in metres will be :
Options: a ) 84 m , b ) 28 m , c ) 120 m , d ) 137 m , e ) none
Rationale: "sol . let the length of the wire b h . radius = 1 / 2 mm = 1 / 20 cm . then , 22 / 7 * 1 / 20 * 1 / 20 * h = 22 ⇔ = [ 22 * 20 * 20 * 7 / 22 ] = 2800 cm = 28 m . answer b"
Answer: b
Python program:
a = 1 / 2
b = a ** 2
c = b * math.pi
d = 22 / c
Problem: two cyclists are moving towards each other at 10 miles / hour . they are now 50 miles apart . at this instance a fly starts from one cyclist and move towards other and moves to and fro till the two cyclist meet each other . if the fly is moving at 15 miles / hour , what is the total distance covered by the fly ?
Options: a ) 37.5 miles , b ) 38.5 miles , c ) 39.5 miles , d ) 36.5 miles , e ) 35.5 miles
Rationale: time taken by cyclists to meet = 50 / 20 2.5 hrs distance covered by fly during 2.5 hrs = 15 * 2.5 = 37.5 miles answer : a
Answer: a
Python program:
a = 50 / 2
b = a / 10
c = b * 15
Problem: students at a school were on average 180 cm tall . the average female height was 170 cm , and the average male height was 184 cms . what was the ratio s of men to women ?
Options: a ) 5 : 2 , b ) 5 : 1 , c ) 4 : 3 , d ) 4 : 1 , e ) 3 : 1
Rationale: ( a ) s = 184 x 5 + 170 x 2 = 1260 . a
Answer: a
Python program:
a = 180 - 170
b = 184 - 180
c = a / b
Problem: the maximum numbers of students among them 1001 pens and 910 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is
Options: a ) 91 , b ) 910 , c ) 1001 , d ) 1911 , e ) none
Rationale: "olution required number of students . = h . c . f of 1001 and 910 . ‹ = › 91 . answer a"
Answer: a
Python program:
a = 1001 - 910
Problem: when a train travels at a speed of 100 kmph , it reaches the destination on time . when the same train travels at a speed of 50 kmph , it reaches its destination 15 min late . what is the length of journey ?
Options: a ) 15 km , b ) 50 km , c ) 60 km , d ) 85 km , e ) 95 km
Rationale: let x be the time reached with the speed 100 km / h 50 km / h - - - - > x + 15 distance is equal so 100 ( km / h ) × xhr = 50 ( km / h ) × ( x + 15 ) hr so 100 x = 50 x + 750 so the would be in km and x = 15 answer : a
Answer: a
Python program:
a = 15 / const_60
b = a * 50
c = b / 50
d = const_60 * c
Problem: a circle graph shows how the megatech corporation allocates its research and development budget : 10 % microphotonics ; 24 % home electronics ; 15 % food additives ; 29 % genetically modified microorganisms ; 8 % industrial lubricants ; and the remainder for basic astrophysics . if the arc of each sector of the graph is proportional to the percentage of the budget it represents , how many degrees of the circle are used to represent basic astrophysics research ?
Options: a ) 8 ° , b ) 10 ° , c ) 18 ° , d ) 36 ° , e ) 50 °
Rationale: "here all percentage when summed we need to get 100 % . as per data 10 + 24 + 15 + 29 + 8 = 86 % . so remaining 14 % is the balance for the astrophysics . since this is a circle all percentage must be equal to 360 degrees . 100 % - - - - 360 degrees then 14 % will be 50 degrees . . imo option e ."
Answer: e
Python program:
a = 10 + 24 
b = a + 15 
c = b + 29 
d = c + 8 
e = 100 - d
f = 3600 / 10
g = e * f
h = g / 100
Problem: a train running at the speed of 60 km / hr crosses a pole in 3 sec . what is the length of the train ?
Options: a ) 50 , b ) 75 , c ) 100 , d ) 120 , e ) 25
Rationale: "speed = 60 * 5 / 18 = 50 / 3 m / sec length of the train = speed * time = 50 / 3 * 3 = 50 m answer : a"
Answer: a
Python program:
a = 60 * 1000
b = a / 3600
c = b * 3
Problem: if the compound interest on a certain sum of money for 3 years at 10 % per annum be rs . 993 , what would be the simple interest ?
Options: a ) rs . 880 , b ) rs . 890 , c ) rs . 895 , d ) rs . 900 , e ) none
Rationale: let p = principal a - amount we have a = p ( 1 + r / 100 ) 3 and ci = a - p atq 993 = p ( 1 + r / 100 ) 3 - p ? p = 3000 / - now si @ 10 % on 3000 / - for 3 yrs = ( 3000 x 10 x 3 ) / 100 = 900 / - answer : d .
Answer: d
Python program:
a = 3 * 100
b = a * 10
c = b * 10
d = c * 3
e = d / 100
Problem: what least number must be subtracted from 427398 so that remaining no . is divisible by 13
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 10
Rationale: "explanation : on dividing 427398 by 13 we get the remainder 10 , so 10 should be subtracted answer : option e"
Answer: e
Python program:
a = 427398 / 13
b = math.floor(a)
c = b * 13
d = 427398 - c
Problem: if k is the greatest positive integer such that 3 ^ k is a divisor of 24 ! then k =
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 10
Rationale: "24 / 3 = 8 24 / 9 = 2 8 + 2 = 10 k = 10 answer : e"
Answer: e
Python program:
a = 24 / 3
b = 1 + a
Problem: the present worth of a certain bill due sometime hence is rs . 800 and the true discount is rs . 36 . the banker ’ s discount is
Options: a ) rs . 34.38 , b ) rs . 38.98 , c ) rs . 37 , d ) rs . 37.62 , e ) none
Rationale: "solution b . g = [ ( t . d ) ² / p . w ] = rs . ( 36 x 36 / 800 ) = rs . 1.62 b . d given , t . d = 36 = ( t . d + b . g ) = rs . ( 36 + 1.62 ) = rs . 37.62 . answer d"
Answer: d
Python program:
a = 36 ** 2
b = a / 800
c = 36 + b