euclaise/mathqa_programs huggingface dataset:
Problem: how many ounces of a 60 % salt solution must be added to 70 ounces of a 20 percent salt solution so that the resulting mixture is 40 % salt ?
Options: a ) 16.67 , b ) 30 , c ) 50 , d ) 60.33 , e ) 70
Rationale: let x = ounces of 60 % salt solution to be added . 2 * 70 + . 6 x = . 4 ( 70 + x ) x = 70 answer e
Answer: e
Python program:
a = 40 / 100
b = a * 70
c = 20 / 100
d = c * 70
e = b - d
f = 40 / 100
g = 20 / 100
h = f - g
i = e / h
Problem: the average of 1 st 3 of 4 numbers is 16 and of the last 3 are 15 . if the sum of the first and the last number is 15 . what is the last numbers ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 5 , e ) 7
Rationale: "a + b + c = 48 b + c + d = 45 a + d = 13 a – d = 3 a + d = 15 2 d = 12 d = 6 answer c"
Answer: c
Python program:
a = 3 * 16
b = 15 - 16
c = b + 3 
d = a - c
e = d - 16
Problem: how many plants will be there in a circular bed whose outer edge measure 33 cms , allowing 4 cm 2 for each plant ?
Options: a ) 18 , b ) 750 , c ) 21 , d ) 120 , e ) none of these
Rationale: "circumference of circular bed = 33 cm area of circular bed = ( 33 ) 2 â  „ 4 ï € space for each plant = 4 cm 2 â ˆ ´ required number of plants = ( 33 ) 2 â  „ 4 ï € ã · 4 = 21.65 = 21 ( approx ) answer c"
Answer: c
Python program:
a = 2 * math.pi
b = 33 / a
c = circle_area / (
Problem: rectangle a has sides a and b , and rectangle b has sides c and d . if a / c = b / d = 4 / 5 , what is the ratio of rectangle a ’ s area to rectangle b ’ s area ?
Options: a ) 5 / 4 , b ) 25 / 16 , c ) 4 / 5 , d ) 16 / 25 , e ) 16 / 5
Rationale: "the area of rectangle a is ab . c = 5 a / 4 and d = 5 b / 4 . the area of rectangle b is cd = 25 ab / 16 . the ratio of rectangle a ' s area to rectangle b ' s area is ab / ( 25 ab / 16 ) = 16 / 25 . the answer is d ."
Answer: d
Python program:
a = 4 ** 2
b = 5 ** 2
c = a / b
Problem: pipe a fills a swimming pool in 4 hours . pipe b empties the pool in 6 hours . if pipe a was opened at 5 : 00 am and pipe b at 6 : 00 am , at what time will the pool be full ?
Options: a ) 13 : 00 , b ) 14 : 00 , c ) 15 : 00 , d ) 17 : 00 , e ) 16 : 00
Rationale: "pipe a fills the pool in 4 hrs . 1 hour ' s work : 1 / 4 pipe b empties the pool in 6 hrs . 1 hour ' s work : 1 / 6 together if they work , 1 hour ' s work = 1 / 4 - 1 / 6 = 1 / 12 given : pipe a started at 5 : 00 a . m and pipe b at 6 : 00 a . m pool filled after 1 hour by pipe a : 1 / 4 or 3 / 12 after 6 : 00 a . m pool filled after 1 hour with both the pipes on : 1 / 12 pool filled after 9 hours with both pipes on : 9 / 12 pool filled in 1 hour + pool filled in 9 hours = 3 / 12 + 9 / 12 = 1 therefore , it takes 10 hrs to fill the pool as pipe a started at 5 : 00 a . m , pool is full at 15 : 00 hrs answer : c"
Answer: c
Python program:
a = 3 / 4
b = 1 / 4
c = 1 / 6
d = b - c
e = 1 / d
f = a * e
Problem: a student multiplied a number by 3 / 5 instead of 5 / 3 , what is the percentage error in the calculation ?
Options: a ) 22 , b ) 64 , c ) 365 , d ) 29 , e ) 36
Rationale: "let the number be x . then , ideally he should have multiplied by x by 5 / 3 . hence correct result was . by mistake he multiplied x by 3 / 5 . hence the result with error = then , error = error % = = 64 % answer : b"
Answer: b
Python program:
a = 5 / 3
b = 3 / 5
c = a - b
d = 5 / 3
e = c / d
f = e * 100
Problem: a team of 6 entered for a shooting competition . the best marks man scored 85 points . if he had scored 92 points , the average scores for . the team would have been 84 . how many points altogether did the team score ?
Options: a ) 288 , b ) 497 , c ) 168 , d ) 127 , e ) 664
Rationale: explanation : 6 * 84 = 504 - 7 = 497 answer : b
Answer: b
Python program:
a = 84 * 6
b = 92 - 85
c = a - b
Problem: if 60 percent of 500 is 50 percent of x , then x = ?
Options: a ) 600 , b ) 620 , c ) 650 , d ) 700 , e ) 720
Rationale: "0.6 * 500 = 0.5 * x x = 6 / 5 * 500 = 600"
Answer: a
Python program:
a = 60 * 500
b = a / 50
Problem: a car gets 40 kilometers per gallon of gasoline . how many gallons of gasoline would the car need to travel 220 kilometers ?
Options: a ) 4.5 , b ) 5.5 , c ) 6.5 , d ) 7.5 , e ) 8.5
Rationale: "each 40 kilometers , 1 gallon is needed . we need to know how many 40 kilometers are there in 220 kilometers ? 220 ÷ 40 = 5.5 × 1 gallon = 5.5 gallons correct answer b"
Answer: b
Python program:
a = 220 / 40
Problem: the sum of 3 numbers is 98 . if the ratio between first and second be 2 : 3 and that between second and third be 5 : 8 , then the second number is ?
Options: a ) 30 , b ) 20 , c ) 58 , d ) 48 , e ) 68
Rationale: let the numbers be x , y and z . then , x + y + z = 98 , x / y = 2 / 3 and y / z = 5 / 8 therefore , x = 2 y / 3 and z = 8 y / 5 . so , 2 y / 3 + y + 8 y / 5 = 98 . 49 y / 15 = 98 y = 30 . answer : a
Answer: a
Python program:
a = 2 / 3
b = a + 1 
c = 8 / 5
d = b + c 
e = 98 / d
Problem: a courtyard is 25 meter long and 18 meter board is to be paved with bricks of dimensions 20 cm by 10 cm . the total number of bricks required is ?
Options: a ) 22877 , b ) 27778 , c ) 20000 , d ) 22500 , e ) 17799
Rationale: "number of bricks = courtyard area / 1 brick area = ( 2500 × 1800 / 20 × 10 ) = 22500 answer : d"
Answer: d
Python program:
a = 25 * 100
b = 18 * 100
c = a * b
d = 20 * 10
e = c / d
Problem: the perimeter of one square is 24 m & that of another is 32 m . perimeter of a square whose area is equal to the sum of the areas of the 2 squares will be
Options: a ) 20 m
b ) 24 m
c ) 28 m
d ) 40 m
e ) 43 m
Rationale: perimeter of square = 4 * side perimeter of first square = 24 m . side of first square = ∴ area of first square = perimeter of second square = 32 m . side of second square = ∴ area of second square = sum of the areas of two squares = 36 + 64 = 100 m 2 ∴ side of square = ∴ perimeter of square = 4 * 10 = 40 m . d
Answer: d
Python program:
a = 24 / 4
b = square_area + ( 
c = 32 / 4
d = math.sqrt(b)
e = 4 * d
Problem: the speeds of three asteroids were compared . asteroids x - 13 and y - 14 were observed for identical durations , while asteroid z - 15 was observed for 2 seconds longer . during its period of observation , asteroid y - 14 traveled three times the distance x - 13 traveled , and therefore y - 14 was found to be faster than x - 13 by 2500 kilometers per second . asteroid z - 15 had an identical speed as that of x - 13 , but because z - 15 was observed for a longer period , it traveled five times the distance x - 13 traveled during x - 13 ' s inspection . asteroid x - 13 traveled how many kilometers during its observation ?
Options: a ) 500 , b ) 625 , c ) 1,000 , d ) 1,500 , e ) 2,500
Rationale: "x 13 : ( t , d , s ) y 14 : ( t , 3 d , s + 2500 mi / hour ) z 15 : ( t + 2 seconds , s , 5 d ) d = ? distance = speed * time x 13 : d = s * t x 14 : 3 d = ( s + 2500 ) * t = = = > 3 d = ts + 2500 t z 15 : 5 d = s * ( t + 2 t ) = = = > 5 d = st + 2 st = = = > 5 d - 2 st = st 3 d = 5 d - 2 st + 2500 t - 2 d = - 2 st + 2500 t 2 d = 2 st - 2500 t d = st - 1250 t x 13 : d = s * t st - 1250 t = s * t s - 1250 = s - 625 = s i got to this point and could n ' t go any further . this seems like a problem where i can set up individual d = r * t formulas and solve but it appears that ' s not the case . for future reference how would i know not to waste my time setting up this problem in the aforementioned way ? thanks ! ! ! the distance of z 15 is equal to five times the distance of x 13 ( we established that x 13 is the baseline and thus , it ' s measurements are d , s , t ) s ( t + 2 ) = 5 ( s * t ) what clues would i have to know to set up the equation in this fashion ? is it because i am better off setting two identical distances together ? st + 2 s = 5 st t + 2 = 5 t 2 = 4 t t = 1 / 2 we are looking for distance ( d = s * t ) so we need to solve for speed now that we have time . speed y 14 - speed x 13 speed = d / t 3 d / t - d / t = 2500 ( remember , t is the same because both asteroids were observed for the same amount of time ) 2 d = 2500 2 = 1250 d = s * t d = 1250 * ( 1 / 2 ) d = 625 answer : b"
Answer: b
Python program:
a = 2500 / 2
b = 1 / 2
c = a * b
Problem: what is the value of 3 x ^ 2 − 2.4 x + 0.3 for x = 0.6 ?
Options: a ) − 0.3 , b ) 0 , c ) 0.06 , d ) 1.08 , e ) 2.46
Rationale: "3 x ^ 2 - 2.4 x + 0.3 for x = 0.6 = 3 ( 0.6 * 0.6 ) - 4 * 0.6 * ( 0.6 ) + 0.3 = - 0.6 * 0.6 + 0.3 = 0.06 correct option : c"
Answer: c
Python program:
a = 3 ** 2
b = 2 ** 4
c = a - b
d = c / 1000
e = d / 1000
f = e * 3
g = 3 ** 2
h = 2 ** 4
i = g - h
j = i / 1000
k = j / 1000
l = f - k
Problem: if x = 1 - 3 t and y = 2 t - 3 , then for what value of t does x = y ?
Options: a ) 5 / 2 , b ) 3 / 2 , c ) 4 / 5 , d ) 2 / 5 , e ) 0
Rationale: "we are given x = 1 – 3 t and y = 2 t – 3 , and we need to determine the value for t when x = y . we should notice that both x and y are already in terms of t . thus , we can substitute 1 – 3 t for x and 2 t – 3 for y in the equation x = y . this gives us : 1 – 3 t = 2 t – 3 4 = 5 t 4 / 5 = t the answer is c ."
Answer: c
Python program:
a = 1 + 2 
b = 2 + 3 
c = a / b
Problem: find the simple interest on the rs . 2000 at 25 / 4 % per annum for the period from 4 th feb 2005 to 18 th april 2005
Options: a ) rs 25 , b ) rs 30 , c ) rs 35 , d ) rs 40 , e ) none of these
Rationale: explanation : one thing which is tricky in this question is to calculate the number of days . always remember that the day on which money is deposited is not counted while the day on which money is withdrawn is counted . so lets calculate the number of days now , time = ( 24 + 31 + 18 ) days = 73 / 365 years = 1 / 5 years p = 2000 r = 25 / 4 % s . i . = = 2000 × 254 × 5 × 100 = 25 answer : a
Answer: a
Python program:
a = 4 + 3 
b = 4 + 1 
c = b * 2
d = a * c
e = d + 3 
f = const_60 * const_60
g = 4 + 1 
h = g * 2
i = f / h
j = 4 + 1 
k = i + j 
l = e / k
m = l * 2000
n = m * 25
o = n / 4
p = o / 100
Problem: volume of a right circular cylinder is 6 o l . if radius of cylinder is doubled , then what will be the increase in volume ?
Options: a ) 120 l
b ) 180 l
c ) 240 l
d ) 300 l
e ) 360 l
Rationale: pi ∗ r ^ 2 ∗ h = 60 double the radius . . . . . pi ∗ ( 2 r ) ^ 2 ∗ h = pi ∗ 4 ∗ r ^ 2 ∗ h = 4 ∗ 60 = 240 important . . we are looking at the increase so 240 - 60 = 180 answer : b
Answer: b
Python program:
a = 6 * 10
b = a * 4
c = 6 * 10
d = b - c
Problem: you enter a weight loss challenge game and manage to lose 10 % of your body weight . for the final weigh in you are forced to wear clothes that add 2 % to your weight . what percentage of weight loss is measured at the final weigh in ?
Options: a ) 13 % , b ) 8.2 % , c ) 9 % , d ) 14 % , e ) 12 %
Rationale: "( 100 % - 10 % ) * ( 100 % + 2 % ) = 0.90 * 1.02 = 8.2 % the weigh in records your weight loss at 8.2 % ! the answer is b"
Answer: b
Python program:
a = 10 / 100
b = 1 - a
c = 2 / 100
d = 1 + c 
e = b * d
f = 1 - e
g = f * 100
Problem: a person was asked to state his age in years . his reply was , ` ` take my age 5 years hence , multiply it by 3 and subtract 3 times my age 5 years ago and you will know how old i am . ' ' what was the age of the person ?
Options: a ) 18 , b ) 92 , c ) 27 , d ) 26 , e ) 30
Rationale: "explanation : let the present age of person be x years . then , 3 ( x + 5 ) - 3 ( x - 5 ) = x < = > ( 3 x + 15 ) - ( 3 x - 15 ) = x < = > x = 30 . . answer : e"
Answer: e
Python program:
a = 5 * 3
b = 5 * 3
c = a + b
Problem: the radius of a semi circle is 6.3 cm then its perimeter is ?
Options: a ) 32.9 , b ) 32.4 , c ) 32.2 , d ) 32.1 , e ) 32.7
Rationale: "36 / 7 r = 6.3 = 32.4 answer : b"
Answer: b
Python program:
a = circumface / (
b = a + 2
Problem: a train is 300 meter long is running at a speed of 54 km / hour . in what time will it pass a tunnel of 1200 meter length ?
Options: a ) 90 seconds , b ) 85 seconds , c ) 40 seconds , d ) 100 seconds , e ) 120 seconds
Rationale: speed = 54 km / hr = 54 * ( 5 / 18 ) m / sec = 15 m / sec total distance = 300 + 1200 = 1500 meter time = distance / speed = 1500 * ( 15 ) = 100 seconds answer : d
Answer: d
Python program:
a = 300 + 1200 
b = 54 * 1000
c = b / 3600
d = a / c
Problem: in a single throw of a die , what is probability of getting a number greater than 4 ?
Options: a ) 2 / 3 , b ) 3 / 5 , c ) 4 / 7 , d ) 8 / 9 , e ) 1 / 3
Rationale: "e = { 5,6 } n ( e ) = 2 p ( s ) = n ( e ) / n ( s ) = 2 / 6 = 1 / 3 ans : e"
Answer: e
Python program:
a = 4 + 2 
b = 2 / a
Problem: a certain bag contains 60 balls — 22 white , 18 green , 8 yellow , 5 red , and 7 purple . if a ball is to be chosen at random , what is the probability that the ball will be neither red nor purple ?
Options: a ) 0.09 , b ) 0.15 , c ) 0.54 , d ) 0.8 , e ) 0.91
Rationale: "according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 22 + 18 + 8 ) / 60 = 48 / 60 = 0.8 . answer : d ."
Answer: d
Python program:
a = 22 + 18 
b = a + 8 
c = b / 60
Problem: a 10 meter long wire is cut into two pieces . if the longer piece is then used to form a perimeter of a square , what is the probability that the area of the square will be more than 4 if the original wire was cut at an arbitrary point ?
Options: a ) 1 / 6
b ) 1 / 5
c ) 3 / 10
d ) 1 / 3
e ) 4 / 10
Rationale: a square with an area of 4 has a perimeter of 8 . for the area to be > 4 , the longer piece must be > 8 . the wire must be cut within 2 meters from either end . the probability of this is 4 / 10 = 2 / 5 . the answer is e .
Answer: e
Python program:
a = 2 / 10
b = 2 * a
Problem: the mean of 50 observations was 40 . it was found later that an observation 45 was wrongly taken as 15 the corrected new mean is
Options: a ) 40 , b ) 36.5 , c ) 46.5 , d ) 20.5 , e ) 40.6
Rationale: "explanation : correct sum = ( 40 * 50 + 45 - 15 ) = 2030 correct mean = = 2030 / 50 = 40.6 answer : e"
Answer: e
Python program:
a = 40 * 50
b = 50 - 2
c = b - 15
d = a + c 
e = d / 50
Problem: the current of a stream runs at the rate of 4 kmph . a boat goes 6 km and back to the starting point in 4 hours , then find the speed of the boat in still water ?
Options: a ) a ) 7 , b ) b ) 2 , c ) c ) 8.73 , d ) d ) 5.77 , e ) e ) 3
Rationale: "s = 4 m = x ds = x + 4 us = x - 4 6 / ( x + 4 ) + 6 / ( x - 4 ) = 4 x = 5.77 answer : d"
Answer: d
Python program:
a = 4 ** 4
b = a / 4
Problem: by selling 14 pencils for a rupee a man loses 20 % . how many for a rupee should he sell in order to gain 20 % ?
Options: a ) 28 , b ) 26 , c ) 25 , d ) 23 , e ) 21
Rationale: "80 % - - - 14 120 % - - - ? 80 / 120 * 14 = 21 answer : e"
Answer: e
Python program:
a = 100 + 20 
b = 100 - 20
c = 1 / b
d = a * c
e = 1 / d
f = e * 14
Problem: a money lender lent rs . 1000 at 3 % per year and rs . 1400 at 5 % per year . the amount should be returned to him when the total interest comes to rs . 350 . find the number of years .
Options: a ) 3.5 , b ) 3.75 , c ) 4 , d ) 4.25 , e ) 4.5
Rationale: ( 1000 xtx 3 / 100 ) + ( 1400 xtx 5 / 100 ) = 350 → t = 3.5 answer a
Answer: a
Python program:
a = 3 * 1000
b = a / 100
c = 1400 * 5
d = c / 100
e = b + d 
f = 350 / e
Problem: caleb spends $ 70.50 on 50 hamburgers for the marching band . if single burgers cost $ 1.00 each and double burgers cost $ 1.50 each , how many double burgers did he buy ?
Options: a ) 5 , b ) 10 , c ) 20 , d ) 41 , e ) 45
Rationale: "solution - lets say , single hamburgersxand double hamburgersy given that , x + y = 50 and 1 x + 1.5 y = 70.50 . by solving the equations y = 41 . ans d ."
Answer: d
Python program:
a = 70 - 50
b = 1 - 50
c = a / b
Problem: tom traveled the entire 100 miles trip . if he did the first 50 miles of at a constant rate 20 miles per hour and the remaining trip of at a constant rate 50 miles per hour , what is the his average speed , in miles per hour ?
Options: a ) 28.36 mph , b ) 26.55 mph , c ) 28.57 mph , d ) 25.56 mph , e ) 28.45 mph
Rationale: "avg speed = total distance / total time = ( d 1 + d 2 ) / ( t 1 + t 2 ) = ( 50 + 50 ) / ( ( 50 / 20 ) + ( 50 / 50 ) ) = 60 * 2 / 3 = 28.57 mph c"
Answer: c
Python program:
a = 100 - 50
b = 50 / a
c = 50 / 20
d = b + c 
e = 100 / d
Problem: when positive integer x is divided by 11 , the quotient is y and the remainder is 4 . when 2 x is divided by 6 , the quotient is 3 y and the remainder is 5 . what is the value of 7 y – x ?
Options: a ) 2 , b ) 1 , c ) 0 , d ) - 1 , e ) - 2
Rationale: "( 1 ) x = 11 y + 4 ( 2 ) 2 x = 18 y + 5 let ' s subtract equation ( 1 ) from equation ( 2 ) . 7 y + 1 = x 7 y - x = - 1 the answer is d ."
Answer: d
Python program:
a = 2 * 4
b = a - 5
c = 6 * 3
d = 2 * 11
e = c - d
f = b / e
g = 7 * f
h = 2 * 4
i = h - 5
j = 6 * 3
k = 2 * 11
l = j - k
m = i / l
n = 11 * m
o = n + 4 
p = g - o
Problem: a total of 30 percent of the geese included in a certain migration study were male . if some of the geese migrated during the study and 30 percent of the migrating geese were male , what was the ratio of the migration rate for the male geese to the migration rate for the female geese ? [ migration rate for geese of a certain sex = ( number of geese of that sex migrating ) / ( total number of geese of that sex ) ]
Options: a ) 1 / 4 , b ) 7 / 12 , c ) 2 / 3 , d ) 1 , e ) 8 / 7
Rationale: "let ' take the number of geese to be 100 . male = 30 . female = 70 . now the second part of the q , let ' s take the number migrated to be 20 . so we have 20 geese that migrated and out of that 20 % are male i . e 20 / 100 * 30 = 6 geese ( males ) and now we know out of the total 20 geese , 6 are male , then 14 have to be female . now the ratio part , male geese ratios = 6 / 30 = 1 / 5 . - a female geese ratios = 14 / 70 = 1 / 5 - b cross multiply equations a and b and you get = 1 . ans d"
Answer: d
Python program:
a = 30 / 100
b = 30 / 100
c = a / b
d = 2 * 4
e = d * 10
f = e / 100
g = 30 / 100
h = f / g
i = c / h
Problem: a clock hangs on the wall of a railway station , 71 ft 9 in long and 10 ft 4 in high . those are the dimension of the wall , not the clock ! while waiting for a train we noticed that the hands of the clock were pointing in opposite directions , and were parallel to one of the diagonals of the wall , what was the exact time ?
Options: a ) 7 : 15
b ) 7 : 5
c ) 7 : 25
d ) 7 : 45
e ) 7 : 55
Rationale: it can have four possiblities time could be 7 : 5 1 : 35 11 : 25 5 : 55 answer : b
Answer: b
Python program:
a = 3 * 4
b = 4 / a
c = 10 + b 
d = 3 * 4
e = 9 / d
f = 71 + e 
g = c / f
Problem: how much 60 % of 50 is greater than 40 % of 30 ?
Options: a ) 18 , b ) 28 , c ) 26 , d ) 27 , e ) 23
Rationale: "( 60 / 100 ) * 50 – ( 40 / 100 ) * 30 30 - 12 = 18 answer : a"
Answer: a
Python program:
a = 60 * 50
b = a / 100
c = 40 * 30
d = c / 100
e = b - d
Problem: you and your friend spent a total of $ 19 for lunch . your friend spent $ 3 more than you . how much did your friend spend on their lunch ?
Options: a ) $ 9 , b ) $ 3 , c ) $ 4 , d ) $ 6 , e ) $ 11
Rationale: my lunch = l , my friends lunch = l + 3 ( l ) + ( l + 3 ) = 19 l + l + 3 - 3 = 19 - 3 2 l = 16 l = 8 my friends lunch l + 3 = 8 + 3 = $ 11 , the answer is e
Answer: e
Python program:
a = 19 - 3
b = a / 2
c = b + 3
Problem: by selling 90 pens , a trader gains the cost of 30 pens . find his gain percentage ?
Options: a ) 33.3 % , b ) 32.3 % , c ) 31.3 % , d ) 30.3 % , e ) 29.3 %
Rationale: "let the cp of each pen be rs . 1 . cp of 90 pens = rs . 90 profit = cost of 30 pens = rs . 30 profit % = 30 / 90 * 100 = 33.3 % answer : a"
Answer: a
Python program:
a = 30 / 90
b = a * 100
Problem: a cistern is normally filled in 2 hrs , but takes 2 hrs longer to fill because of a leak on its bottom , if cistern is full , how much time citern would empty ?
Options: a ) 4 hours , b ) 20 hours , c ) 30 hours , d ) 40 hours , e ) 50 hours
Rationale: "if leakage / hour = 1 / x , then 1 / 2 - 1 / x = 1 / 4 , solving 1 / x = 1 / 4 so in 4 hours full cistern will be empty . answer : a"
Answer: a
Python program:
a = 1 / 2
b = 2 + 2 
c = 1 / b
d = a - c
e = 1/(d)
Problem: two trains of length 100 m and 200 m are 100 m apart . they start moving towards each other on parallel tracks , at speeds 54 kmph and 72 kmph . in how much time will the trains cross each other ?
Options: a ) 70 / 7 sec , b ) 80 / 7 sec , c ) 40 / 7 sec , d ) 60 / 7 sec , e ) 90 / 7 sec
Rationale: "b relative speed = ( 54 + 72 ) * 5 / 18 = 7 * 5 = 35 mps . the time required = d / s = ( 100 + 100 + 200 ) / 35 = 400 / 35 = 80 / 7 sec ."
Answer: b
Python program:
a = 54 + 72 
b = a * const_0_2778
c = 100 / b
Problem: effective annual rate of interest corresponding to nominal rate of 6 % per annum compounded half yearly will be
Options: a ) 6.09 % , b ) 6.10 % , c ) 6.12 % , d ) 6.14 % , e ) none of these
Rationale: explanation : let the amount rs 100 for 1 year when compounded half yearly , n = 2 , rate = 6 / 2 = 3 % amount = 100 ( 1 + 3 / 100 ) 2 = 106.09 effective rate = ( 106.09 - 100 ) % = 6.09 % option a
Answer: a
Python program:
a = 6 / 2
b = a / 100
c = b + 1 
d = c ** 2
e = d * 100
f = e - 100
Problem: in a certain business school class , p students are accounting majors , q students are finance majors , r students are marketing majors , and s students are strategy majors . if pqrs = 1365 , and if 1 < p < q < r < s , how many students in the class are finance majors ?
Options: a ) 3 , b ) 5 , c ) 8 , d ) 11 , e ) 17
Rationale: "pqrs = 1365 = 3 * 5 * 7 * 13 since 1 < p < q < r < s , the number of students who are finance majors is q = 5 . the answer is b ."
Answer: b
Python program:
a = 2 + 3 
b = 2 + 3 
c = b + 2 
d = a * c
e = 10 + 3 
f = d * e
g = 1365 / f
Problem: a train 500 m long is running at a speed of 78 km / hr . if it crosses a tunnel in 1 min , then the length of the tunnel is ?
Options: a ) 298 m , b ) 300 m , c ) 800 m , d ) 967 m , e ) 1181 m
Rationale: "speed = 78 * 5 / 18 = 65 / 3 m / sec . time = 1 min = 60 sec . let the length of the train be x meters . then , ( 500 + x ) / 60 = 65 / 3 x = 800 m . answer : c"
Answer: c
Python program:
a = 78 - 1
b = a * const_0_2778
c = 500 / b
Problem: the average age of 3 men is increased by years when two of them whose ages are 21 years and 23 years are replaced by two new men . the average age of the two new men is
Options: a ) 22 , b ) 30 , c ) 25 , d ) 38 , e ) 27
Rationale: "total age increased = ( 3 * 2 ) years = 6 years . sum of ages of two new men = ( 21 + 23 + 6 ) years = 50 years average age of two new men = ( 50 / 2 ) years = 25 years . answer : c"
Answer: c
Python program:
a = 21 + 23 
b = a / 2
c = 1 * 3
d = b + c
Problem: points a , b , and , c have xy - coordinates ( 2,0 ) , ( 8,12 ) , and ( 14,0 ) , respectively . points x , y , and z have xy - coordinates ( 6,0 ) , ( 8,4 ) , and ( 10,0 ) , respectively . what fraction s of the area of triangle abc is the area of triangle xyz ?
Options: a ) 1 / 9 , b ) 1 / 8 , c ) 1 / 6 , d ) 1 / 5 , e ) 1 / 3
Rationale: "if you notice , both triangles abc and xyz have a side on x axis . we can take these sides as bases for each triangle , therefore area of abc is 1 / 2 * 12 * 12 ( height of abc is the y coordinate of the third point ( 8,12 ) ) similarly area of xyz is 1 / 2 * 4 * 4 dividing area of xyz with that of abc gives s = 1 / 9 . a"
Answer: a
Python program:
a = 4 ** 2
b = a / 2
c = 10 + 2 
d = c ** 2
e = d / 2
f = b / e
Problem: a van takes 6 hours to cover a distance of 270 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 50 kmph , b ) 30 kmph , c ) 70 kmph , d ) 80 kmph , e ) 90 kmph
Rationale: "time = 6 distence = 270 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 270 / 9 = 30 kmph b"
Answer: b
Python program:
a = 3 / 2
b = a * 6
c = 270 / b
Problem: working together , printer a and printer b would finish the task in 40 minutes . printer a alone would finish the task in 60 minutes . how many pages does the task contain if printer b prints 4 pages a minute more than printer a ?
Options: a ) 250 , b ) 375 , c ) 450 , d ) 480 , e ) 500
Rationale: 40 * a + 40 * b = x pages in 40 mins printer a will print = 40 / 60 * x pages = 2 / 3 * x pages thus in 40 mins printer printer b will print x - 2 / 3 * x = 1 / 3 * x pages also it is given that printer b prints 4 more pages per min that printer a . in 40 mins printer b will print 160 more pages than printer a thus 2 / 3 * x - 1 / 3 * x = 160 = > x = 480 pages answer : d
Answer: d
Python program:
a = 60 / 40
b = a - 1
c = 4 / b
d = c * const_60