euclaise/mathqa_programs huggingface dataset:
Problem: two kinds of vodka are mixed in the ratio 1 : 2 and 2 : 1 and they are sold fetching the profit 10 % and 25 % respectively . if the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4 / 3 and 5 / 3 times respectively , then the mixture will fetch the profit of
Options: a ) 18 % , b ) 20 % , c ) 25 % , d ) 23 % , e ) can not be determined
Rationale: answer : c .
Answer: c
Python program:
a = 10 * 4
b = a / 2
c = 10 + 5 
d = b + c
Problem: the average of 10 consecutive integers is 11 . then , 9 is deducted from the first consecutive number , 8 is deducted from the second , 7 is deducted form the third , and so on until the last number which remains unchanged . what is the new average ?
Options: a ) 5 , b ) 5.5 , c ) 6 , d ) 6.5 , e ) 7
Rationale: "the total subtracted is ( 9 + 8 + . . . + 1 ) = ( 9 * 10 ) / 2 = 45 on average , each number will be reduced by 45 / 10 = 4.5 therefore , the overall average will be reduced by 4.5 the answer is d ."
Answer: d
Python program:
a = 10 * 11
b = 4 + 1 
c = b * 9
d = a - c
e = d / 10
Problem: let the number which when multiplied by 15 is increased by 196 .
Options: a ) 14 , b ) 20 , c ) 26 , d ) 28 , e ) 30
Rationale: "solution let the number be x . then , 15 x - x = 196 ‹ = › 14 x = 196 x ‹ = › 14 . answer a"
Answer: a
Python program:
a = 15 - 1
b = 196 / a
Problem: running at their respective constant rates , machine x takes 2 days longer to produce w widgets than machine y . at these rates , if the two machines together produce 5 / 4 w widgets in 3 days , how many days would it take machine x alone to produce 6 w widgets ?
Options: a ) 36 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: "let y produce w widgets in y days hence , in 1 day y will produce w / y widgets . also , x will produce w widgets in y + 2 days ( given , x takes two more days ) hence , in 1 day x will produce w / y + 2 widgets . hence together x and y in 1 day will produce { w / y + w / y + 2 } widgets . together x and y in 3 days will produce = 3 * [ { w / y + w / y + 2 } ] widgets . it is given that in 3 days together they produce ( 5 / 4 ) w widgets . equating , 3 * [ { w / y + w / y + 2 } ] = ( 5 / 4 ) w take out w common and move 3 to denominator of rhs w { 1 / y + 1 / ( y + 2 ) } = ( 5 / 12 ) w canceling w from both sides { 1 / y + 1 / ( y + 2 ) } = 5 / 12 2 y + 2 / y ( y + 2 ) = 5 / 12 24 y + 24 = 5 y ^ 2 + 10 y 5 y ^ 2 - 14 y - 24 = 0 5 y ^ 2 - 20 y + 6 y - 24 = 0 5 y ( y - 4 ) + 6 ( y - 4 ) = 0 ( 5 y + 6 ) + ( y - 4 ) = 0 y = - 6 / 5 or y = 4 discarding y = - 6 / 5 as no of days can not be negative y = 4 hence it takes y , 4 days to produce w widgets . therefore , it will take x ( 4 + 2 ) = 6 days to produce w widgets . hence it will take x 6 * 6 = 36 days to produce 2 w widgets . answer : a"
Answer: a
Python program:
a = 3 * 4
b = a * 2
c = 3 * 4
d = b - c
e = d / 2
Problem: a rectangular parking space is marked out by painting three of its sides . if the length of the unpainted side is 9 feet , and the sum of the lengths of the painted sides is 37 feet , then what is the area of the parking space in square feet ?
Options: a ) 46
b ) 81
c ) 126
d ) 252
e ) none of these
Rationale: solution clearly , we have : l = 9 and l + 2 b = 37 or b = 14 . ∴ area = ( l × b ) = ( 9 × 14 ) sq . ft . = 126 sq . ft . answer c
Answer: c
Python program:
a = 37 + 37 
b = a + 37 
c = b + 10 
d = c + 4
Problem: lagaan is levied on the 60 percent of the cultivated land . the revenue department collected total rs . 3 , 64,000 through the lagaan from the village of mutter . mutter , a very rich farmer , paid only rs . 480 as lagaan . the percentage of total land of mutter over the total taxable land of the village is :
Options: a ) 0.20833 , b ) 0.14544 , c ) 0.21978 , d ) 0.35466 , e ) 0.63435
Rationale: "total land of sukhiya = \ inline \ frac { 480 x } { 0.6 } = 800 x \ therefore cultivated land of village = 364000 x \ therefore required percentage = \ inline \ frac { 800 x } { 364000 } \ times 100 = 0.21978 c"
Answer: c
Python program:
a = 60 / 100
b = 480 / a
c = 3 * 100
d = c * 1000
e = 4 * 10
f = e + 4 
g = f * 1000
h = d + g 
i = b / h
j = i * 100
Problem: if p / q = 4 / 5 , then the value of 6 / 7 + { ( 2 q - p ) / ( 2 q + p ) } is ?
Options: a ) 3 / 7 , b ) 34 , c ) 10 / 7 , d ) 2 , e ) 3
Rationale: "answer given exp . = 6 / 7 + { ( 2 q - p ) / ( 2 q + p ) } dividing numerator as well as denominator by q , exp = 6 / 7 + { 2 - p / q ) / ( 2 + p / q ) } = 6 / 7 + { ( 2 - 4 / 5 ) / ( 2 + 4 / 5 ) } = 6 / 7 + 6 / 14 = 6 / 7 + 3 / 7 = 10 / 7 correct option : c"
Answer: c
Python program:
a = 6 / 7
b = 4 / 5
c = 2 - b
d = 4 / 5
e = 2 + d 
f = c / e
g = a + f
Problem: two persons start at the same point , walk in opposite directions with 6 km / hr and 7 km / hr respectively . what is the distance separated after 3 and half hrs ?
Options: a ) 45.5 km , b ) 27.250 km , c ) 28.250 km , d ) 29.250 km , e ) 25.250 km
Rationale: as the two persons are moving in the opposite direction , so they will be separateed in 1 hour = 6 + 7 = 13 km . they will be separated in 2.5 hours = 13 * 3.5 = 45.5 km answer : a
Answer: a
Python program:
a = 2 / 4
b = 3 + a 
c = 6 * b
d = 2 / 4
e = 3 + d 
f = 7 * e
g = c + f
Problem: on day one , a store sold 86 cups . on each of the next d days , the company sold 50 cups . if the average daily sales of cups over this time period ( including day one ) is 53 cups , what is the value of d ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: 86 + 50 d = 53 ( d + 1 ) . 3 d = 33 . d = 11 . the answer is c .
Answer: c
Python program:
a = 86 + 50 
b = a + 53 
c = b / 3
d = c + 1 
e = d - 53
Problem: there are two concentric circles with radii 8 and 4 . if the radius of the outer circle is increased by 25 % and the radius of the inner circle decreased by 25 % , by what percent does the area between the circles increase ?
Options: a ) 75 , b ) 80 , c ) 85 , d ) 90 , e ) 95
Rationale: "the area of a circle is pir ^ 2 , where r is the radius . the area of the big circle is 64 pi . the area of the small circle is 16 pi . the area a 1 between the circles is 48 pi . when the big circle ' s radius increases , the new area is 100 pi . when the small circle ' s radius decreases , the new area is 9 pi . the area a 2 between the circles is 91 pi . the ratio of a 2 / a 1 is 91 / 48 = 1.9 which is an increase of 90 % . the answer is d ."
Answer: d
Python program:
a = 100 + 25 
b = a / 100
c = 8 * b
d = c ** 2
e = 100 - 25
f = e / 100
g = 4 * f
h = g ** 2
i = d - h
j = 8 ** 2
k = 4 ** 2
l = j - k
m = i - l
n = 8 ** 2
o = 4 ** 2
p = n - o
q = m / p
r = q * 100
Problem: alice can bake a pie in 5 minutes . bob can bake a pie in 6 minutes . compute how many more pies alice can bake than bob in 60 minutes .
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: alice can bake 60 / 5 = 12 pies in 60 minutes . bob can bake 60 / 6 = 10 pies in 60 minutes . alice can therefore bake 12 - 10 = 2 more pies than bob . correct answer b
Answer: b
Python program:
a = 60 / 5
b = 60 / 6
c = a - b
Problem: a grocer has a sale of rs . 5420 , rs . 5660 , rs . 6200 , rs . 6350 and rs . 6500 for 5 consecutive months . find the sale he should have in the sixth month , so that he gets an average sale of rs . 6100 ?
Options: a ) rs . 5870 , b ) rs . 5991 , c ) rs . 6470 , d ) rs . 6850 , e ) none of these
Rationale: "explanation : total sale for 5 months = rs . ( 5420 + 5660 + 6200 + 6350 + 6500 ) = rs . 30,130 therefore , required sale = rs . [ ( 6100 * 6 ) – 30,130 ] = rs . ( 36600 – 30,130 ) = rs . 6470 answer c"
Answer: c
Python program:
a = 5 + 1 
b = a * 6100
c = 5420 + 5660 
d = c + 6200 
e = d + 6350 
f = e + 6500 
g = b - f
Problem: when a random experiment is conducted , the probability that event a occurs is 1 / 6 . if the random experiment is conducted 4 independent times , what is the probability that event a occurs exactly twice ?
Options: a ) 17 / 216 , b ) 19 / 216 , c ) 23 / 216 , d ) 25 / 216 , e ) 35 / 216
Rationale: "one case is : 1 / 6 * 1 / 6 * 5 / 6 * 5 / 6 = 25 / 1296 the total number of possible cases is 4 c 2 = 6 p ( event a occurs exactly twice ) = 6 * ( 25 / 1296 ) = 25 / 216 the answer is d ."
Answer: d
Python program:
a = 2 / 6
b = 1 - a
Problem: a , b , c subscribe rs . 50,000 for a business . a subscribes rs . 4000 more than b and b rs . 5000 more than c . out of a total profit of rs . 35,000 , c receives :
Options: a ) s . 14,000 , b ) s . 14,200 , c ) s . 4,400 , d ) s . 8,400 , e ) s . 4,800
Rationale: "let c = x . then , b = x + 5000 and a = x + 5000 + 4000 = x + 9000 . so , x + x + 5000 + x + 9000 = 50000 3 x = 36000 x = 12000 a : b : c = 21000 : 17000 : 12000 = 21 : 17 : 12 . c ' s share = rs . ( 35000 x 12 / 50 ) = rs . 8,400 . d"
Answer: d
Python program:
a = 10 * 5000
b = a - 5000
c = 4000 + 5000 
d = b - c
e = d / 3
f = 4000 + 5000 
g = e + f 
h = 10 * 5000
i = g / h
j = 3 + 4 
k = j * 5000
l = i * k
m = l / 1000
n = math.floor(m)
o = n - 1
Problem: a building contractor employs 20 male , 15 female and 5 child workers . to a male worker he pays rs . 35 per day , to a female worker rs . 20 per day and a child worker rs . 8 per day . the average wage per day paid by the contractor is ?
Options: a ) 22 , b ) 23 , c ) 28 , d ) 29 , e ) 26
Rationale: "20 15 5 35 20 8 500 + 300 + 40 = 1040 / 40 = 26 answer : e"
Answer: e
Python program:
a = 20 * 35
b = 15 * 20
c = a + b 
d = 5 * 8
e = c + d 
f = 20 + 15 
g = f + 5 
h = e / g
Problem: ( ( 1 ^ 5 m ) / ( 5 ^ 5 m ) ) ( ( 1 ^ 18 ) / ( 4 ^ 18 ) ) = 1 / ( 2 ( 10 ) ^ 35 ) what is m ?
Options: a ) 7 , b ) 18 , c ) 34 , d ) 35 , e ) 36
Rationale: ( ( 1 ^ 5 m ) / ( 5 ^ 5 m ) ) ( ( 1 ^ 18 ) / ( 4 ^ 18 ) ) = 1 / ( 2 ( 10 ) ^ 35 ) ( ( 1 / 5 ) ^ 5 m ) * ( ( 1 / 2 ) ^ 36 ) = 1 / ( 2 * ( 2 * 5 ) ^ 35 ) ) 2 ^ 36 will cancel out , since 1 can be written as 1 ^ 35 , so ( 1 / 5 ) ^ 5 m = ( 1 / 5 ) ^ 35 ( ( 1 / 5 ) ^ 5 m ) * ( ( 1 / 2 ) ^ 36 ) = 1 / [ ( 2 ^ 36 ) * ( 5 ^ 35 ) ] so , m = 7 answer a
Answer: a
Python program:
a = 1 ** 18
b = 10 ** 35
c = b * 2
d = a * c
e = 4 ** 18
f = d / e
g = math.log(f)
h = 5 ** 5
i = math.log(h)
j = g / i
Problem: eggs are sold in packages of 6 or 11 only . if doris bought 79 eggs exactly , what could be the number of large packs doris bought ?
Options: a ) 6 . , b ) 2 . , c ) 3 . , d ) 5 . , e ) 4 .
Rationale: no strategy involved . simple question demanding fast calculation . 11 x 5 = 55 = > 79 - 55 = 24 = > 24 / 6 is an integer ans d . 5 . good luck
Answer: d
Python program:
a = 6 * 4
b = 79 - a
c = b / 11
Problem: how long does a train 200 m long running at the speed of 72 km / hr takes to cross a bridge 132 m length ?
Options: a ) 82.1 sec , b ) 12.1 sec , c ) 16.1 sec , d ) 13.1 sec , e ) 16.6 sec
Rationale: "speed = 72 * 5 / 18 = 20 m / sec total distance covered = 200 + 132 = 332 m . required time = 332 / 20 = 16.6 sec . answer : e"
Answer: e
Python program:
a = 200 + 132 
b = 72 * const_0_2778
c = a / b
Problem: two tains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post . if the length of each train be 125 metres , in what time ( in seconds ) will they cross each other travelling in opposite direction ?
Options: a ) 6 , b ) 14 , c ) 16 , d ) 20 , e ) 18
Rationale: "sol . speed of the first train = [ 150 / 10 ] m / sec = 15 m / sec . speed of the second train = [ 150 / 15 ] m / sec = 10 m / sec . relative speed = ( 15 + 10 ) = m / sec = 25 m / sec . ∴ required time = ( 125 + 125 ) / 25 secc = 6 sec . answer a"
Answer: a
Python program:
a = 125 + 125 
b = 125 / 15
c = 125 / 10
d = b + c 
e = a / d
Problem: find out the c . i on rs . 5000 at 4 % p . a . compound half - yearly for 1 1 / 2 year ?
Options: a ) 306.06 , b ) 306.02 , c ) 306.04 , d ) 306.09 , e ) 306.12
Rationale: "a = 5000 ( 51 / 50 ) 3 = 5306.04 5000 - - - - - - - - - - - 306.04 answer : c"
Answer: c
Python program:
a = 4 / 100
b = 1 + a 
c = 3 / 2
d = b ** c
e = 5000 * d
f = e - 5000
Problem: micheal and adam can do together a piece of work in 20 days . after they have worked together for 14 days micheal stops and adam completes the remaining work in 10 days . in how many days micheal complete the work separately .
Options: a ) 50 days , b ) 100 days , c ) 120 days , d ) 110 days , e ) 90 days
Rationale: "rate of both = 1 / 20 together they do = 1 / 20 * 14 = 7 / 10 left work = 1 - 7 / 10 = 3 / 10 adam completes 3 / 10 work in 10 day so he took 10 * 10 / 3 = 100 / 3 days to complete the left work alone . thus the rate of adam is 3 / 100 rate of micheal = 1 / 20 - 3 / 100 = 1 / 50 thus micheal takes 50 days to complete the whole work . ans . a"
Answer: a
Python program:
a = 1/(20)
b = 1/(20)
c = b * 14
d = 1 - c
e = 1/(d)
f = e * 10
g = 1/(f)
h = a - g
i = 1/(h)
Problem: a number is selected at random from the first 30 natural numbers . what is the probability that the number is a multiple of either 3 or 17 ?
Options: a ) 17 / 30 , b ) 2 / 5 , c ) 7 / 15 , d ) 4 / 15 , e ) 11 / 30
Rationale: "number of multiples of 3 from 1 through 30 = 30 / 3 = 10 number of multiples of 17 from 1 through 30 = 30 / 17 = 1 number of multiples of 3 and 17 both from 1 through 30 = number of multiples of 17 * 3 ( = 51 ) = 0 total favourable cases = 10 + 1 - 0 = 11 probability = 11 / 30 answer : option e"
Answer: e
Python program:
a = 30 / 3
b = math.floor(a)
c = 30 / 17
d = b + c 
e = d / 30
Problem: by selling an article at rs . 800 , a shopkeeper makes a profit of 35 % . at what price should he sell the article so as to make a loss of 25 % ?
Options: a ) s . 416 , b ) s . 480 , c ) s . 429 , d ) s . 128 , e ) s . 419
Rationale: "sp = 800 profit = 25 % cp = ( sp ) * [ 100 / ( 100 + p ) ] = 800 * [ 100 / 125 ] = 640 loss = 35 % = 35 % of 640 = rs . 224 sp = cp - loss = 640 - 224 = rs . 416 answer : a"
Answer: a
Python program:
a = 800 * 100
b = 35 + 100 
c = a / b
d = 800 * 100
e = 35 + 100 
f = d / e
g = f * 25
h = g / 100
i = c - h
Problem: a present value of a machine is $ 900 . its value depletion rate is 10 % per annum then find the machine value after 2 years ?
Options: a ) $ 900 , b ) $ 810 , c ) $ 915 , d ) $ 715 , e ) $ 729
Rationale: "p = $ 900 r = 10 % t = 2 years machine value after 2 years = p [ ( 1 - r / 100 ) ^ t ] = 900 * 9 / 10 * 9 / 10 = $ 729 answer is e"
Answer: e
Python program:
a = 10 / 100
b = 1 - a
c = b ** 2
d = 900 * c
Problem: a motorist knows 6 different routes from bristol to birmingham . from birmingham to sheffield he knows 3 different routes and from sheffield to carlisle he knows two different routes . how many routes does he know from bristol to carlisle ?
Options: a ) 4 , b ) 8 , c ) 12 , d ) 24 , e ) 36
Rationale: explanation : total number of routes from bristol to carlisle = ( 6 x 3 x 2 ) = 36 . answer : e
Answer: e
Python program:
a = 6 * 3
b = a * 2
Problem: the grade point average of one third of the classroom is 54 ; the grade point average of the rest is 45 . what is the grade point average of the whole class ?
Options: a ) 52 , b ) 54 , c ) 48 , d ) 58 , e ) 60
Rationale: "let n = total students in class total points for 1 / 3 class = 54 n / 3 = 18 n total points for 2 / 3 class = 45 * 2 n / 3 = 30 n total points for whole class = 18 n + 30 n = 48 n 48 n total class points / n total students = 48 grade point average for total class answer : c"
Answer: c
Python program:
a = 45 / 3
b = a * 2
c = 54 / 3
d = b + c
Problem: in what time will a train 100 m long cross an electric pole , it its speed be 72 km / hr ?
Options: a ) 2.5 , b ) 5 , c ) 2.4 , d ) 2.8 , e ) 2.1
Rationale: "speed = 72 * 5 / 18 = 20 m / sec time taken = 100 / 20 = 5 sec . answer : b"
Answer: b
Python program:
a = 72 * const_0_2778
b = 100 / a
Problem: if x is an integer that has exactly 3 positive divisors ( these include 1 and x ) , how many positive divisors does x ^ 3 have ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: since factors of ' 4 ' are { 1 , 2,4 } 4 ^ 3 = 64 number of factors / divisors of 64 = 2 ^ 6 we know that when a number is expressed as a product of the prime factors as below : n = a ^ x * b ^ y * c ^ z then no . of divisors = ( x + 1 ) * ( y + 1 ) * ( z + 1 ) then here ( 6 + 1 ) = 7 answer : d
Answer: d
Python program:
a = 3 + 3 
b = a + 1
Problem: three 6 faced dice are thrown together . the probability that all the three show the same number on them is -
Options: a ) 1 / 39 , b ) 1 / 36 , c ) 1 / 32 , d ) 1 / 31 , e ) 1 / 30
Rationale: "explanation : it all 3 numbers have to be same basically we want triplets . 111 , 222 , 333 , 444 , 555 and 666 . those are six in number . further the three dice can fall in 6 * 6 * 6 = 216 ways . hence the probability is 6 / 216 = 1 / 36 answer : b"
Answer: b
Python program:
a = 1 / 6
b = 1 / 6
c = a * b
d = 1 / 6
e = c * d
f = 1 / 6
g = e * f
Problem: how many bricks , each measuring 5 cm x 11 cm x 6 cm , will be needed to build a wall of 8 m x 6 m x 2 cm ?
Options: a ) 5600 , b ) 6000 , c ) 2909 , d ) 7200 , e ) 8600
Rationale: "number of bricks = volume of the wall / volume of 1 brick = ( 800 x 600 x 2 ) / ( 5 x 11 x 6 ) = 2909 . answer : option c"
Answer: c
Python program:
a = 8 * 100
b = 6 * 100
c = a * b
d = c * 2
e = 5 * 11
f = e * 6
g = d / f
Problem: a can do a piece of work in 7 days and b can do it in 6 days how long will they both work together to complete the work ?
Options: a ) 6 / 11 , b ) 8 / 13 , c ) 3 / 13 , d ) 9 / 11 , e ) 10 / 13
Rationale: "explanation : a ’ s one day work = 1 / 5 b ’ s one day work = 1 / 6 ( a + b ) ’ s one day work = 1 / 7 + 1 / 6 = 13 / 42 = > time = 42 / 13 = 3 3 / 13 days answer : option c"
Answer: c
Python program:
a = 1 / 7
b = 1 / 6
c = a + b 
d = 1 / c
Problem: 60 % of the population of a village is 23040 . the total population of the village is ?
Options: a ) 38400 , b ) 24000 , c ) 24936 , d ) 25640 , e ) none
Rationale: answer ∵ 60 % of p = 23040 ∴ p = ( 23040 x 100 ) / 60 = 38400 correct option : a
Answer: a
Python program:
a = 100 / 60
b = a * 23040
Problem: when positive integer x is divided by positive integer y , the remainder is 9 . if x / y = 96.25 , what is the value of y ?
Options: a ) 96 , b ) 75 , c ) 36 , d ) 25 , e ) 12
Rationale: "guys , one more simple funda . 5 / 2 = 2.5 now . 5 x 2 = 1 is the remainder 25 / 4 = 6.25 now . 25 x 4 = 1 is the remainder 32 / 5 = 6.4 now . 4 x 5 = 2 is the remainder given x / y = 96.25 and remainder is 9 so . 25 x y = 9 hence y = 36 ans c"
Answer: c
Python program:
a = math.floor(96, 25)
b = 96 - 25
c = 9 / b
Problem: 378 × ? = 252
Options: a ) 2 / 3 , b ) 3 / 4 , c ) 1 / 2 , d ) 2 / 8 , e ) none of these
Rationale: "explanation : 378 × ? = 252 ? = 252 / 378 = 126 / 189 = 14 / 21 = 2 / 3 answer is a"
Answer: a
Python program:
a = 378 / 252
b = a * 100
Problem: the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 20 kg . what is the weight of the new person ?
Options: a ) 75 , b ) 65 , c ) 85 , d ) 40 , e ) 80
Rationale: total increase in weight = 8 × 2.5 = 20 if x is the weight of the new person , total increase in weight = x − 20 = > 20 = x - 20 = > x = 20 + 20 = 40 answer is d .
Answer: d
Python program:
a = 8 * 2
b = a + 20
Problem: liam is pulled over for speeding just as he is arriving at work . he explains to the police officer that he could not afford to be late today , and has arrived at work only four minutes before he is to start . the officer explains that if liam had driven 5 mph slower for his whole commute , he would have arrived at work exactly on time . if liam ' s commute is 20 miles long , how fast was he actually driving ? ( assume that liam drove at a constant speed for the duration of his commute . )
Options: a ) 50 mph , b ) 45 mph , c ) 48 mph , d ) 52 mph , e ) 40 mph
Rationale: "let t be the number of hours he would need to reach office on time . when he is driving with over speed , he reached office 4 min earlier ! so the equation for this is s ( t - 4 / 60 ) = 20 where s is the speed and 20 is the distance . if he decreases his speed by 5 mph then he would have reached his office on time : ( s - 5 ) t = 20 if you solve above equations , you will arrive at t = 2 / 3 hr and s = 40 mph therefore answer is e"
Answer: e
Python program:
a = 5 * 4
b = 20 + a
Problem: rs . 1690 is divided so that 4 times the first share , thrice the 2 nd share and twice the third share amount to the same . what is the value of the third share ?
Options: a ) s . 528 , b ) s . 542 , c ) s . 780 , d ) s . 540 , e ) s . 549
Rationale: "a + b + c = 1690 4 a = 3 b = 2 c = x a : b : c = 1 / 4 : 1 / 3 : 1 / 2 = 3 : 4 : 6 6 / 13 * 1690 = rs . 780 answer : c"
Answer: c
Python program:
a = 4 + 2 
b = a + 3 
c = 1690 / b
d = 4 * c
Problem: if 41 / 88 = 0.46590 , what is the 77 th digit to the right of the decimal point of the fraction ?
Options: a ) 6 , b ) 2 , c ) 5 , d ) 0 , e ) 9
Rationale: "we are not concerned what 41 / 88 means . . we have to look at the decimal . . 0.6590 means 0.465909090 . . . . so leaving girst , second and third digit to the right of decimal , all odd numbered are 0 and all even numbered are 9 . . here 77 is odd , so ans is 0 answer is d"
Answer: d
Python program:
a = 2 + 3
Problem: a train running at the speed of 100 km / hr crosses a pole in 18 seconds . what is the length of the train ?
Options: a ) 300 , b ) 400 , c ) 500 , d ) 600 , e ) 700
Rationale: speed = ( 100 * 5 / 18 ) m / sec = ( 250 / 9 ) m / sec length of the train = ( speed x time ) = ( 250 / 9 * 18 ) m = 500 m . answer : c
Answer: c
Python program:
a = 100 * 1000
b = a / 3600
c = b * 18
Problem: there has been successive increases of 15 % and then 10 % in the price of gas from the previous month . by what percentage should a driver reduce gas consumption so that the expenditure does not change ?
Options: a ) 12 % , b ) 15 % , c ) 18 % , d ) 21 % , e ) 24 %
Rationale: "let p be the original price per unit of gas . let x be the original gas consumption . let y be the reduced gas consumption . y * 1.1 * 1.15 * p = x * p y = x / ( 1.1 * 1.15 ) which is about 0.79 x which is a decrease of about 21 % . the answer is d ."
Answer: d
Python program:
a = 100 + 15 
b = 100 + 15 
c = b * 10
d = c / 100
e = a + d 
f = 100 / e
g = 1 - f
h = g * 100
Problem: two numbers are less than a third number by 30 % and 37 % . how much percent is the second number is less than the first ?
Options: a ) 10 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 30 %
Rationale: let the third number be x first number = 70 % of x = 7 x / 10 ; second number = 63 % of x = 63 x / 100 ; difference = 7 x / 10 - 63 x / 100 = 7 x / 100 ; required percentage = 7 x / 100 * 10 / 7 x * 100 = 10 % answer is a
Answer: a
Python program:
a = 30 + 1 
b = a - 30
c = b * 10
Problem: there are 300 seniors at morse high school , and 40 % of them have cars . of the remaining grades ( freshmen , sophomores , and juniors ) , only 10 % of them have cars . if 15 % of all the students at morse have cars , how many students are in those other 3 lower grades ?
Options: a ) 600 , b ) 900 , c ) 1200 , d ) 1350 , e ) 1500
Rationale: let the total no of students be n . the no of seniors having cars is 40 % of 300 i . e . 120 . the rest of the students with other three grades who have cars is 10 % of ( n - 300 ) . the total no of students with cars is 15 % of n . thus , 0.15 n = 120 + 0.1 ( n - 300 ) on solving this , we get n = 1800 . hence , the no of students with other three grades is 1800 - 300 , i . e . 1500 ( e ) .
Answer: e
Python program:
a = 15 * 100
Problem: in an examination , a student scores 6 marks for every correct answer and loses 1 mark for every wrong answer . if he attempts all 60 questions and secures 280 marks , the no of questions he attempts correctly is :
Options: a ) a ) 20 , b ) b ) 38 , c ) c ) 90 , d ) d ) 88 , e ) e ) 37
Rationale: "let the number of correct answers be x . number of incorrect answers = ( 60 – x ) . 6 x – ( 60 – x ) = 280 = > 7 x = 340 = > x = 20 answer : a"
Answer: a
Python program:
a = 280 + 60 
b = 6 + 1 
c = a / b