euclaise/mathqa_programs huggingface dataset:
Problem: if the price of gasoline increases by 25 % and ron intends to spend only 15 % more on gasoline , by how much percent should he reduce the quantity of gasoline that he buys ?
Options: a ) 6.66 % , b ) 8 % , c ) 10 % , d ) 12 % , e ) 12.5 %
Rationale: "let price of original price of gasoline = 10 $ and let original consumption of gasoline = 10 amount spend on gasoline originally = 10 * 10 = 100 $ the price of gasoline increases by 25 % and ron intends to spend only 15 % more on gasoline increased price of gasoline = 12.5 $ now ron intends to spend on gasoline = 1.15 * 100 = 115 $ consumption of gasoline needs to be = 115 / 12.5 = 1150 / 125 = 46 / 5 = 9.2 reduction in consumption of gasoline = 10 - 9.2 = . 8 % reduction in consumption of gasoline = . 8 / 10 * 100 % = 8 % answer b"
Answer: b
Python program:
a = 15 / 100
b = 1 + a 
c = 25 / 100
d = 1 + c 
e = b / d
f = 1 - e
g = f * 100
Problem: a rower can row 7 km / h in still water . when the river is running at 1 km / h , it takes the rower 1 hour to row to big rock and back . how many kilometers is it to big rock ?
Options: a ) 3.19 , b ) 3.28 , c ) 3.35 , d ) 3.43 , e ) 3.56
Rationale: "let x be the distance to big rock . time = x / 6 + x / 8 = 1 x = 48 / 14 = 3.43 km the answer is d ."
Answer: d
Python program:
a = 7 - 1
b = 7 + 1 
c = 7 - 1
d = b + c 
e = a / d
f = 7 + 1 
g = e * f
Problem: a cistern is normally filled in 4 hours but takes two hours longer to fill because of a leak in its bottom . if the cistern is full , the leak will empty it in ?
Options: a ) 33 , b ) 88 , c ) 40 , d ) 99 , e ) 12
Rationale: "1 / 4 - 1 / x = 1 / 6 x = 12 answer : e"
Answer: e
Python program:
a = 1 / 4
b = 4 + 2 
c = 1 / b
d = a - c
e = 1/(d)
Problem: 25.25 / 1500 is equal to :
Options: a ) 1.012526333 , b ) 0.012625333 , c ) 0.125263333 , d ) 0.126253333 , e ) 0.016833333
Rationale: "25.25 / 2000 = 2525 / 200000 = 0.016833333 answer : e"
Answer: e
Python program:
a = 25 / 25
Problem: if jake loses 20 pounds , he will weigh twice as much as his sister . together they now weigh 224 pounds . what is jake ’ s present weight , in pounds ?
Options: a ) 131 , b ) 135 , c ) 156 , d ) 177 , e ) 188
Rationale: "lets say j is the weight of jack and s is the wt of his sister . if he loses 20 pounds , he s twice as heavy as his sister . j - 20 = 2 * s also , together they weight 224 pounds j + s = 224 solvong the 2 equation , we get j = 156 pounds ! c"
Answer: c
Python program:
a = 224 - 20
b = a / 3
c = b * 2
d = c + 20
Problem: in a certain lottery , the probability that a number between 12 and 20 , inclusive , is drawn is 1 / 6 . if the probability that a number 12 or larger is drawn is 1 / 2 , what is the probability that a number less than or equal to 20 is drawn ?
Options: a ) 1 / 18 , b ) 1 / 6 , c ) 2 / 3 , d ) 1 / 2 , e ) 5 / 6
Rationale: "you can simply use sets concept in this question . the formula total = n ( a ) + n ( b ) - n ( a and b ) is applicable here too . set 1 : number 12 or larger set 2 : number 20 or smaller 1 = p ( set 1 ) + p ( set 2 ) - p ( set 1 and set 2 ) ( combined probability is 1 because every number will be either 12 or moreor 20 or lessor both ) 1 / 2 + p ( set 2 ) - 1 / 6 = 2 / 3 p ( set 2 ) = 2 / 3 answer ( c )"
Answer: c
Python program:
a = 12 / 3
b = 12 + a 
c = 2 / 0
d = b - c
Problem: if the sides of a rectangle are increased by 15 % , what is the percentage increase in the area ?
Options: a ) 32.25 % , b ) 40 % , c ) 37.50 % , d ) 36.75 % , e ) 32 %
Rationale: "say both sides of the rectangle are equal to 100 ( so consider that we have a square ) . in this case the area is 100 * 100 = 10,000 . the area of new rectangle would be 115 * 115 = 13,225 , which is 32.25 % greater than the old area . answer : a ."
Answer: a
Python program:
a = 15 / 100
b = a + 1 
c = b ** 2
d = c - 1
e = d * 100
Problem: a fashion designer sold a pair of jeans to a retail store for 40 percent more than it cost to manufacture the pair of jeans . a customer bought the pair of jeans for 40 percent more than the retailer paid for them . the price the customer paid was what percent greater than the cost of manufacturing the jeans ?
Options: a ) 65 % , b ) 70 % , c ) 75 % , d ) 85 % , e ) 96 %
Rationale: "find the product of the two increases : ( 14 / 10 ) * ( 14 / 10 ) which is 1.96 and a 96 % increase . e"
Answer: e
Python program:
a = 40 / 100
b = 1 + a 
c = 100 * b
d = 40 / 100
e = 1 + d 
f = c * e
g = f / 100
h = g - 1
i = h * 100
Problem: if 50 apprentices can finish a job in 4 hours , and 30 journeymen can finish the same job in 5,5 hours , how much of the job should be completed by 10 apprentices and 15 journeymen in one hour ?
Options: a ) 1 / 9 , b ) 29 / 180 , c ) 26 / 143 , d ) 1 / 5 , e ) 31 / 220
Rationale: "50 apprentices can finish the job in 4 hours , thus : 10 apprentices can finish the job in 4 * 5 = 20 hours ; in 1 hour 10 apprentices can finish 1 / 20 of the job . 30 journeymen can finish the same job in 4,5 hours , thus : 15 journeymen can finish the job in 5.5 * 2 = 11 hours ; in 1 hour 15 journeymen can finish 1 / 11 of the job . therefore , in 1 hour 10 apprentices and 15 journeymen can finish 1 / 20 + 1 / 11 = 31 / 220 of the job . answer : e"
Answer: e
Python program:
a = 50 * 4
b = a / 10
c = 1 / b
d = 30 * 5
e = d / 15
f = 1 / e
g = c + f
Problem: calculate the l . c . m of 1 / 5 , 6 / 7 , 5 / 6 , 3 / 5 is :
Options: a ) 15 , b ) 30 , c ) 20 , d ) 40 , e ) 10
Rationale: "required l . c . m = l . c . m . of 1 , 6 , 5 , 3 / h . c . f . of 5 , 7 , 6 , 5 = 30 / 1 = 30 answer is b"
Answer: b
Python program:
a = 1 * 6
b = 5 * 3
c = a * b
Problem: find the average of all prime numbers between 1 and 10
Options: a ) 2.5 , b ) 1.35 , c ) 4.25 , d ) 6.12 , e ) 7.13
Rationale: "prime numbers between 1 and 10 are 2,3 , 5,7 required average = ( 2 + 3 + 5 + 7 ) / 4 = 17 / 4 = 4.25 answer is c"
Answer: c
Python program:
a = 1 + 1 
b = 1 + 1 
c = b + 2 
d = a + c 
e = 10 - 1
f = 10 - 2
g = e + f 
h = d + g 
i = h / 1
Problem: the average age of a class of 20 students is 19 years . the average increased by 2 when the teacher ' s age also included . what is the age of the teacher ?
Options: a ) 40 years , b ) 41 years , c ) 42 years , d ) 43 years , e ) 44 years
Rationale: "if age of the teacher was 19 , average would not have changed . since average increased by 2 , age of the teacher = 19 + 22 × 1 = 41 answer : b"
Answer: b
Python program:
a = 20 + 2 
b = 19 + 2 
c = a * b
d = 20 * 19
e = c - d
Problem: there were 35 students in a hostel . due to the admission of 7 new students , ; he expenses of the mess were increased by rs . 42 per day while the average expenditure per head diminished by rs 1 . wbat was the original expenditure of the mess ?
Options: a ) 520 , b ) 720 , c ) 425 , d ) 625 , e ) 420
Rationale: "let the original average expenditure be rs . x . then , 42 ( x - 1 ) - 35 x = 42 7 x = 84 x = 12 . original expenditure = rs . ( 35 x 12 ) = rs . 420 . answer is e ."
Answer: e
Python program:
a = 42 + 42 
b = 42 - 35
c = a / b
d = c * 35
e = 42 + 42 
f = 42 - 35
g = e / f
h = 42 - g
i = 42 + 42 
j = 42 - 35
k = i / j
l = h - k
m = l + 2 
n = d - m
Problem: evaluate : | 7 - 8 ( 3 - 12 ) | - | 5 - 11 | = ?
Options: a ) 40 , b ) 50 , c ) 73 , d ) 70 , e ) 80
Rationale: "according to order of operations , inner brackets first . hence | 7 - 8 ( 3 - 12 ) | - | 5 - 11 | = | 7 - 8 * ( - 9 ) | - | 5 - 11 | according to order of operations , multiplication within absolute value signs ( which may be considered as brackets when it comes to order of operations ) next . hence = | 7 + 72 | - | 5 - 11 | = | 79 | - | - 6 | = 79 - 6 = 73 correct answer c ) 73"
Answer: c
Python program:
a = 3 - 12
b = 8 * a
c = 7 - b
d = 5 - 11
e = c - negate
Problem: if 14 lions can kill 14 deers in 14 minutes how long will it take 100 lions to kill 100 deers ?
Options: a ) 1 minutes , b ) 14 minute , c ) 100 minutes , d ) 10000 minutes , e ) 1000 minutes
Rationale: "we can try the logic of time and work , our work is to kill the deers so 14 ( lions ) * 14 ( min ) / 14 ( deers ) = 100 ( lions ) * x ( min ) / 100 ( deers ) hence answer is x = 14 answer : b"
Answer: b
Python program:
a = 14 / 14
b = a * 14
Problem: in a 100 m race , sam beats john by 3 seconds . on the contrary , if sam allowed john to start 24 m ahead of sam , then sam and john reach the finishing point at the same time . how long does sam take to run the 100 m race ?
Options: a ) 4 seconds , b ) 25.33 seconds , c ) 29 seconds , d ) 21 seconds , e ) 6.25 seconds
Rationale: their difference is 3 second but this difference is 0 if john allows sam to start the race from 24 m ahead . that means jhon was 24 m away from finishing line when they started together . so he will cover 24 m in 3 seconds . so his speed = 24 / 3 = 8 metre / second . so time taken = 100 / 3 = 33.33 seconds . so sam took = 25.33 seconds . correct answer = b
Answer: b
Python program:
a = 100 - 24
b = a / 3
Problem: if | x - 25 | = 50 what is the sum of all the values of x .
Options: a ) 0 , b ) - 100 , c ) - 50 , d ) 50 , e ) 100
Rationale: there will be two cases x - 25 = 50 and x - 25 = - 50 solve for x = > x = 50 + 25 = > x = 75 or x = - 50 + 25 = > x = - 25 the sum of both values will be 75 + - 25 = 50 answer is d
Answer: d
Python program:
a = 50 + 25 
b = 50 - 25
c = a - b
Problem: product of two co - prime numbers is 117 . their l . c . m should be :
Options: a ) 1 , b ) 117 , c ) 116 , d ) equal to their h . c . f , e ) can not be calculated
Rationale: "h . c . f of co - prime numbers is 1 . so , l . c . m = 117 / 1 = 117 . answer : b"
Answer: b
Python program:
a = 117 * 1
Problem: the price of a tv was increased by 30 percent . the new price was then increased by 40 percent . a single increase of what percent is equivalent to these two successive increases ?
Options: a ) 82 % , b ) 75 % , c ) 65 % , d ) 50 % , e ) 45 %
Rationale: "consider base price - $ 100 30 % increase = 1.30 * 100 = $ 130 another 40 % increase on new price = 1.4 * 130 = $ 182 so final price of radio - $ 182 therefore a 82 % increase correct option - a"
Answer: a
Python program:
a = 100 + 30 
b = a / 100
c = 40 + 100 
d = c / 100
e = b * d
f = e - 1
g = f * 100
Problem: terry is having lunch at a salad bar . there are two types of lettuce to choose from , as well as 3 types of tomatoes , and 4 types of olives . he must also choose whether or not to have one of the two types of soup on the side . if terry has decided to have the salad and soup combo and he picks one type of lettuce , one type of tomato , and one type of olive for his salad , how many total options does he have for his lunch combo ?
Options: a ) 9 , b ) 11 , c ) 24 , d ) 48 , e ) 54
Rationale: terry can pick one lunch salad bar . . . . we can choose lettuce 2 c 1 , tomatoes - 3 c 1 and olives - 4 c 1 . . . two types of soups , if he picks one then 2 c 1 ways . terry decided to have the combo : soup + salad . . . hmmm . . . using the above information , we get ( 2 c 1 * 2 c 1 * 3 c 1 * 4 c 1 ) = 48 . . ans option d is correct answer . .
Answer: d
Python program:
a = 2 * 4
b = 2 * 3
c = a * b
Problem: what will be the reminder when ( 31 ^ 31 + 31 ) is divided by 32 ?
Options: a ) 72 , b ) 43 , c ) 91 , d ) 40 , e ) 30
Rationale: "( x ^ n + 1 ) will be divisible by ( x + 1 ) only when n is odd ; ( 31 ^ 31 + 1 ) will be divisible by ( 31 + 1 ) ; ( 31 ^ 31 + 1 ) + 30 when divided by will give 30 as remainder . correct option : e"
Answer: e
Python program:
a = 31 ** 31
b = a + 31 
c = 31 ** 31
d = c + 31 
e = d / 32
f = math.floor(e)
g = 32 * f
h = b - g
Problem: if m equals the sum of the odd integers from 1 to 111 , inclusive , and t equals the sum of the even integers from 2 to 50 , inclusive , what is the value of m + t ?
Options: a ) 400 , b ) 5550 , c ) 6922 , d ) 3786 , e ) 5553
Rationale: use following formulae for such problems : sum of evenly spaced integers = ( # of integers ) * ( mean of integers ) # of integers = [ ( last - first ) / 2 ] + 1 mean of integers = ( last + first ) / 2 in above problem : # of integers = [ ( 111 - 1 ) / 2 ] + 1 = 56 and [ ( 50 - 2 ) / 2 ] + 1 = 25 mean of integers = ( 111 + 1 ) / 2 = 56 and ( 50 + 2 ) / 2 = 26 sum of integers = ( 56 * 56 ) = 3136 and ( 25 * 26 ) = 650 thus their sum ( m + t ) = 3786 answer : d
Answer: d
Python program:
a = 111 + 1 
b = a / 2
c = b ** 2
d = 50 / 2
e = 50 / 2
f = e + 1 
g = d * f
h = c + g
Problem: a meeting has to be conducted with 6 managers . find the number of ways in which the managers be selected from among 10 managers , if 2 managers will not attend the meeting together ?
Options: a ) 120 , b ) 110 , c ) 105 , d ) 140 , e ) 135
Rationale: "we can either choose all 6 people from 8 manager who have no problems or choose 5 from the 8 and 1 from the 2 managers who have a problem sitting together so 8 c 6 + ( 8 c 5 * 2 c 1 ) this is 28 + 112 = 140 answer : d"
Answer: d
Python program:
a = math.comb(10, 6)
b = 10 - 2
c = math.comb(b, 2)
d = a - c
Problem: the smallest value of n , for which 2 n + 3 is not a prime number , is
Options: a ) 4,5 , b ) 3,4 , c ) 2,6 , d ) 5,6 , e ) 2,3
Rationale: "( 2 ã — 1 + 3 ) = 5 . ( 2 ã — 2 + 3 ) = 7 . ( 2 ã — 3 + 3 ) = 9 . ( 2 ã — 4 + 3 ) = 15 . which is not prime , n = 3,4 . answer : b"
Answer: b
Python program:
a = 2 + 2
Problem: the average age of a class of 12 students is 19 years . the average increased by 2 when the teacher ' s age also included . what is the age of the teacher ?
Options: a ) 40 years , b ) 34 years , c ) 42 years , d ) 43 years , e ) 44 years
Rationale: "if age of the teacher was 12 , average would not have changed . since average increased by 2 , age of the teacher = 12 + 22 × 1 = 34 answer : b"
Answer: b
Python program:
a = 12 + 2 
b = 19 + 2 
c = a * b
d = 12 * 19
e = c - d
Problem: a certain basketball team that has played 2 / 3 of its games has a record of 14 wins and 6 losses . what is the greatest number of the remaining games that the team can lose and still win at least 3 / 4 of all of its games ?
Options: a ) 1 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "14 wins , 6 losses - total 20 games played . the team has played 2 / 3 rd of all games so total number of games = 30 3 / 4 th of 30 is 22.5 so the team must win 23 games and can afford to lose at most 7 total games . it has already lost 6 games so it can lose another 1 at most . answer ( a )"
Answer: a
Python program:
a = 3 / 2
b = 14 + 6 
c = a * b
d = 3 / 4
e = 3 / 2
f = 14 + 6 
g = e * f
h = d * g
i = math.floor(h)
j = i + 1 
k = c - j
Problem: a train , 125 meters long travels at a speed of 45 km / hr crosses a bridge in 30 seconds . the length of the bridge is
Options: a ) 250 m , b ) 245 m , c ) 235 m , d ) 220 m , e ) 240 m
Rationale: "explanation : assume the length of the bridge = x meter total distance covered = 125 + x meter total time taken = 30 s speed = total distance covered / total time taken = ( 125 + x ) / 30 m / s = > 45 ã — ( 10 / 36 ) = ( 125 + x ) / 30 = > 45 ã — 10 ã — 30 / 36 = 125 + x = > 45 ã — 10 ã — 10 / 12 = 125 + x = > 15 ã — 10 ã — 10 / 4 = 125 + x = > 15 ã — 25 = 125 + x = 375 = > x = 375 - 125 = 250 answer : option a"
Answer: a
Python program:
a = 45 * const_0_2778
b = a * 30
c = b - 125
Problem: in a division sum , the quotient is 36 , the divisor 85 and the remainder 26 , find the dividend ?
Options: a ) 3066 , b ) 3586 , c ) 3086 , d ) 3968 , e ) 3286
Rationale: "explanation : 36 * 85 + 26 = 3086 answer : c"
Answer: c
Python program:
a = 36 * 85
b = a + 26
Problem: a company conducted a survey about its two brands , a and b . x percent of respondents liked product a , ( x – 20 ) percent liked product b , 23 percent liked both products , and 23 percent liked neither product . what is the minimum number q of people surveyed by the company ?
Options: a ) 46 , b ) q . 80 , c ) q . 90 , d ) q . 100 , e ) 200
Rationale: "100 = x + x - 20 + 23 - 23 x = 60 , so , product a = 60 % , product b = 40 % , both = 23 % , neither = 23 % 23 % of the total no . of people should be an integer . so , a , bc are out . 60 % of d and 40 % of d are both integers . so , d satisfies all conditions . so , answer is d ."
Answer: d
Python program:
a = 100 - 23
b = a + 23 
c = b + 20 
d = c / 2
e = d - 20
f = 100 - 23
g = f + 23 
h = g + 20 
i = h / 2
j = e + i
Problem: two trains 141 meters and 165 meters in length respectively are running in opposite directions , one at the rate of 80 km and the other at the rate of 65 kmph . in what time will they be completely clear of each other from the moment they meet ?
Options: a ) 7.16 , b ) 7.59 , c ) 7.12 , d ) 7.15 , e ) 7.11
Rationale: "t = ( 141 + 165 ) / ( 80 + 65 ) * 18 / 5 t = 7.59 answer : b"
Answer: b
Python program:
a = 141 + 165 
b = 80 + 65 
c = b * const_0_2778
d = a / c
Problem: a pharmaceutical company received $ 6 million in royalties on the first $ 20 million in sales of the generic equivalent of one of its products and then $ 9 million in royalties on the next $ 108 million in sales . by approximately what percent did the ratio of royalties to sales decrease from the first $ 20 million in sales to the next $ 108 million in sales ?
Options: a ) 8 % , b ) 15 % , c ) 45 % , d ) 52 % , e ) 72 %
Rationale: "solution : this is a percent decrease problem . we will use the formula : percent change = ( new – old ) / old x 100 to calculate the final answer . we first set up the ratios of royalties to sales . the first ratio will be for the first 20 million in sales , and the second ratio will be for the next 108 million in sales . because all of the sales are in millions , we do not have to express all the trailing zeros in our ratios . first 20 million royalties / sales = 6 / 20 = 3 / 10 next 108 million royalties / sales = 9 / 108 = 1 / 12 because each ratio is not an easy number to use , we can simplify each one by multiplying each by the lcm of the two denominators , which is 60 . keep in mind that we are able to do this only because our answer choices are expressed in percents . first 20 million royalties / sales = ( 6 / 20 ) x 60 = 18 next 108 million royalties / sales = 9 / 108 = ( 1 / 12 ) x 60 = 5 we can plug 18 and 5 into our percent change formula : ( new – old ) / old x 100 [ ( 5 – 18 ) / 18 ] x 100 - 650 / 9 x 100 at this point we can stop and consider the answer choices . since we know that 650 / 9 is just a bit less than ½ , we know that - 650 / 9 x 100 is about a 72 % decrease . answer e ."
Answer: e
Python program:
a = 6 / 20
b = a * 100
c = 9 / 108
d = c * 100
e = b - d
f = 6 / 20
g = f * 100
h = e / g
i = h * 100
Problem: one pipe can fill a tank three times as fast as another pipe . if together the two pipes can fill the tank in 86 minutes , then the slower pipe alone will be able to fill the tank in
Options: a ) 81 min , b ) 108 min , c ) 144 min , d ) 192 min , e ) none
Rationale: "solution let the slower pipe alone fill the tank in x minutes . then , faster pipes will fill it in x / 3 minutes . therefore , 1 / x + 3 / x = 1 / 36 ‹ = › 4 / x = 1 / 36 ‹ = › x = 144 min . answer c"
Answer: c
Python program:
a = 1 + 4 
b = a * 86
Problem: the amounts of time that three secretaries worked on a special project are in the ratio of 2 to 3 to 5 . if they worked a combined total of 90 hours , how many hours did the secretary who worked the longest spend on the project ?
Options: a ) 80 , b ) 70 , c ) 56 , d ) 45 , e ) 14
Rationale: "10 x = 90 = > x = 9 therefore the secretary who worked the longest spent 9 x 5 = 45 hours on the project option ( c )"
Answer: c
Python program:
a = 2 + 3 
b = a + 5 
c = 90 / b
d = c * 5
Problem: one train is travelling 45 kmph and other is at 10 meters a second . ratio of the speed of the two trains is ?
Options: a ) 3 : 3 , b ) 5 : 7 , c ) 5 : 4 , d ) 7 : 2 , e ) 8 : 5
Rationale: c 5 : 4 45 * 5 / 18 = 10 25 : 20 = > 5 : 4
Answer: c
Python program:
a = 45 * const_0_2778
b = a / 10
Problem: in the xy - plane , a triangle has vertices ( 00 ) , ( 40 ) and ( 410 ) . if a point ( a , b ) is selected at random from the triangular region , what is the probability that a - b > 0 ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 2 / 5
Rationale: the area of the right triangle is ( 1 / 2 ) * 4 * 10 = 20 . only the points ( a , b ) below the line y = x satisfy a - b > 0 . the part of the triangle which is below the line y = x has an area of ( 1 / 2 ) ( 4 ) ( 4 ) = 8 . p ( a - b > 0 ) = 8 / 20 = 2 / 5 the answer is e .
Answer: e
Python program:
a = 40 / 10
b = a + 1 
c = 2 / b
Problem: a train 150 m long takes 6 sec to cross a man walking at 5 kmph in a direction opposite to that of the train . find the speed of the train ?
Options: a ) 75 kmph , b ) 85 kmph , c ) 95 kmph , d ) 105 kmph , e ) 115 kmph
Rationale: let the speed of the train be x kmph speed of the train relative to man = x + 5 = ( x + 5 ) * 5 / 18 m / sec 150 / [ ( x + 5 ) * 5 / 18 ] = 6 30 ( x + 5 ) = 2700 x = 85 kmph answer is b
Answer: b
Python program:
a = 150 / 6
b = a / const_0_2778
c = b - 5
Problem: working together , wayne and his son can shovel the entire driveway in 3 hours . if wayne can shovel 6 times as fast as his son can , how many hours would it take for his son to shovel the entire driveway on his own ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 7 , e ) 12
Rationale: w : the time for wyane to do the job s : the time for his son to do the job we have 1 / w + 1 / s = 1 / 6 and w = 6 s then we have 1 / ( 6 * s ) + 1 / s = 1 / 6 < = > 7 / ( 6 * s ) = 1 / 6 < = > s = 7 ans : d
Answer: d
Python program:
a = 6 + 1 
b = 3 * a
c = b / 3
Problem: the cost of 10 kg of mangos is equal to the cost of 24 kg of rice . the cost of 6 kg of flour equals the cost of 2 kg of rice . the cost of each kg of flour is $ 21 . find the total cost of 4 kg of mangos , 3 kg of rice and 5 kg of flour ?
Options: a ) 347.8 , b ) 987.8 , c ) 877.8 , d ) 898.8 , e ) 667.4
Rationale: "let the costs of each kg of mangos and each kg of rice be $ a and $ r respectively . 10 a = 24 r and 6 * 21 = 2 r a = 12 / 5 r and r = 63 a = 151.2 required total cost = 4 * 151.2 + 3 * 63 + 5 * 21 = 604.8 + 189 + 105 = $ 898.80 d"
Answer: d
Python program:
a = 24 / 10
b = 21 * 6
c = b / 2
d = a * c
e = 4 * d
f = 21 * 6
g = f / 2
h = 3 * g
i = e + h 
j = 5 * 21
k = i + j
Problem: how many pieces of 85 cm length can be cut from a rod of 25.5 meters long ?
Options: a ) 50 , b ) 40 , c ) 30 , d ) 20 , e ) 10
Rationale: "number of pieces = 2550 / 85 = 30 the answer is c ."
Answer: c
Python program:
a = 25 * 5
b = a / 85
Problem: a father is 4 times as old as his son . in 20 years , he ' ll be twice as old . how old are they now ?
Options: a ) 540 , b ) 1040 , c ) 2040 , d ) 1030 , e ) 15,30
Rationale: if f is age of father and s is age of son f = 4 s f + 20 = 2 * ( s + 20 ) 4 s + 20 = 2 s + 40 2 s = 20 s = 10 f = 40 answer : b
Answer: b
Python program:
a = 20 / 2
b = a * 4
c = 1000 + b
Problem: how many positive integers h less than 10000 are such that the product of their digits is 210 ?
Options: a ) 24 , b ) 30 , c ) 48 , d ) 54 , e ) 72
Rationale: 210 is the answer when 2 , 3 , 5 and 7 are multiplied . 210 can also be arrive using 56 and 7 and 1 , 5 , 6 and 7 . so sum of arrangements of 2357 , 567 and 1567 . this translates to 4 ! + 3 ! + 4 ! , this equals to 24 + 6 + 24 = 54 , d is the answer .
Answer: d
Python program:
a = 4 + 1 
b = 210 / a
c = b / 3
d = c / 2
e = d - 3
f = math.factorial(e)
g = 4 + 1 
h = 210 / g
i = h / 3
j = i / 2
k = j - 3
l = math.factorial(k)
m = f + l 
n = 4 + 1 
o = 210 / n
p = o / 3
q = p / 2
r = 4 + 1 
s = 210 / r
t = s / 3
u = t / 2
v = u - 3
w = q - v
x = math.factorial(w)
y = m + x
Problem: two trains of lengths 156.62 and 100 meters are running on parallel lines with respective speeds of 30 km / hr and 36 km / hr . the time of crossing each other , if they run in the opposite direction is
Options: a ) 322 sec , b ) 14 sec , c ) 11 sec , d ) 13 sec , e ) 34 sec
Rationale: explanation : total distance to be covered = 156.62 + 100 = 256.62 m trains are running in opposite directions , hence relative speed = 30 + 36 = 66 km / hr = 18.33 m / sec time = distance / relative speed = 256.62 / 18.33 sec = 14 sec therefore , the time of crossing each other in the opposite direction is 14 seconds . answer : b
Answer: b
Python program:
a = 156 + 62 
b = 30 + 36 
c = b * const_0_2778
d = a / c