euclaise/mathqa_programs huggingface dataset:
Problem: harkamal purchased 8 kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 50 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) a ) 1000 , b ) b ) 1010 , c ) c ) 1065 , d ) d ) 1075 , e ) e ) 1080
Rationale: "cost of 8 kg grapes = 70 × 8 = 560 . cost of 9 kg of mangoes = 50 × 9 = 450 . total cost he has to pay = 560 + 450 = 1010 . b )"
Answer: b
Python program:
a = 8 * 70
b = 9 * 50
c = a + b
Problem: in a group of 250 readers who read science fiction or literacy works or both , 180 read science fiction and 88 read literacy works . how many read both science fiction and literacy works ?
Options: a ) 268 , b ) 180 , c ) 150 , d ) 18 , e ) 88
Rationale: "consider total number of reader n ( s u l ) = 250 people who read science fiction n ( s ) = 180 people who read literacy works n ( l ) = 88 both science fiction and literacy n ( s â ˆ © l ) = ? n ( s u l ) = n ( s ) + n ( l ) - n ( s â ˆ © l ) 250 = 180 + 88 - n ( s â ˆ © l ) n ( s â ˆ © l ) = 268 - 250 n ( s â ˆ © l ) = 18 so people read both science fiction and literacy works are 18 answer : d"
Answer: d
Python program:
a = 180 + 88 
b = a - 250
Problem: in a certain circle there are 10 points . what is the number of the triangles connecting 5 points of the 10 points ?
Options: a ) 80 , b ) 96 , c ) 108 , d ) 120 , e ) 252
Rationale: "imo : e here we have to select 5 points out of 10 points . order is not important so the answer will be 10 c 5 = 252 answer e"
Answer: e
Python program:
a = math.factorial(10)
b = 10 / 2
c = math.factorial(b)
d = math.factorial(5)
e = c * d
f = a / e
Problem: solution x is 10 percent alcohol by volume , and solution y is 30 percent alcohol by volume . how many milliliters of solution y must be added to 200 milliliters of solution x to create a solution that is 14 percent alcohol by volume ?
Options: a ) 50 , b ) 100 , c ) 150 , d ) 200 , e ) 250
Rationale: "14 % is 4 % - points higher than 10 % but 16 % - points lower than 30 % . thus there should be 4 parts of solution x for 1 part of solution y . we should add 50 ml of solution y . the answer is a ."
Answer: a
Python program:
a = 14 - 10
b = 30 - 14
c = a / b
d = c * 200
Problem: the difference between the place value and the face value of 6 in the numerical 856973 is
Options: a ) 973 , b ) 6973 , c ) 5994 , d ) 9554 , e ) none of them
Rationale: "= ( place value of 6 ) - ( face value of 6 ) = ( 6000 - 6 ) = 5994 answer is c"
Answer: c
Python program:
a = 10 * 6
b = a - 6
Problem: if n = 8 ^ 8 – 5 , what is the units digit of n ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5
Rationale: "8 ^ 8 - 8 = 8 ( 8 ^ 7 - 1 ) = = > 8 ( 2 ^ 21 - 1 ) last digit of 2 ^ 21 is 2 based on what explanation livestronger is saying . 2 ^ 24 - 1 yields 2 - 1 = 1 as the unit digit . now on multiply this with 5 , we get unit digit as 5 answer : e"
Answer: e
Python program:
a = math.log(5)
b = 8 ** 8
c = math.log(b)
d = a / c
Problem: patrick purchased 80 pencils and sold them at a loss equal to the selling price of 16 pencils . the cost of 80 pencils is how many times the selling price of 80 pencils ?
Options: a ) 0.75 , b ) 1.2 , c ) 1.8 , d ) 2.4 , e ) 4.25
Rationale: "say the cost price of 80 pencils was $ 80 ( $ 1 per pencil ) and the selling price of 1 pencil was p . selling at a loss : 80 - 80 p = 16 p - - > p = 5 / 6 . ( cost price ) / ( selling price ) = 1 / ( 5 / 6 ) = 6 / 5 = 1.2 . answer : b ."
Answer: b
Python program:
a = 80 + 16 
b = 80 / a
c = 1/(b)
Problem: how many odd numbers between 10 and 1,200 are the squares of integers ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: "the square of an odd number is an odd number : 10 < odd < 1,000 10 < odd ^ 2 < 1,000 3 . something < odd < 31 . something ( by taking the square root ) . so , that odd number could be any odd number from 5 to 31 , inclusive : 5 , 7 , 9 , 11 , 13 , 15 , 17 , 19 , 21 , 23 , 25 , 27 , 29 , and 31 . 16 numbers . answer : e ."
Answer: e
Python program:
a = 10 + 4
Problem: if 6 women take an hour to dig a ditch , then how long should 18 women take a dig to ditch of the same type ?
Options: a ) 25 min , b ) 20 min , c ) 28 min , d ) 15 min , e ) 10 min
Rationale: if 6 women take an hour to dig a ditch , then 18 men will take 6 * 60 / 18 = 20 mins to dig a ditch of the same type . answer : b
Answer: b
Python program:
a = 18 / 6
b = const_60 / a
Problem: if the price of a book is first decreased by 50 % and then increased by 60 % , then the net change in the price will be ?
Options: a ) 20 % decrease , b ) 10 % increase , c ) 10 % decrease , d ) 15 % increase , e ) 25 % decrease
Rationale: "let the original price be $ 100 new final price = 160 % of ( 50 % of $ 100 ) = 160 / 100 * 50 / 100 * 100 = $ 80 decrease is 20 % answer is a"
Answer: a
Python program:
a = 100 * 50
b = a / 100
c = 100 - b
d = c / 100
e = 100 * 60
f = e / 100
g = 100 + f 
h = g / 100
i = d * h
j = i * 100
k = 100 - j
Problem: if a farmer sells 15 of his chickens , his stock of feed will last for 4 more days than planned , but if he buys 10 more chickens , he will run out of feed 6 days earlier than planned . if no chickens are sold or bought , the farmer will be exactly on schedule . how many chickens does the farmer have ?
Options: a ) 20 , b ) 50 , c ) 40 , d ) 30 , e ) 60
Rationale: "let x = total feed required for the planned period n = number of chicken t = total time of the planned feed x = nt 1 ) x = ( n - 15 ) * ( t + 4 ) 2 ) x = ( n + 10 ) * ( t - 6 ) equating 1 & 2 ( n - 15 ) * ( t + 4 ) = ( n + 10 ) * ( t - 6 ) or nt + 4 n - 15 t - 60 = nt - 6 n + 10 t - 60 10 n = 25 t n = 5 / 2 * t or t = 2 n / 5 x = n * 2 n / 5 substituting this value in 1 n * 2 n / 5 = ( n - 15 ) * ( 2 n / 5 + 4 ) 2 n = 60 n = 30 d"
Answer: d
Python program:
a = 2 + 4 
b = 6 * 4
c = a * b
Problem: a bag contains 10 red jellybeans and 10 blue jellybeans . if 3 jellybeans are removed one at a time , at random and are not replaced , what is the probability q that all 3 jellybeans removed from the bag are blue ?
Options: a ) 9 / 100 , b ) 2 / 19 , c ) 1 / 8 , d ) 3 / 20 , e ) 3 / 10
Rationale: "method - 1 10 red jellybeans and 10 blue jellybeans total outcomes = no . of ways to choose 3 jelly bean at random out of a total 20 jellybeans = 20 c 3 = 1140 favourable outcomes = no . of ways to choose 3 jelly bean such that they are all blue out of 10 blue = 10 c 3 = 120 probability = favourable outcomes / total outcomes = 10 c 3 / 20 c 3 probability q = 120 / 1140 = 2 / 19 answer : option b method - 2 probability of first jelly bean to be blue = 10 / 20 [ total 10 blue out of total 20 jellybeans ] probability of second jelly bean to be blue = 9 / 19 [ total 9 blue remaining out of total 19 jellybeans remaining ] probability of third jelly bean to be blue = 8 / 18 [ total 8 blue remaining out of total 18 jellybeans remaining ] required probability = ( 10 / 20 ) * ( 9 / 19 ) * ( 8 / 18 ) = 2 / 19 answer : option b"
Answer: b
Python program:
a = math.comb(10, 3)
b = 10 + 10 
c = math.comb(b, 3)
d = a / c
Problem: find the value of x from this equation ? 7 ( x - 1 ) = 21
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: 1 . divide both sides by 7 : 2 . simplify both sides : x - 1 = 3 3 . add 1 to both sides : x - 1 + 1 = 3 + 1 4 . simplify both sides : x = 4 b
Answer: b
Python program:
a = 21 / 7
b = a + 1
Problem: a person incurs 10 % loss by selling a watch for $ 100 . at what price should the watch be sold to earn 10 % profit ?
Options: a ) $ 100 , b ) $ 122 , c ) $ 150 , d ) $ 210 , e ) $ 170
Rationale: "let the new selling price be $ x ( 100 - loss % ) : ( 1 st s . p . ) = ( 100 + gain % ) : ( 2 nd s . p . ) ( 100 - 10 ) / 100 = ( 100 + 10 ) / x x = 110 * 100 / 90 = 122 approximately answer is b"
Answer: b
Python program:
a = 10 / 100
b = 1 - a
c = 100 / b
Problem: a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 30 paisa . if the share of y is rs . 27 , what is the total amount ?
Options: a ) 388 , b ) 105 , c ) 288 , d ) 266 , e ) 281
Rationale: x : y : z = 100 : 45 : 30 20 : 9 : 6 9 - - - 27 35 - - - ? = > 105 answer : b
Answer: b
Python program:
a = 100 / 45
b = a * 27
c = 30 / 45
d = c * 27
e = b + d 
f = e + 27
Problem: an association of mathematics teachers has 1,500 members . only 525 of these members cast votes in the election for president of the association . what percent of the total membership voted for the winning candidate if the winning candidate received 40 percent of the votes cast ?
Options: a ) 75 % , b ) 58 % , c ) 42 % , d ) 34 % , e ) 14 %
Rationale: "total umber of members = 1500 number of members that cast votes = 525 since , winning candidate received 40 percent of the votes cast number of votes for winning candidate = ( 40 / 100 ) * 525 = 210 percent of total membership that voted for winning candidate = ( 210 / 1500 ) * 100 = 14 % answer e"
Answer: e
Python program:
a = 40 / 100
b = a * 525
c = 4 ** 2
d = 100 * c
e = b / d
f = e * 100
Problem: to fill a tank , 25 buckets of water is required . how many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to 3 / 5 of its present ?
Options: a ) 41.66667 , b ) 60.5 , c ) 63.5 , d ) 62.5 , e ) 64.5
Rationale: "let capacity of 1 bucket = x capacity of the tank = 25 x new capacity of the bucket = 3 x / 5 hence , number of buckets needed = 25 x / ( 3 x / 5 ) = ( 25 × 5 ) / 3 = 41.66667 answer is a ."
Answer: a
Python program:
a = 4 + 1 
b = 25 * a
c = b / 2
Problem: salesperson a ' s compensation for any week is $ 300 plus 6 percent of the portion of a ' s total sales above $ 1,000 for that week . salesperson b ' s compensation for any week is 8 percent of b ' s total sales for that week . for what amount of total weekly sales would both salepeople earn the same compensation ?
Options: a ) $ 21,000 , b ) $ 12,000 , c ) $ 15,000 , d ) $ 4,500 , e ) $ 4,000
Rationale: "sometime , setting up an equation is an easy way to go with : 300 + 0.06 ( x - 1000 ) = 0.08 x x = 12,000 ans : b"
Answer: b
Python program:
a = 6 / 100
b = a * 1
c = 300 - b
d = 8 / 100
e = 6 / 100
f = d - e
g = c / f
h = 6 / 100
i = h * 1
j = 300 - i
k = 8 / 100
l = 6 / 100
m = k - l
n = j / m
o = g + n 
p = o / 1
Problem: ritesh and co . generated revenue of rs . 1,800 in 2006 . this was 12.5 % of its gross revenue . in 2007 , the gross revenue grew by rs . 2,500 . what is the percentage increase in the revenue in 2007 ?
Options: a ) 17.36 % , b ) 20 % , c ) 25 % , d ) 50 % , e ) none of these
Rationale: "explanation : given , ritesh and co . generated revenue of rs . 1,800 in 2006 and that this was 12.5 % of the gross revenue . hence , if 1800 is 12.5 % of the revenue , then 100 % ( gross revenue ) is : = > ( 100 / 12.5 ) × 1800 . = > 14,400 . hence , the total revenue by end of 2007 is rs . 14,400 . in 2006 , revenue grew by rs . 2500 . this is a growth of : = > ( 2500 / 14400 ) × 100 . = > 17.36 % . answer : a"
Answer: a
Python program:
a = 1 + 4 
b = 2 * a
c = b * 100
d = 2 * c
e = 1 + 4 
f = e * 100
g = d + f 
h = 1 + 4 
i = 2 * h
j = i * 100
k = 2 + 4 
l = k * 100
m = j + l 
n = 12 / 5
o = m / n
p = g / o
q = p * 100
Problem: there are 28 stations between kolkatta and chennai . how many second class tickets have to be printed , so that a passenger can travel from any station to any other station ?
Options: a ) 870 , b ) 970 , c ) 1070 , d ) 1000 , e ) 800
Rationale: the total number of stations = 30 from 30 stations we have to choose any two stations and the direction of travel ( i . e . , kolkatta to chennai is different from chennai to kolkatta ) in 30 p 2 ways . 30 p 2 = 30 * 29 = 870 answer : a
Answer: a
Python program:
a = 3 * 10
b = a * 28
Problem: a contractor is engaged for 30 days on the condition that he receives rs . 25 for each day he works & is fined rs . 7.50 for each day is absent . he gets rs . 490 in all . for how many days was he absent ?
Options: a ) 8 , b ) 10 , c ) 15 , d ) 17 , e ) 19
Rationale: 30 * 25 = 750 490 - - - - - - - - - - - 260 25 + 7.50 = 32.5 260 / 32.5 = 8 a
Answer: a
Python program:
a = 30 * 7
b = a + 490 
c = 25 + 7 
d = b / c
e = 30 - d
Problem: albert is 2 times mary ’ s age and 4 times as old as betty . mary is 10 years younger than albert . how old is betty ?
Options: a ) 5 , b ) 8 , c ) 10 , d ) 12 , e ) 15
Rationale: "a = 2 m = m + 10 m = 10 a = 20 a = 4 b , and so b = 5 the answer is a ."
Answer: a
Python program:
a = 2 * 10
b = a / 4
Problem: a worker is paid rs . 20 / - for a full days work . he works 11 / 32 / 31 / 8.3 / 4 days in a week . what is the total amount paid for that worker ?
Options: a ) 56.5 rupees , b ) 58.5 rupees , c ) 57.5 rupees , d ) 59.5 rupees , e ) 55.5 rupees
Rationale: the total days worked = 1 + 0.333 + 0.667 + 0.125 + 0.75 = 2.875 days amount for 2.875 days is ( 2.875 * 20 ) 57.5 rupees answer : c
Answer: c
Python program:
a = 1 / 3
b = 1 + a 
c = 2 / 3
d = b + c 
e = 2 * 4
f = 1 / e
g = d + f 
h = 3 / 4
i = g + h 
j = i * 20
Problem: how many odd factors does 270 have ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: "start with the prime factorization : 270 = 2 * 3 * 5 for odd factors , we put aside the factor of two , and look at the other prime factors . set of exponents = { 1 , 1 } plus 1 to each = { 2 , 2 } product = 2 * 2 = 4 therefore , there are 4 odd factors of 270 . answer : b ."
Answer: b
Python program:
a = 4 + 2 
b = a + 1 
c = b + 1
Problem: find a number such that when 15 is subtracted from 7 times the number , the results is more than twice the number ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: solution let the number be x . = then , 7 x - 15 = 2 x + 10 = 5 x = 25 ‹ = › x = 5 . hence the required number is 5 . answer d
Answer: d
Python program:
a = 15 + 10 
b = 7 - 2
c = a / b
Problem: having received his weekly allowance , a student spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 1.00 at the candy store . what is this student ’ s weekly allowance ?
Options: a ) $ 2.75 , b ) $ 3.25 , c ) $ 3.75 , d ) $ 4.25 , e ) $ 4.75
Rationale: "let x be the value of the weekly allowance . ( 2 / 3 ) ( 2 / 5 ) x = 100 cents ( 4 / 15 ) x = 100 x = $ 3.75 the answer is c ."
Answer: c
Python program:
a = 3 * 5
b = a * 1
c = b / 4
Problem: if 2 | 2 – e | = 5 , what is the sum of all the possible values for e ?
Options: a ) 1 / 2 , b ) 2 , c ) 5 / 2 , d ) 4 , e ) 5
Rationale: if e < 2 , then 2 - e = 5 / 2 ; e = - 1 / 2 if e > 2 , then e - 2 = 5 / 2 ; e = 9 / 2 9 / 2 - 1 / 2 = 8 / 2 = 4 = d
Answer: d
Python program:
a = 5 / 2
b = 2 - a
c = 5 / 2
d = c + 2 
e = b + d
Problem: the market value of a certain machine decreased by 10 percent of its purchase price each year . if the machine was purchased in 1982 for its market value of $ 8,000 , what was its market value two years later ?
Options: a ) $ 8,000 , b ) $ 5,600 , c ) $ 3,200 , d ) $ 6,400 , e ) $ 800
Rationale: d market value in 1982 = $ 8000 market value in 1983 = $ 8000 - ( $ 8000 x 10 / 100 ) = 8000 - 800 = $ 7200 market value in 1984 = market value in 1983 - ( 10 % of $ 8000 ) = 7200 - 800 = $ 6400
Answer: d
Python program:
a = 100 * 10
b = 2 * 4
c = a * b
d = 100 * 10
e = 2 * 4
f = d * e
g = 10 / 100
h = g * 2
i = f * h
j = c - i
Problem: fox jeans regularly sell for $ 15 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 5 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discounts rates is 18 percent , what is the discount rate on pony jeans ?
Options: a ) 9 % , b ) 10 % , c ) 34.4 % , d ) 12 % , e ) 15 %
Rationale: "you know that fox jeans costs $ 15 , and pony jeans costs $ 18 , you also know that 3 pairs of fox jeans and 2 pairs of pony jeans were purchased . so 3 ( 15 ) = 45 - fox 2 ( 18 ) = 36 - pony the total discount discount is $ 5 and you are asked to find the percent discount of pony jeans , so 45 ( 18 - x ) / 100 + 36 ( x ) / 100 = 5 or 45 * 18 - 45 * x + 36 * x = 5 * 100 or 9 x = - 5 * 100 + 45 * 18 x = 310 / 9 = 34.4 c"
Answer: c
Python program:
a = 18 / 100
b = 18 / 100
c = 18 * 2
d = b * c
e = 5 - d
f = 15 * 3
g = 18 * 2
h = f - g
i = e / h
j = a - i
k = j * 100
Problem: if | y + 5 | = 8 , what is the sum of all the possible values of y ?
Options: a ) - 14 , b ) - 13 , c ) - 8 , d ) - 12 , e ) - 10
Rationale: "there will be two cases y + 5 = 8 or y + 5 = - 8 = > y = 3 or y = - 13 sum of both the values will be - 13 + 3 = - 10 answer : e"
Answer: e
Python program:
a = 8 - 5
b = negate - (
c = a + b
Problem: a and b complete a work in 10 days . a alone can do it in 14 days . if both together can do the work in how many days ?
Options: a ) 5.8 days , b ) 4.78 days , c ) 6.25 days , d ) 3.15 days , e ) 2.75 days
Rationale: 1 / 10 + 1 / 14 = 6 / 35 35 / 6 = 5.8 days answer : a
Answer: a
Python program:
a = 1/(10)
b = 1/(14)
c = a + b 
d = 1/(c)
Problem: if jake loses 33 pounds , he will weigh twice as much as his sister . together they now weigh 153 pounds . what is jake ' s present weight , in pounds ?
Options: a ) 131 , b ) 135 , c ) 113 , d ) 147 , e ) 188
Rationale: "j = jake ’ s current weight , in pounds s = sister ’ s current weight , in pounds we are told that “ if jake loses 8 pounds , he will weigh twice as much as his sister . we put this into an equation : j – 33 = 2 s j = 2 s + 33 ( equation 1 ) next , we are told that “ together they now weigh 153 pounds . ” we can also put this into an equation . j + s = 153 ( equation 2 ) to solve this equation , we can substitute 2 s + 8 from equation 1 for the variable j in equation 2 : 2 s + 33 = 153 - s 3 s = 120 s = 40 j + 40 = 153 j = 113 answer : c"
Answer: c
Python program:
a = 153 - 33
b = a / 3
c = b * 2
d = c + 33
Problem: the value of a machine depreciates at 24 % per annum . if its present value is $ 1 , 50,000 , at what price should it be sold after two years such that a profit of $ 24,000 is made ?
Options: a ) $ 250640 , b ) $ 430640 , c ) $ 120640 , d ) $ 110640 , e ) $ 150640
Rationale: "the value of the machine after two years = 0.76 * 0.76 * 1 , 50,000 = $ 86,640 sp such that a profit of $ 24,000 is made = 86,640 + 24,000 = $ 1 , 10,640 d"
Answer: d
Python program:
a = 24 / 100
b = 1 - a
c = 24 / 100
d = 1 - c
e = b * d
f = 100 * 100
g = math.sqrt(100)
h = f * g
i = math.sqrt(100)
j = i / 2
k = j * 100
l = k * 100
m = h + l 
n = e * m
o = 24 + 2 
p = o * 100
q = math.sqrt(100)
r = p * q
s = n + r
Problem: a vendor buys 10 t - shirts at an average price of $ 14 per t - shirt . he then buys 15 more t - shirts at an average price of $ 11 per t - shirt . what is the average price v per t - shirt that the vendor paid for these purchases ?
Options: a ) $ 12.20 , b ) $ 12.50 , c ) $ 12.55 , d ) $ 12.70 , e ) $ 13.00
Rationale: "correct answer : a explanation : the relevant formula for this problem is average v = ( sum ) / ( number of terms ) . another way to look at the formula is sum = average x number of terms . for the first purchase , the vendor ' s sum ( total cost ) was $ 140 , since 14 x 10 = 140 . for the second purchase , the vendor ' s cost was $ 165 , since 11 x 15 = 165 . the grand sum is then $ 140 + $ 165 , which equals $ 305 . the total number of shirts purchased was 25 , so to get the average price per shirt , we divide 305 by 25 , which equals $ 12.20 . as a result , the correct answer is a . note : a relative understanding of weighted average offers a shortcut to this problem . because the true average of 11 and 14 is 12.5 , but the vendor sells more shirts at the lower price than at the higher price , the weighted average must be less than $ 12.50 ; only answer choice a is a possibility ."
Answer: a
Python program:
a = 10 + 14 
b = a / 2
c = const_0_25 + const_0_25 
d = b + c
Problem: if 5 machines can produce 20 units in 10 hours , how long would it take 20 machines to produce 120 units ?
Options: a ) 50 hours , b ) 40 hours , c ) 15 hours , d ) 12 hours , e ) 8 hours
Rationale: "here , we ' re told that 5 machines can produce 20 units in 10 hours . . . . that means that each machine works for 10 hours apiece . since there are 5 machines ( and we ' re meant to assume that each machine does the same amount of work ) , then the 5 machines equally created the 20 units . 20 units / 5 machines = 4 units are made by each machine every 10 hours now that we know how long it takes each machine to make 4 units , we can break this down further if we choose to . . . 10 hours / 4 units = 2.5 hours per unit when 1 machine is working . the prompt asks us how long would it take 20 machines to produce 120 units . if 20 machines each work for 2.5 hours , then we ' ll have 20 units . since 120 units is ' 6 times ' 20 , we need ' 6 times ' more time . ( 2.5 hours ) ( 6 times ) = 15 hours final answer : [ reveal ] spoiler : c"
Answer: c
Python program:
a = 20 / 10
b = a / 5
c = b * 20
d = 120 / c
Problem: 66 cubic centimetres of silver is drawn into a wire 1 mm in diameter . the length if the wire in meters will be :
Options: a ) 76 m
b ) 80 m
c ) 84 m
d ) 88 m
e ) none of these
Rationale: explanation : let the length of the wire be h radius = 1 / 2 mm = 120 cm π r 2 h = 66 22 / 7 ∗ 1 / 20 ∗ 1 / 20 ∗ h = 66 = > h = 66 ∗ 20 ∗ 20 ∗ 7 / 22 = 8400 cm = 84 m option c
Answer: c
Python program:
a = 1 / 2
b = a ** 2
c = b * math.pi
d = 66 / c
Problem: a certain sum of money is divided among a , b and c so that for each rs . a has , b has 65 paisa and c 40 paisa . if c ' s share is rs . 48 , find the sum of money ?
Options: a ) 288 , b ) 262 , c ) 246 , d ) 205 , e ) 267
Rationale: "a : b : c = 100 : 65 : 40 = 20 : 13 : 8 8 - - - - 48 41 - - - - ? = > rs . 246 answer : c"
Answer: c
Python program:
a = 48 / 40
b = 100 + 65 
c = b + 40 
d = a * c
Problem: a is four times as fast as b . if b alone can do a piece of work in 60 days , in what time can a and b together complete the work ?
Options: a ) 10 , b ) 12 , c ) 22 , d ) 28 , e ) 20
Rationale: a can do the work in 60 / 4 i . e . , 15 days . a and b ' s one day ' s work = 1 / 15 + 1 / 60 = ( 4 + 1 ) / 60 = 1 / 12 so a and b together can do the work in 12 days . answer : b
Answer: b
Python program:
a = 60 / 4
b = 1/(a)
c = 1/(60)
d = b + c 
e = 1/(d)
Problem: 8 men can do a piece of work in 12 days . 4 women can do it in 48 days and 10 children can do it in 24 days . in how many days can 10 men , 4 women and 10 children together complete the piece of work ?
Options: a ) 5 days , b ) 15 days , c ) 28 days , d ) 6 days , e ) 7 days
Rationale: explanation : 1 man ’ s 1 day ’ s work = 1 / 8 × 12 = 1 / 96 10 men ’ s 1 day ’ s work = 1 × 10 / 96 = 5 / 48 1 woman ’ s 1 day ’ s work = 1 / 192 4 women ’ s 1 day ’ s work = 1 / 192 × 4 = 1 / 48 1 child ’ s 1 day ’ s work = 1 / 240 10 children ’ s 1 day ’ s work = 1 / 24 therefore , ( 10 men + 4 women + 10 children ) ’ s 1 day ’ s work = 5 / 48 + 1 / 48 + 1 / 24 = 8 / 48 = 1 / 6 the required no . of days = 6 days answer : option d
Answer: d
Python program:
a = 24 * 10
b = 1/(a)
c = 10 * b
d = 12 * 8
e = 1/(d)
f = e * 10
g = 48 * 4
h = 1/(g)
i = h * 4
j = f + i 
k = c + j 
l = 1/(k)
Problem: if a positive integer n has 211 factors , then how many prime factors does n have ?
Options: a ) 3 , b ) 2 , c ) can not be determined , d ) 4 , e ) 1
Rationale: let the factor be a ^ x * b ^ y . . . . . so ( x + 1 ) ( y + 1 ) . . . . . = 211 . . now 211 is a prime number . . . so only one variable x or y is 210 and the others are 0 . . ( 210 + 1 ) ( 0 + 1 ) . . . so the number becomes a ^ 210 . . thus only one prime factor is there .
Answer: e
Python program:
a = 211 / 211
Problem: rahim bought 65 books for rs . 1150 from one shop and 50 books for rs . 920 from another . what is the average price he paid per book ?
Options: a ) rs . 17 , b ) rs . 18 , c ) rs . 12 , d ) rs . 11 , e ) rs . 10
Rationale: "average price per book = ( 1150 + 920 ) / ( 65 + 50 ) = 2070 / 115 = rs . 18 answer : b"
Answer: b
Python program:
a = 1150 + 920 
b = 65 + 50 
c = a / b