euclaise/mathqa_programs huggingface dataset:
Problem: a , b and c started a partnership business by investing rs . 30000 , rs . 45000 , rs . 50000 respectively . at the end of the year , the profit were distributed among them . if c ' s share of profit is 36000 , what is the total profit ?
Options: a ) 70000 , b ) 60000 , c ) 80000 , d ) 90000 , e ) 50000
Rationale: "a : b : c = 30000 : 45000 : 50000 = 6 : 9 : 10 let total profit = p then p ã — 10 / 25 = 36000 p = ( 36000 ã — 25 ) / 10 = 90000 answer is d ."
Answer: d
Python program:
a = 30000 / 50000
b = a * 36000
c = 45000 / 50000
d = c * 36000
e = b + d 
f = e + 36000
Problem: if the number is decreased by 5 and divided by 7 the result is 7 . what would be the result if 4 is subtracted and divided by 10 ?
Options: a ) 4 , b ) 7 , c ) 8 , d ) 5 , e ) 3
Rationale: "explanation : let the number be x . then , ( x - 5 ) / 7 = 7 = > x - 5 = 49 x = 54 . : ( x - 4 ) / 10 = ( 54 - 4 ) / 10 = 5 answer : option d"
Answer: d
Python program:
a = 7 * 7
b = a + 5 
c = b - 4
d = c / 10
Problem: integer m has 4 different prime factors and n has 3 different prime factors . if m and n has the greatest common factor of 15 , how many different prime factors does mn have ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: as m and n has gcf of 15 , 3 * 5 should be common factor for both m and n . m = 3 * 5 * p 1 * p 2 n = 3 * 5 * p 3 mn = 3 ^ 2 * 5 ^ 2 * p 1 * p 2 * p 3 mn has prime numbers of 3,5 , p 1 , p 2 p 3 b
Answer: b
Python program:
a = 4 + 1
Problem: if x ^ 2 + ( 1 / x ^ 2 ) = 5 , x ^ 4 + ( 1 / x ^ 4 ) = ?
Options: a ) 23 , b ) 11 , c ) 12 , d ) 14 , e ) 15
Rationale: "- > x ^ 4 + ( 1 / x ^ 4 ) = ( x ^ 2 ) ^ 2 + ( 1 / x ^ 2 ) ^ 2 = ( x ^ 2 + 1 / x ^ 2 ) ^ 2 - 2 x ^ 2 ( 1 / x ^ 2 ) = 5 ^ 2 - 2 = 23 . thus , the answer is a ."
Answer: a
Python program:
a = 2 ** 2
b = a - 2
Problem: on a sum of money , the s . i . for 2 years is $ 600 , while the c . i . is $ 609 , the rate of interest being the same in both the cases . the rate of interest is ?
Options: a ) 2 % , b ) 3 % , c ) 4 % , d ) 5 % , e ) 6 %
Rationale: "difference in c . i . and s . i for 2 years = $ 609 - $ 600 = $ 9 s . i for one year = $ 300 s . i . on $ 300 for 1 year = $ 9 rate = ( 100 * 9 ) / ( 300 ) = 3 % the answer is b ."
Answer: b
Python program:
a = 609 - 600
b = 100 * a
c = 600 / 2
d = b / c
Problem: in arun ' s opinion , his weight is greater than 62 kg but leas than 72 kg . his brother does not agree with arun and he thinks that arun ' s weight is greater than 60 kg but less than 70 kg . his mother ' s view is that his weight can not be greater than 65 kg . if all of them are correct in their estimation , what is the average of diferent probable weights of arun ?
Options: a ) 86.5 kg , b ) 63.5 kg , c ) 46.5 kg , d ) 26.5 kg , e ) 16.5 kg
Rationale: "let arun ' s weight be x kg . according to arun , 62 < x < 72 . according to arun ' s brother , 60 < x < 70 . according to arun ' s mother , x < 65 . the values satisfying all the above conditions are 63 and 64 . required average = ( 63 + 64 ) / 2 = 63.5 kg answer : b"
Answer: b
Python program:
a = 62 + 1 
b = 65 + a 
c = b / 2
Problem: x and y are two towns . ganesh covers the distance from x to y at an average speed of 60 km / hr . however , he covers the distance from y to x at an average speed of 36 km / hr . his average speed during the whole journey in km / hr . is :
Options: a ) 45 , b ) 43 , c ) 40 , d ) 38 , e ) 29
Rationale: solution : average speed = 2 xy / x + y = 2 * 60 * 36 / 60 + 36 = 45 answer : a
Answer: a
Python program:
a = 60 - 10
b = a + 100 
c = 60 - 10
d = c + 100 
e = b + d 
f = 60 - 10
g = f + 100 
h = g / 60
i = 60 - 10
j = i + 100 
k = j / 36
l = h + k 
m = e / l
Problem: ( 12 ) ^ 3 x 6 ^ 4 ÷ 432 = ?
Options: a ) 5184 , b ) 5060 , c ) 5148 , d ) 5084 , e ) none of them
Rationale: = ( 12 ) ^ 3 x 6 ^ 4 / 432 = ( 12 ) ^ 3 x 6 ^ 4 / 12 x 6 ^ 2 = ( 12 ) ^ 2 x 6 ^ 2 = ( 72 ) ^ 2 = 70 answer is e
Answer: e
Python program:
a = 12 ** 3
b = 6 ** 4
c = a * b
d = c / 432
Problem: two cylinders are of the same height . their radii are in the ratio 1 : 3 . if the volume of the first cylinder is 40 cc . find the volume of the second cylinder ?
Options: a ) 360 cc
b ) 60 cc
c ) 300 cc
d ) 36 cc
e ) 39 cc
Rationale: r 1 = x r 2 = 3 x π * x 2 * h = 40 π 9 x 2 h = 40 * 9 = 360 answer : a
Answer: a
Python program:
a = 3 * 3
b = 40 * a
Problem: a grocer has a sale of rs . 2500 , rs . 4000 , rs . 3540 for 3 consecutive months . how much sale must he have in the fourth month so that he gets an average sale of rs . 2890 ?
Options: a ) rs . 3500 , b ) rs . 1520 , c ) rs . 4996 , d ) rs . 4000 , e ) rs . 900
Rationale: total sale for 5 months = rs . ( 2500 + 4000 + 3540 ) = rs . 10040 . required sale = rs . [ ( 2890 x 4 ) - 10040 ] = rs . ( 11560 - 10040 ) = rs . 1520 . b )
Answer: b
Python program:
a = 2890 * 4
b = a - 2500
c = b - 4000
d = c - 3540
Problem: if 3 ^ x * 4 ^ y = 4 , 782,969 and x – y = 14 , then x = ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "since 4 , 782,969 is an odd number , it is not a multiple of 4 . this means that y must equal zero . since x - y = 14 and y = 0 , then x = 14 . the answer is e ."
Answer: e
Python program:
a = 782 * 969
Problem: if x , y , and z are positive real numbers such that x + y - z = 100 , y - z + x = 120 , and z - x + y = 50 , then find the x + y + z value ?
Options: a ) 100 , b ) 120 , c ) 150 , d ) 200 , e ) 160
Rationale: "x + y - z = 100 , - - - - - - 1 ) y - z + x = 120 , - - - - - - 2 ) z - x + y = 50 - - - - - - 3 ) from ( 1 ) & ( 2 ) 2 z = 20 z = 10 from ( 2 ) & ( 3 ) 2 y = 170 y = 85 then x = 100 - 75 = 25 x + y + z = 120 correct option is b"
Answer: b
Python program:
a = 120 - 100
b = 50 - a
Problem: if the cost price of 10 articles is equal to the selling price of 20 articles , what is the % profit or loss made by the merchant ?
Options: a ) 25 % loss , b ) 25 % profit , c ) 20 % loss , d ) 20 % profit , e ) 50 % loss
Rationale: "let the cost price of 1 article be $ 1 . therefore , cost price of 10 articles = 10 * 1 = $ 10 the selling price of 20 articles = cost price of 10 articles = $ 10 . now , we know the selling price of 20 articles . let us find the cost price of 20 articles . cost price of 20 articles = 20 * 1 = $ 20 . therefore , profit made on sale of 20 articles = selling price of 20 articles - cost price of 20 articles = 10 - 20 = - $ 10 . as the profit is in the negative , the merchant has made a loss of $ 10 . therefore , % loss = loss / cp * 100 % loss = - 10 / 20 * 100 = 50 % loss . e"
Answer: e
Python program:
a = 100 * 20
b = a / 10
c = 100 - b
d = 100 * 20
e = d / 10
f = c / e
g = 100 * f
Problem: ( 0.76 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.76 ) ( power 2 ) + 0.076 + ( 0.1 ) ( power 2 ) is :
Options: a ) 0.66 , b ) 0.68 , c ) 0.96 , d ) 0.69 , e ) 0.76
Rationale: "given expression = ( 0.76 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.76 ) ( power 2 ) + ( 0.76 x 0.1 ) + ( 0.1 ) ( power 2 ) = a ( power 3 ) - b ( power 3 ) / a ( power 2 ) + ab + b ( power 2 ) = ( a - b ) = ( 0.76 - 0.1 ) = 0.66 answer is a ."
Answer: a
Python program:
a = 0 ** 76
b = 0 ** 1
c = a - b
d = 0 ** 76
e = d + 0 
f = 0 ** 1
g = e + f 
h = c / g
Problem: one - third of 1206 is what percent of 134 ?
Options: a ) 3 , b ) 30 , c ) 300 , d ) none of these , e ) can not be determined
Rationale: "answer let one - third of 1206 is n % of 134 . ∵ 1206 / 3 = ( n x 134 ) / 100 ∴ n = ( 402 x 100 ) / 134 = 300 correct option : c"
Answer: c
Python program:
a = 1206 / 3
b = a / 134
c = 100 * b
Problem: the digit sum of the year 2007 is 2 + 0 + 0 + 7 = 9 , which is a square number . how many years during the 20 - first century have a square digital sum ?
Options: a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17
Rationale: the twenty - first century runs from the year 2001 to 2100 inclusive , so with the exception of the year 2100 , for which the digital sum is three anyway , the first two digits of all the other years are fixed as 20 . hence for the sum of all the digits to be square the sum of the last two digits number be two less than a perfect square . as the maximum sum of the last two digits is 18 , the greatest sum will be 20 . therefore we can obtain digital sums of 4 , 9 , or 16 , with the last two digits adding to 2 , 7 , or 14 respectively . 4 : 2002 , 2011 , 2020 9 : 2007 , 2016 , 2025 , 2034 , 2043 , 2052 , 2061 , 2070 16 : 2059 , 2068 , 2077 , 2086 , 2095 that is , there are sixteen years during the twenty - first century for which the digital sum is square . answer : d
Answer: d
Python program:
a = 9 + 7
Problem: a certain automobile company ’ s best - selling model is the speedster . the speedster , like all of their other models , comes in coupe and convertible styles . 2 / 3 of the current inventory is speedsters , of which 4 / 5 are convertibles . if there are 40 vehicles that are not speedsters , how many speedster convertibles are there ?
Options: a ) 30 , b ) 64 , c ) 60 , d ) 70 , e ) 90
Rationale: total vehicle = 2 / 3 of speedster + 1 / 3 of others . speedster convertibles = 2 / 3 total vehicle * 4 / 5 given : 1 / 3 constitutes 40 vehicles . hence 2 / 3 constitutes 80 speedster convertibls = 80 * 4 / 5 = 64 b
Answer: b
Python program:
a = 2 / 3
b = 1 - a
c = 40 / b
d = 2 / 3
e = c * d
f = 4 / 5
g = e * f
Problem: earl can stuff advertising circulars into envelopes at the rate of 36 envelopes per minutes and ellen requires a minutes and half to stuff the same number of envelops . working together , how long will it take earl and ellen to stuff 180 envelopes
Options: a ) 6 minutes , b ) 5 minutes , c ) 7 minutes , d ) 3 minutes , e ) 4 minutes
Rationale: earl takes 1 min . for 36 envelopes . ellen takes 3 / 2 mins for the same . so ellen can stuff ( ( 36 ) / ( 3 / 2 ) ) in 1 min . i . e . , 24 envelopes a min . so both of them when work together can stuff 36 + 24 = 60 envelopes in 1 min . for 180 envelopes they will take 180 / 60 mins . i . e . , 3 mins . answer : d
Answer: d
Python program:
a = 3 / 2
b = 36 / a
c = 36 + b 
d = 180 / c
Problem: boy sells a book for rs . 810 he gets a loss of 10 % , to gain 10 % , what should be the sp ?
Options: a ) 430 , b ) 990 , c ) 550 , d ) 590 , e ) 600
Rationale: "cost price = 810 / 90 x 100 = 900 to gain 10 % = 900 x 10 / 100 = 90 sp = cp + gain = 900 + 90 = 990 answer : b"
Answer: b
Python program:
a = 10 / 100
b = 1 - a
c = 810 / b
d = 10 / 100
e = 1 - d
f = 810 / e
g = 10 / 100
h = f * g
i = c + h
Problem: a discount electronics store normally sells all merchandise at a discount of 2 percent to 50 percent off the suggested retail price . if , during a special sale , an additional 20 percent were to be deducted from the discount price , what would be the lowest possible price of an item costing $ 100 before any discount ?
Options: a ) $ 100.00 , b ) $ 40.00 , c ) $ 50.00 , d ) $ 30.00 , e ) $ 10.00
Rationale: "original price : 100 $ max first discount = - 50 % thus : 100 â ˆ — ( 1 â ˆ ’ 50 / 100 ) = 50 second discount on the discounted price = - 20 % thus : 50 â ˆ — ( 1 â ˆ ’ 20 / 100 ) = 40 answer b ."
Answer: b
Python program:
a = 50 + 20 
b = a / 100
c = 100 * b
Problem: how many pieces of 85 cm length can be cut from a rod of 34 meters long ?
Options: a ) 50 , b ) 40 , c ) 30 , d ) 20 , e ) 10
Rationale: "number of pieces = 3400 / 85 = 40 the answer is b ."
Answer: b
Python program:
a = 34 * 100
b = a / 85
Problem: if 525 / 999 = 0.525 , what is the 81 st digit to the right of the decimal point in the decimal equivalent of the fraction ?
Options: a ) - 1 , b ) 0 , c ) 3 , d ) 4 , e ) 5
Rationale: "0 . [ u ] 125 [ / u = 0.525525525 . . . . . every 3 rd digit is 5 and every multiple of 3 will be the digit 5 . since 81 is multiple of 3 , the 81 st digit is 5 . answer e"
Answer: e
Python program:
a = 2 + 3
Problem: p and q invested in a business . the profit earned was divided in the ratio 4 : 5 . if p invested rs 52000 , the amount invested by q is
Options: a ) 30000 , b ) 50000 , c ) 40000 , d ) 20000 , e ) 65000
Rationale: "let the amount invested by q = q 52000 : q = 4 : 5 ⇒ 52000 × 5 = 4 q ⇒ q = ( 52000 × 5 ) / 4 = 65000 answer is e ."
Answer: e
Python program:
a = 52000 / 4
b = a * 5
Problem: the number 152 is equal to the sum of the cubes of two integers . what is the product of those integers ?
Options: a ) 8 , b ) 15 , c ) 21 , d ) 27 , e ) 39
Rationale: "actually , decomposition into factors can easily give you the answer here . you should just do the decomposition of the right thing i . e . the options since they represent the product of those integers . since the sum of cubes is 152 , the numbers can not be larger than 5 since 6 ^ 3 itself is 216 . 21 , 27 , 39 - the factors are too large so ignore 8 - ( 2 , 4 ) does not satisfy 15 - ( 3 , 5 ) yes . 3 ^ 3 + 5 ^ 3 = 152 - answer answer : b"
Answer: b
Python program:
a = 152 / 2
b = 1 / 3
c = a ** b
d = math.floor(c)
e = 152 / 2
f = 1 / 3
g = e ** f
h = math.floor(g)
i = h ** 3
j = 152 - i
k = 1 / 3
l = j ** k
m = d * l
Problem: a goods train runs at the speed of 72 km / hr and crosses a 280 m long platform in 26 sec . what is the length of the goods train ?
Options: a ) 240 , b ) 277 , c ) 276 , d ) 270 , e ) 281
Rationale: "speed = 72 * 5 / 18 = 20 m / sec . time = 26 sec . let the length of the train be x meters . then , ( x + 280 ) / 26 = 20 x = 240 m . answer : a"
Answer: a
Python program:
a = 72 / 3600
b = a * 1000
c = b * 26
d = c - 280
Problem: a rectangular farm has to be fenced one long side , one short side and the diagonal . if the cost of fencing is rs . 13 per meter . the area of farm is 1200 m 2 and the short side is 30 m long . how much would the job cost ?
Options: a ) 1276 , b ) 1560 , c ) 2832 , d ) 1299 , e ) 1236
Rationale: "explanation : l * 30 = 1200 è l = 40 40 + 30 + 50 = 120 120 * 13 = 1560 answer : option b"
Answer: b
Python program:
a = 1200 / 30
b = 30 + a 
c = 30 ** 2
d = 1200 / 30
e = d ** 2
f = c + e 
g = math.sqrt(f)
h = b + g 
i = h * 13
Problem: a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 50 sq . feet , how many feet of fencing will be required ?
Options: a ) 34 , b ) 40 , c ) 25 , d ) 88 , e ) 78
Rationale: "we have : l = 20 ft and lb = 50 sq . ft . so , b = 2.5 ft . length of fencing = ( l + 2 b ) = ( 20 + 5 ) ft = 25 ft . answer : c"
Answer: c
Python program:
a = 50 / 20
b = a * 2
c = b + 20
Problem: the average weight of 24 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg . find the average weights of all the boys in the class .
Options: a ) 48.975 , b ) 42.255 , c ) 50 , d ) 51.255 , e ) 52.253
Rationale: "explanation : average weight of 24 boys = 50.25 total weight of 24 boys = 50.25 × 24 average weight of remaining 8 boys = 45.15 total weight of remaining 8 boys = 45.15 × 8 total weight of all boys in the class = ( 50.25 × 24 ) + ( 45.15 × 8 ) total boys = 24 + 8 = 32 average weight of all the boys = ( 50.25 × 24 ) + ( 45.15 × 8 ) / 32 = 48.975 answer : option a"
Answer: a
Python program:
a = 24 * 50
b = 8 * 45
c = a + b 
d = 24 + 8 
e = c / d
Problem: if ' y ' is a positive integer exactly divisible by 4 or 5 but not divisible by 8 . what could possibly be the value of ' y ' ?
Options: a ) 40 , b ) 80 , c ) 20 , d ) 24 , e ) 36
Rationale: 40 and 80 are both divisible by 4 and 5 but also by 8 . so they are not the right answer . 24 and 36 are both clearly not divisible by 5 ( not correct ) 20 is both divisible by 4 and 5 but not by 8 . answer : ( c )
Answer: c
Python program:
a = 4 * 5
Problem: two goods trains each 625 m long are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 40 , b ) 45 , c ) 48 , d ) 60 , e ) 44
Rationale: "relative speed = 45 + 30 = 75 km / hr . 75 * 5 / 18 = 125 / 6 m / sec . distance covered = 625 + 625 = 1250 m . required time = 1250 * 6 / 125 = 60 sec . answer : option d"
Answer: d
Python program:
a = 45 + 30
Problem: how many figures are required to number the pages the pages of a book containing 1000 pages ?
Options: a ) 2793 , b ) 2333 , c ) 2993 , d ) 2893 , e ) 2693
Rationale: 1 to 9 = 9 * 1 = 9 10 to 99 = 90 * 2 = 180 100 to 999 = 900 * 3 = 2700 1000 = 4 - - - - - - - - - - - 2893 answer : d
Answer: d
Python program:
a = 1000 / 10
b = a / 10
c = b - 1
d = 1000 / 10
e = d - 1
f = 1000 / 10
g = f / 10
h = g - 1
i = e - h
j = c + i 
k = 1000 - 1
l = 1000 / 10
m = l - 1
n = k - m
o = n * 3
p = j + o
Problem: a merchant sells an item at a 20 % discount , but still makes a gross profit of 50 percent of the cost . what percent of the cost would the gross profit on the item have been if it had been sold without the discount ?
Options: a ) 20 % , b ) 40 % , c ) 87.5 % , d ) 60 % , e ) 75 %
Rationale: "original sp = x cost = c current selling price = . 8 x ( 20 % discount ) . 8 x = 1.5 c ( 50 % profit ) x = 1.5 / . 8 * c x = 15 / 8 c original selling price is 1.875 c which is 87.5 % profit answer c"
Answer: c
Python program:
a = 100 - 20
b = a - 50
c = 100 - b
Problem: a taxi company charges $ 1.40 for the first quarter of a mile and fifteen cents for each additional quarter of a mile . what is the maximum distance someone could travel with $ 4.90 ?
Options: a ) 4 miles , b ) 4 1 / 4 miles , c ) 4 3 / 4 miles , d ) 5 1 / 2 miles , e ) 6 miles
Rationale: "if we start out with $ 4.90 and have to spend $ 1.40 for the first quarter - mile , we will have $ 3.50 left to spend on quarter - mile intervals . since $ 3.50 / $ 0.15 = 23.33 , we can buy 23.33 more quarter - miles , and will travel 24.33 quarter miles in all : 24.33 × 1 / 4 = 6 miles . the correct answer is choice ( e ) ."
Answer: e
Python program:
a = 4 - 90
b = a * 100
c = b / 3
d = c / 4
Problem: the difference between a number and its three - fifths is 50 . what is the number ?
Options: a ) 75 , b ) 100 , c ) 125 , d ) can not be determined , e ) none of these
Rationale: "suppose the number is n . then n - 3 ⁄ 5 n = 50 ⇒ 2 n ⁄ 5 = 50 ∴ n = 50 × 52 = 125 answer . c"
Answer: c
Python program:
a = 50 + 4 
b = a ** 4
Problem: john and david can finish a job together in 6 hours . if john can do the job by himself in 8 hours , what percent of the job does david do ?
Options: a ) 35 % , b ) 45 % , c ) 25 % , d ) 30 % , e ) 20 %
Rationale: "you can also plug in numbers . for example , bob and alice work at a donut factory and make 24 donuts which is the job ( i picked this as a smart number ) . john on his own works 24 / 8 = 3 donuts per hour . john and david work 24 / 6 = 4 donuts per hour so david works 1 donuts / hour to find out the percentage , david works 1 donuts / hr x 6 hours = 6 donuts per hour . therefore 6 donuts / 24 donuts = 1 / 4 = 25 % answer : c"
Answer: c
Python program:
a = 1/(8)
b = 6 - a
c = b * 100
Problem: a and b finish the job in 15 days . while a , b and c can finish it in 10 days . c alone will finish the job in
Options: a ) 40 days , b ) 30 days , c ) 60 days , d ) 70 days , e ) 50 days
Rationale: "explanation : 10 = ( 15 * x ) / ( 15 + x ) 150 + 10 x = 15 x 5 x = 150 x = 30 answer : option b"
Answer: b
Python program:
a = 10 * 15
b = 15 - 10
c = a / b
Problem: in what ratio should a variety of rice costing rs . 10 per kg be mixed with another variety of rice costing rs . 13.25 per kg to obtain a mixture costing rs . 10.75 per kg ?
Options: a ) 2 : 1 , b ) 1 : 2 , c ) 5 : 1 , d ) 4 : 1 , e ) 3 : 1
Rationale: "let us say the ratio of the quantities of cheaper and dearer varieties = x : y by the rule of allegation , x / y = ( 13.25 - 10.75 ) / ( 10.75 - 10 ) = 6 / 3 = 2 / 1 answer : a"
Answer: a
Python program:
a = 13 - 25
b = 13 - 25
c = a / b
d = 13 - 25
e = 13 - 25
f = d / e
g = 1 - f
h = c / g
Problem: a 9 - 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 / 5 , b ) 2 / 7 , c ) 2 / 9 , d ) 3 / 10 , e ) 4 / 11
Rationale: "the longer wire will form a square with an area more than 4 if the wire is cut at a point within one meter of either end . the probability of this is 2 / 9 . the answer is c ."
Answer: c
Python program:
a = square_perimeter / (
Problem: the value of a scooter depreciates in such a way that its value of the end of each year is 3 / 4 of its value of the beginning of the same year . if the initial value of the scooter is rs . 40,000 , what is the value at the end of 1 year ?
Options: a ) 3277 , b ) 2977 , c ) 30000 , d ) 6077 , e ) 17112
Rationale: "explanation : 40,000 * ( 3 / 4 ) ^ 1 answer : c"
Answer: c
Python program:
a = 100 * 100
b = 4 * a
c = 3 / 4
d = c ** 1
e = b * d
Problem: the greatest number by which the product of 3 consecutive multiples of 4 is always divisible is
Options: a ) 54 , b ) 76 , c ) 152 , d ) 384 , e ) none of these
Rationale: solution required number = product of first three multiplies of 3 = ( 4 ã — 8 ã — 12 ) = 384 . answer d
Answer: d
Python program:
a = 4 * 2
b = 4 * a
c = 4 * 3
d = b * c
Problem: if both 5 ^ 2 and 3 ^ 3 are factors of n x ( 2 ^ 5 ) x ( 6 ^ 2 ) x ( 7 ^ 3 ) , what is the smallest possible positive value of n ? .
Options: a ) 25 , b ) 27 , c ) 45 , d ) 75 , e ) 125
Rationale: if both 5 ^ 2 & 3 ^ 3 are factors , then they must be present in the number . leaving rest of the prime factors and splitting 6 ^ 2 into 3 ^ 2 * 2 ^ 3 . the number is lacking 5 ^ 2 & a 3 , so that 5 ^ 2 and 3 ^ 3 is a factor . hence the smallest number is 5 ^ 2 * 3 = 75 answer : d
Answer: d
Python program:
a = 5 ** 2
b = a * 3
Problem: rajesh spends 40 % of his monthly salary on food , 20 % of the medicines and saves 60 % of the remaining amount . if his monthly salary is rs . 15000 , how much money does he save every month ?
Options: a ) rs . 1000 , b ) rs . 2596 , c ) rs . 4320 , d ) rs . 6489 , e ) rs . 4789
Rationale: explanation : ramesh ' s monthly income = rs . 15000 he spends 40 % on food . the total money spent on food = 40 / 100 * 15000 = rs . 6000 now , his monthly remaining income = rs . 15000 – rs . 6000 = rs . 9000 out of rs . 9000 , he spends 20 % on medicines . the total money spent on medicines = 20 / 100 * 9000 = rs . 1800 now , his monthly remaining income = rs . 9000 – rs . 1800 = rs . 7200 out of rs . 7200 , he saves 600 % . amount saved = 60 / 100 * 7200 = rs . 4320 answer : c
Answer: c
Python program:
a = 60 / 100
b = 100 - 40
c = b / 100
d = a * c
e = 100 - 20
f = e / 100
g = d * f
h = g * 15000
Problem: the average ( arithmetic mean ) of 14 , 32 , and 53 is 3 more than the average of 21 , 47 , and x . what is x ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: "the average of 14 , 32 , and 53 is 33 . the average of 21 , 47 and x is 30 . then 21 + 47 + x = 90 . x = 22 . the answer is c ."
Answer: c
Python program:
a = 14 + 32 
b = a + 53 
c = 3 * 3
d = c + 21 
e = d + 47 
f = b - e
Problem: how long does a train 165 meters long running at the rate of 36 kmph take to cross a bridge 660 meters in length ?
Options: a ) 33 , b ) 72 , c ) 55 , d ) 82.5 , e ) 62
Rationale: "explanation : t = ( 660 + 165 ) / 36 * 18 / 5 t = 82.5 answer : option d"
Answer: d
Python program:
a = 165 + 660 
b = 36 * const_0_2778
c = a / b
Problem: if √ 2 n = 64 , then the value of n is :
Options: a ) 6 , b ) 12 , c ) 24 , d ) 48 , e ) none
Rationale: sol . √ 2 n = 64 ⇔ ( 2 n ) 1 / 2 ⇔ 2 n / 2 = 26 ⇔ n / 2 = 6 ⇔ n = 12 . answer b
Answer: b
Python program:
a = math.log(64)
b = a * 2
Problem: a & b started a partnership business . a ' s investment was thrice the investment of b and the period of his investment was two times the period of investments of b . if b received rs 4500 as profit , what is their total profit ?
Options: a ) 28000 , b ) 30000 , c ) 31500 , d ) 34000 , e ) none of these
Rationale: "explanation : suppose b ' s investment = x . then a ' s investment = 3 x suppose bs period of investment = y , then a ' s period of investment = 2 y a : b = 3 x * 2 y : xy = 6 : 1 total profit * 1 / 7 = 4500 = > total profit = 4500 * 7 = 31500 . answer : option c"
Answer: c
Python program:
a = 1 * 1
b = 3 * 2
c = 1 * 1
d = b + c 
e = a / d
f = 4500 / e