euclaise/mathqa_programs huggingface dataset:
Problem: a man , a woman and a boy can together complete a piece of work in 3 days . if a man alone can do it in 6 days and a boy alone in 12 days , how long will a woman take to complete the work ?
Options: a ) 12 days , b ) 10 days , c ) 9 days , d ) 8 days , e ) 11 days
Rationale: "explanation : ( 1 man + 1 woman + 1 boy ) ’ s 1 day ’ s work = 1 / 3 1 man ’ s 1 day work = 1 / 6 1 boy ’ s 1 day ’ s work = 1 / 1 ( 1 man + 1 boy ) ‘ s 1 day ’ s work = 1 / 6 + 1 / 12 = 1 / 4 therefore , 1 woman ’ s 1 day ’ s work = 1 / 3 – 1 / 4 = 1 / 12 therefore , the woman alone can finish the work in 12 days . answer : option a"
Answer: a
Python program:
a = 1/(3)
b = 1/(6)
c = 1/(12)
d = b + c 
e = a - d
f = 1/(e)
Problem: carmen made a sculpture from small pieces of wood . the sculpture is 2 feet 6 inches tall . carmen places her sculpture on a base that is 12 inches tall . how tall are the sculpture andbase together ?
Options: a ) 3.1 feet , b ) 3.2 feet , c ) 3.3 feet , d ) 3.4 feet , e ) 3.83 feet
Rationale: "we know 1 feet = 12 inch then 2 feet = 24 inch 24 + 10 = 34 then 34 + 12 = 44 46 / 12 = 3.83 feet answer : e"
Answer: e
Python program:
a = 2 + 6 
b = a * 2
c = b + 6 
d = c + 12 
e = 2 + 6 
f = d / e
Problem: the cost of 3 pens and 5 pencils is rs . 340 . also the cost of one pen and one pencil is in the ratio of 4 : 1 respectively . what is the cost of one dozen pens ?
Options: a ) rs . 960 , b ) rs . 250 , c ) rs . 300 , d ) rs . 150 , e ) none of these
Rationale: "explanation : let the cost of one pen is ‘ 4 x ’ and pencil is ‘ x ’ 3 x 4 x + 5 x = rs . 340 12 x + 5 x = rs . 340 x = 340 / 17 = 20 : . cost of 1 pen = 4 x = 4 x 20 = 80 : . cost of 12 pens , i . e . ( one dozen ) = 80 x 12 = rs . 960 answer : option a"
Answer: a
Python program:
a = 3 * 4
b = 3 + 1 
c = 340 / b
d = a * c
Problem: the length of a room is 5.5 m and width is 3.75 m . what is the cost of paying the floor by slabs at the rate of $ 400 per sq . metre .
Options: a ) $ 8250 , b ) $ 8350 , c ) $ 8650 , d ) $ 8450 , e ) $ 8500
Rationale: "area = 5.5 × 3.75 sq . metre . cost for 1 sq . metre . = $ 400 hence , total cost = 5.5 × 3.75 × 400 = $ 8250 a"
Answer: a
Python program:
a = 5 * 5
b = 400 * a
Problem: the temperature of a certain cup of coffee 10 minutes after it was poured was 120 degrees fahrenheit . if the temperature f of the coffee t minutes after it was poured can be determined by the formula f = 120 ( 2 ^ - at ) + 60 , where f is in degrees fahrenheit and a is a constant . then the temperature of the coffee 80 minutes after it was poured was how many degrees fahrenheit ?
Options: a ) 45 , b ) 56 , c ) 60.4 , d ) 85 , e ) 90
Rationale: "answer : b the temperature of coffee 10 minutes after it was poured ( 120 f ) will help in solving the constant “ a ” . 120 = 120 ( 2 ^ 10 a ) + 60 2 ^ - 1 = 2 ^ 10 a a = - 1 / 10 the temperature of coffee 80 minutes after it was poured is : f = 120 ( 2 ^ - 80 / 10 ) + 60 f = 120 * 1 / 256 + 60 f = 15 / 32 + 60 f = 1935 / 32 = 60.4 c"
Answer: c
Python program:
a = 60 / 10
b = 1 - 2
c = a * b
d = 2 ** c
e = d * 120
f = e + 60
Problem: the average of 11 results is 20 . the average of first 5 of them is 15 and that of last 5 is 22 . find the 6 th result ?
Options: a ) 35 , b ) 50 , c ) 100 , d ) 120 , e ) 150
Rationale: "6 th result = sum of 11 results - sum of 10 results = 11 * 20 - 5 * 15 - 5 * 22 = 220 - 75 - 110 = 35 answer is a"
Answer: a
Python program:
a = 11 * 20
b = 5 * 22
c = a - b
d = 5 * 15
e = c - d
Problem: 1 / 3 + 1 / 2 - 5 / 6 + 1 / 5 + 1 / 4 - 9 / 20 - 5 / 6 =
Options: a ) 0 , b ) 2 / 15 , c ) 2 / 5 , d ) 9 / 20 , e ) 5 / 6
Rationale: we need to determine the result of 1 / 3 + 1 / 2 - 5 / 6 + 1 / 5 + 1 / 4 - 9 / 20 let ’ s add the given fractions in two groups . in the group of the first three fractions , notice that 1 / 3 and 1 / 2 share a common denominator of 6 with 5 / 6 . 1 / 2 + 1 / 3 = 3 / 6 + 2 / 6 = 5 / 6 thus , 5 / 6 – 5 / 6 = 0 looking at the 2 nd group of the fractions ( 1 / 5 , 1 / 4 , and 9 / 20 ) , notice that 1 / 5 and 1 / 4 share a common denominator of 20 with 9 / 20 . 1 / 5 + 1 / 4 = 4 / 20 + 5 / 20 = 9 / 20 thus , 9 / 20 – 9 / 20 = 0 . thus , the result of 1 / 3 + 1 / 2 – 5 / 6 + 1 / 5 + 1 / 4 – 9 / 20 is 5 / 6 . answer : e
Answer: e
Python program:
a = 5 / 6
Problem: the product of three consecutive numbers is 210 . then the sum of the smallest two numbers is ?
Options: a ) 11 , b ) 15 , c ) 20 , d ) 38 , e ) 56
Rationale: "product of three numbers = 210 210 = 2 * 3 * 5 * 7 = 5 * 6 * 7 . so , the three numbers are 5 , 6 and 7 . and sum of smallest of these two = 5 + 6 = 11 . answer : option a"
Answer: a
Python program:
a = 2 ** 210
b = math.factorial(210)
c = a * b
Problem: frank the fencemaker needs to fence in a rectangular yard . he fences in the entire yard , except for one full side of the yard , which equals 40 feet . the yard has an area of 240 square feet . how many feet offence does frank use ?
Options: a ) 14 , b ) 52 , c ) 54 , d ) 180 , e ) 240
Rationale: "area = length x breadth 240 = 40 x breadth so , breadth = 6 units fencing required is - breadth + breadth + length 6 + 6 + 40 = > 52 feet answer must be ( b ) 52"
Answer: b
Python program:
a = 240 / 40
b = 240 / 40
c = a + b 
d = c + 40
Problem: the total of 334 of 20 paise and 25 paise make a sum of rs . 71 . the no of 20 paise coins is
Options: a ) 250 , b ) 277 , c ) 278 , d ) 200 , e ) 288
Rationale: "explanation : let the number of 20 paise coins be x . then the no of 25 paise coins = ( 334 - x ) . 0.20 * ( x ) + 0.25 ( 334 - x ) = 71 = > x = 250 . . answer : a ) 250"
Answer: a
Python program:
a = 334 * 25
b = 71 * 100
c = a - b
d = 25 - 20
e = c / d
Problem: the function f ( n ) is defined as the product of all the consecutive positive integers between 1 and n ^ 2 , inclusive , whereas the function g ( n ) is defined as the product of the squares of all the consecutive positive integers between 1 and n , inclusive . the exponent on 3 in the prime factorization of f ( 3 ) / g ( 3 ) is
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "f ( 3 ) / g ( 3 ) = product ( 1 to 3 ^ 2 ) / 1.2 ^ 2.3 ^ 2 = 1 . 2.3 . 4.5 . 6.7 . 8.9 / 1 . 4.9 = 1 . 2.3 . ( 2 ^ 2 ) . 5 . ( 2.3 ) . 7 . ( 2 ^ 3 ) . 9 / 1 . ( 2 ^ 2 ) . 9 = 1 . ( 2 ^ 7 ) . 3.5 . 7.9 / 1 . ( 2 ^ 2 ) . 9 loof for 2 ^ 7 / 2 ^ 2 = 2 ^ 5 - - - - exponent 1 answer : a"
Answer: a
Python program:
a = 2 ** 2
Problem: what will be the compound interest on rs . 45000 after 3 years at the rate of 12 % per annum
Options: a ) rs 18221.76 , b ) rs 18123.30 , c ) rs 18123.40 , d ) rs 18123.50 , e ) none of these
Rationale: "explanation : ( 45000 × ( 1 + 12 / 100 ) 3 ) = > 45000 × 28 / 25 × 28 / 25 × 28 / 25 = > 63221.76 so compound interest will be 63221.76 - 45000 = rs 18221.76 option a"
Answer: a
Python program:
a = 4 * 100
b = a * 100
c = 12 / 100
d = 1 + c 
e = d ** 3
f = b * e
g = 4 * 100
h = g * 100
i = f - h
Problem: the guests at a football banquet consumed a total of 337 pounds of food . if no individual guest consumed more than 2 pounds of food , what is the minimum number of guests that could have attended the banquet ?
Options: a ) 160 , b ) 161 , c ) 162 , d ) 163 , e ) 169
Rationale: "to minimize one quantity maximize other . 168 * 2 ( max possible amount of food a guest could consume ) = 336 pounds , so there must be more than 168 guests , next integer is 169 . answer : e ."
Answer: e
Python program:
a = 337 / 2
b = math.floor(a)
c = b + 1
Problem: a plant manager must assign 10 new workers to one of five shifts . she needs a first , second , and third shift , and two alternate shifts . each of the shifts will receive 2 new workers . how many different ways can she assign the new workers ?
Options: a ) 2430 , b ) 2700 , c ) 3300 , d ) 4860 , e ) 5400
Rationale: "my take selecting team of 2 out of 10 to assign to the shifts = 10 c 2 = 45 ways . now 2 out of 10 means total of 5 group possible . so putting them in shifts = counting methode : first , second , third , alt , alt = 5 * 4 * 3 * 2 * 1 = 120 here alt and alt are the same : so 120 / 2 = 60 ways . total ways of selecting = ( selecting 2 out of 10 ) * arranging those teams in shifts = 45 * 60 = 2700 ans : b"
Answer: b
Python program:
a = 10 / 2
b = math.factorial(a)
c = b / 2
d = math.factorial(10)
e = 10 - 2
f = math.factorial(e)
g = math.factorial(2)
h = f * g
i = d / h
j = c * i
Problem: there are 5 red shoes & 4 green shoes . if two of red shoes are drawn what is the probability of getting red shoes
Options: a ) 1 / 18 , b ) 1 / 14 , c ) 5 / 18 , d ) 1 / 15 , e ) 1 / 16
Rationale: taking 2 red shoe the probability is 5 c 2 from 9 shoes probability of taking 2 red shoes is 5 c 2 / 9 c 2 = 5 / 18 answer : c
Answer: c
Python program:
a = math.comb(5, 2)
b = 5 + 4 
c = math.comb(b, 2)
d = a / c
Problem: to fill a tank , 200 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 4 - fifths of its present ?
Options: a ) 50 , b ) 100 , c ) 150 , d ) 200 , e ) 250
Rationale: let the capacity of 1 bucket = x . then , the capacity of tank = 200 x . new capacity of bucket = 4 / 5 x therefore , required number of buckets = ( 200 x ) / ( 4 x / 5 ) = ( 200 x ) x 5 / 4 x = 1000 / 4 = 250 answer is e .
Answer: e
Python program:
a = 10 / 2
b = 4 / a
c = 200 / b
Problem: what is the probability of getting a sum 9 from two throw of a dice ?
Options: a ) 1 / 6 , b ) 1 / 8 , c ) 1 / 9 , d ) 1 / 12 , e ) 1 / 13
Rationale: "in two throws of die , n ( s ) = 36 let e = event of getting a sum 9 = { ( 3,6 ) , ( 4,5 ) , ( 5,4 ) , ( 6,3 ) } p ( e ) = 4 / 36 = 1 / 9 answer c 1 / 9"
Answer: c
Python program:
a = 3 + 3 
b = math.comb(a, 3)
c = 2 / b
Problem: john was 31 years old when he married betty . they just celebrated their fifth wedding anniversary , and betty ' s age is now 7 / 9 of john ' s . how old is betty ?
Options: a ) 24 , b ) 26 , c ) 28 , d ) 30 , e ) 32
Rationale: "assume betty ' s age on marriage = x years . john ' s age on marriage = 31 john ' s age after 5 years = 36 years . betty ' s age after 5 years = x + 5 given : x + 5 = 7 / 9 ( 36 ) = 28 therefore betty ' s current age = 28 option c"
Answer: c
Python program:
a = 7 / 9
b = 31 + 4 
c = a * b
Problem: tom purchased 8 kg of apples at the rate of 70 per kg and 9 kg of mangoes at the rate of 65 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) a ) 1040 , b ) b ) 1145 , c ) c ) 1055 , d ) d ) 1060 , e ) e ) 1075
Rationale: "cost of 8 kg apples = 70 × 8 = 560 . cost of 9 kg of mangoes = 65 × 9 = 585 . total cost he has to pay = 560 + 585 = 1145 . b )"
Answer: b
Python program:
a = 8 * 70
b = 9 * 65
c = a + b
Problem: a man can row 4 kmph is still water . if the river is running at 2 kmph it takes 90 min to row to a place and back . how far is the place
Options: a ) 2 km , b ) 4 km , c ) 5 km , d ) 2.25 km , e ) none of these
Rationale: explanation : speed in still water = 4 kmph speed of the stream = 2 kmph speed upstream = ( 4 - 2 ) = 2 kmph speed downstream = ( 4 + 2 ) = 6 kmph total time = 90 minutes = 90 ⁄ 60 hour = 3 ⁄ 2 hour let l be the distance . then ( l / 6 ) + ( l / 2 ) = 32 = > l + 3 l = 9 = > 4 l = 9 = > l = 9 ⁄ 4 = 2.25 km . answer : option d
Answer: d
Python program:
a = 90 / const_60
b = 4 + 2 
c = 1/(b)
d = 4 - 2
e = 1/(d)
f = c + e 
g = a / f
Problem: what is the least number should be added to 929 , so the sum of the number is completely divisible by 30 ?
Options: a ) 1 , b ) 2 , c ) 5 , d ) 6 , e ) 8
Rationale: "( 929 / 30 ) gives remainder 29 29 + 1 = 30 , so we need to add 1 answer : a"
Answer: a
Python program:
a = 929 / 30
b = math.floor(a)
c = b + 1 
d = c * 30
e = d - 929
Problem: the sale price sarees listed for rs . 495 after successive discount is 15 % and 10 % is ?
Options: a ) 288 , b ) 378 , c ) 342 , d ) 662 , e ) 262
Rationale: "495 * ( 85 / 100 ) * ( 90 / 100 ) = 378 answer : b"
Answer: b
Python program:
a = 495 * 15
b = a / 100
c = 495 - b
d = 495 * 15
e = d / 100
f = 495 - e
g = f * 10
h = g / 100
i = c - h
Problem: how many numbers from 29 to 119 are exactly divisible by 11 ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 8 , e ) 12
Rationale: "29 / 11 = 2 and 119 / 11 = 10 = = > 10 - 2 = 8 numbers answer : d"
Answer: d
Python program:
a = 119 / 11
b = math.floor(a)
c = b * 11
d = 29 / 11
e = math.floor(d)
f = e + 1 
g = f * 11
h = c - g
i = h / 11
j = i + 1
Problem: the points a ( 0 , 0 ) , b ( 0 , 4 a - 2 ) and c ( 2 a + 1 , 2 a + 6 ) form a triangle . if angle abc = 90 , what is the area of triangle abc ?
Options: a ) 58 , b ) 70 , c ) 63 , d ) 65 , e ) 72
Rationale: 1 / 2 bh = 1 / 2 ( 2 a + 1 ) ( 2 a + 6 ) now 4 a - 2 = 2 a + 6 2 a = 8 . a = 4 therefore , a ( 0,0 ) ; b ( 0,14 ) ; c ( 9,14 ) 1 / 2 * 9 * 14 = 63 answer : c
Answer: c
Python program:
a = 6 + 2 
b = a / 2
c = b * 4
d = c - 2
e = 6 + 2 
f = e / 2
g = 4 - 2
h = f * g
i = h + 1 
j = d * i
k = j / 2
Problem: a fellow borrowed a certain sum of money at 8 % per annum at simple interest and in 8 years the interest amounted to rs . 900 less than the sum lent . what was the sum lent ?
Options: a ) 1050 , b ) 1220 , c ) 2500 , d ) 1060 , e ) 1110
Rationale: "p - 900 = ( p * 8 * 8 ) / 100 p = 2500 answer : c"
Answer: c
Python program:
a = 8 * 8
b = a / 100
c = 1 - b
d = 900 / c
Problem: aarti can do a piece of work in 3 days . in how many days will she complete 10 time of work of same type ?
Options: a ) 6 days , b ) 18 days , c ) 21 days , d ) 30 days , e ) 13 days
Rationale: "we have the important relation , more work , more time ( days ) a piece of work can be done in 3 days . 10 times of work of same type can be done in 3 x 10 = 30 days answer d"
Answer: d
Python program:
a = 3 * 3
Problem: two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 29 kmph and 21 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ?
Options: a ) 457 km , b ) 444 km , c ) 547 km , d ) 600 km , e ) 453 km
Rationale: "1 h - - - - - 5 ? - - - - - - 60 12 h rs = 29 + 21 = 50 t = 12 d = 50 * 12 = 600 answer : d"
Answer: d
Python program:
a = 21 - 29
b = 60 / a
c = b * 29
d = 21 - 29
e = 60 / d
f = e * 21
g = c + f
Problem: when sold at a 40 % discount , a sweater nets the merchant a 30 % profit on the wholesale cost at which he initially purchased the item . by what % is the sweater marked up from wholesale at its normal retail price ?
Options: a ) 20 % , b ) 40 % , c ) 50 % , d ) 53.85 % , e ) 100 %
Rationale: "we should be careful about what are we measuring % on / what is the base . . let the marked up price = 100 . . selling price = 100 - 40 % of 100 = 60 . . profit = 30 % . . therefore the wholesale purchase cost = x . . . . 1.3 x = 60 or x = 46.15 . . . marked price was 100 so . . . so answer is 53.85 % . . d"
Answer: d
Python program:
a = 100 - 40
b = 30 / 100
c = 1 + b 
d = a / c
e = 100 - d
Problem: what is the greatest positive integer x such that 3 ^ x is a factor of 9 ^ 10 ?
Options: a ) 5 , b ) 9 , c ) 10 , d ) 20 , e ) 30
Rationale: "9 ^ 10 = ( 3 ^ 2 ) ^ 10 = 3 ^ 20 the answer is d . 20"
Answer: d
Python program:
a = 9 - 10
b = a * 10
Problem: the simple interest and the true discount on a certain sum for a given time and at a given rate are rs . 85 and rs . 78 respectively . the sum is :
Options: a ) 1360 , b ) 1450 , c ) 1600 , d ) 947 , e ) none
Rationale: sol . sum = s . i . * t . d . / ( s . i ) - ( t . d . ) = 85 * 78 / ( 85 - 78 ) = rs . 947 . answer d
Answer: d
Python program:
a = 85 * 78
b = 85 - 78
c = a / b
Problem: a cycle is bought for rs . 675 and sold for rs . 1080 , find the gain percent ?
Options: a ) 22 , b ) 60 , c ) 99 , d ) 88 , e ) 11
Rationale: "675 - - - - 180 100 - - - - ? = > 60 % answer : b"
Answer: b
Python program:
a = 1080 - 675
b = a / 675
c = b * 100
Problem: two workers a and b are engaged to do a work . a working alone takes 8 hours more to complete the job than if both worked together . if b worked alone , he would need 4 1 / 2 hours more to complete the job than they both working together . what time would they take to do the work together ?
Options: a ) 4 hours , b ) 5 hours , c ) 6 hours , d ) 7 hours , e ) none of these
Rationale: let a and be together take x hours to complete the work . then , a alone takes ( x + 8 ) hrs and b alone takes ( x + 9 / 2 ) hrs to complete the work . then , 1 / ( x + 8 ) + 1 / ( x + 9 / 2 ) = 1 / x , 1 / ( x + 8 ) + 2 / ( 2 x + 9 ) = 1 / x x ( 4 x + 25 ) = ( x + 8 ) ( 2 x + 9 ) 2 x ^ 2 = 72 , x ^ 2 = 36 , x = 6 correct option : c
Answer: c
Python program:
a = 1 / 2
b = 4 + a 
c = b * 8
d = math.sqrt(c)
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 80 sq . feet , how many feet of fencing will be required ?
Options: a ) 28 , b ) 40 , c ) 68 , d ) 88 , e ) 78
Rationale: "we have : l = 20 ft and lb = 80 sq . ft . so , b = 4 ft . length of fencing = ( l + 2 b ) = ( 20 + 8 ) ft = 28 ft . answer : a"
Answer: a
Python program:
a = 80 / 20
b = a * 2
c = b + 20
Problem: a can do a work in 6 days . b can do in 12 days . if both a & b are working together in how many days they can finish the work ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 10 , e ) 15
Rationale: 1 day work of a = 1 / 6 1 day work of b = 1 / 12 1 day work of a & b = 1 / 6 + 1 / 12 = 1 / 4 a & b finish the work in 4 days answer is a
Answer: a
Python program:
a = 1 / 6
b = 1 / 12
c = a + b 
d = 1 / c
Problem: if 2 and 3 are positive integers , then 2 * 3 + 2 is
Options: a ) 8 , b ) 10 , c ) 12 , d ) 12 , e ) 16
Rationale: answer : a
Answer: a
Python program:
a = math.lcm(2, 3)
Problem: a 240 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds . what is the length of the other train ?
Options: a ) 230 m , b ) 240 m , c ) 260 m , d ) 320 m , e ) 330 m
Rationale: "relative speed = ( 120 + 80 ) km / hr = ( 200 x ( 5 / 18 ) ) m / sec = ( 500 / 9 ) m / sec . let the length of the other train be x metres . then , ( x + 240 ) / 9 = 500 / 9 x + 240 = 500 x = 260 . c"
Answer: c
Python program:
a = 120 + 80 
b = a * const_0_2778
c = b * 9
d = c - 240
Problem: kavi had a stock of 600 bags in his bookshop . he sold 25 on monday , 70 on tuesday , 100 on wednesday , 110 on thursday and 145 on friday . what percentage of the bags were not sold ?
Options: a ) 10 % , b ) 25 % , c ) 64 % , d ) 42 % , e ) 17 %
Rationale: let n be the total number of bags sold . hence n = 25 + 70 + 100 + 110 + 145 = 450 let m be the bags not sold m = 600 - n = 600 - 450 = 150 percentage bags not sold / total number of bags = 150 / 600 = 0.25 = 25 % correct answer b
Answer: b
Python program:
a = 25 + 70 
b = a + 100 
c = b + 110 
d = c + 145 
e = 600 - d
f = e / 600
g = f * 100
Problem: a man rows his boat 85 km downstream and 45 km upstream , taking 2 1 / 2 hours each time . find the speed of the stream ?
Options: a ) 6 , b ) 7 , c ) 5 , d ) 8 , e ) 9
Rationale: "speed downstream = d / t = 85 / ( 2 1 / 2 ) = 34 kmph speed upstream = d / t = 45 / ( 2 1 / 2 ) = 18 kmph the speed of the stream = ( 34 - 18 ) / 2 = 8 kmph answer : d"
Answer: d
Python program:
a = 85 / 2
b = 45 / 2
c = a - b
d = c / 2
Problem: if f ( x ) = 1 / x and x is a natural number , what can not be the answer for f ( f ( x ) ) ?
Options: a ) 1 / 7 , b ) 3 , c ) 12 / 3 , d ) 6 / 6 , e ) 1
Rationale: answer a is impossible because the invers of 1 / x is x , and the only way to have something other than a natural number is to input something other than a natural number . with the specification that only natural numbers may be used 1 / 7 is not a possibility for f ( f ( x ) )
Answer: a
Python program:
a = 1 * 1
b = 2 * 4
c = b - 1
d = a / c
Problem: the product of the squares of two positive integers is 900 . how many pairs of positive integers satisfy this condition ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "ans : e - 4 pairs ( x ˆ 2 ) ( y ˆ 2 ) = 900 [ square root both sides ] xy = 30 20 = 1 x 30 , 3 x 10 , 6 x 5 , 5 x 6 , 10 x 3 , 30 x 1 , 15 x 2 , 2 x 15 cancel the repeats this leaves us with exactly 4 options . hence , e"
Answer: e
Python program:
a = 2 + 3 
b = a - 2
Problem: what is the least value of x . so that 23 x 57 is divisible by 3 .
Options: a ) 2 , b ) 0 , c ) 1 , d ) 3 , e ) 4
Rationale: "explanation : the sum of the digits of the number is divisible by 3 , then the number is divisible by 3 . 2 + 3 + x + 5 + 7 = 17 + x least value of x may be 1 therefore 17 + 1 = 18 is divisible by 3 . answer : option c"
Answer: c
Python program:
a = math.lcm(23, 57)
b = a / 57
c = b / 4
d = c / 4
Problem: six women can do a work in 10 days . ten men can complete the same work in 4 days . what is the ratio between the capacity of a man and a woman ?
Options: a ) 1 : 2 , b ) 2 : 1 , c ) 2 : 3 , d ) 3 : 2 , e ) none of these
Rationale: "explanation : ( 6 ã — 10 ) women can complete the work in 1 day . â ˆ ´ 1 woman ' s 1 day ' s work = 1 / 60 ( 10 ã — 4 ) men can complete the work in 1 day . â ˆ ´ 1 man ' s 1 day ' s work = 1 / 40 so , required ratio = 1 / 60 : 1 / 40 = 3 : 2 answer : d"
Answer: d
Python program:
a = 10 * 4
b = 1 / a
c = 4 * 10
d = 1 / c
e = b / d
Problem: if 28 less than 5 times a certain number is 232 . what is the number ?
Options: a ) 32 , b ) 42 , c ) 52 , d ) 62 , e ) 72
Rationale: 5 x − 28 subtraction is built backwards , multiply the unknown by 5 5 x − 28 = 232 is translates to equals + 28 + 28 add 28 to both sides 5 x = 260 the variable ismultiplied by 5 5 5 divide both sides by 5 x = 52 the number is 52 . correct answer c
Answer: c
Python program:
a = 5 * 28
b = a + 232 
c = 5 * 28
d = b - c
e = 5 * 28
f = d - e
g = 4 * 10
h = f - g
Problem: a rope of which a calf is tied is increased from 10 m to 23 m , how much additional grassy ground shall it graze ?
Options: a ) 1217 , b ) 1348.2 , c ) 1210 , d ) 1212 , e ) 1312
Rationale: π ( 232 – 102 ) = 1348.2 answer : b
Answer: b
Python program:
a = 23 ** 2
b = 10 ** 2
c = a - b
d = 10 * 2
e = d + 2 
f = 4 + 3 
g = e / f
h = c * g
Problem: a boat having a length 3 m and breadth 2 m is floating on a lake . the boat sinks by 1 cm when a man gets into it . the mass of the man is :
Options: a ) 50 kg , b ) 60 kg , c ) 70 kg , d ) 80 kg , e ) none of these
Rationale: explanation : in this type of question , first we will calculate the volume of water displaces then will multiply with the density of water . volume of water displaced = 3 * 2 * 0.01 = 0.06 m cube mass of man = volume of water displaced * density of water = 0.06 * 1000 = 60 kg option b
Answer: b
Python program:
a = 3 * 2
b = 1 / 100
c = a * b
d = c * 1000
Problem: tanks a and b are each in the shape of a right circular cylinder . the interior of tank a has a height of 10 meters and a circumference of 6 meters , and the interior of tank b has a height of 6 meters and a circumference of 10 meters . the capacity of tank a is what percent of the capacity of tank b ?
Options: a ) 60 % , b ) 80 % , c ) 100 % , d ) 120 % , e ) 125 %
Rationale: "the radius of tank a is 6 / ( 2 * pi ) . the capacity of tank a is 10 * pi * 36 / ( 4 * pi ^ 2 ) = 180 / ( 2 * pi ) the radius of tank b is 10 / ( 2 * pi ) . the capacity of tank b is 6 * pi * 100 / ( 4 * pi ^ 2 ) = 300 / ( 2 * pi ) tank a / tank b = 180 / 300 = 6 / 10 = 60 % the answer is a ."
Answer: a
Python program:
a = 6 / 10
b = a ** 2
c = 10 / 6
d = b * c
e = d * 100
Problem: the tax on a commodity is diminished by 30 % but its consumption is increased by 10 % . find the decrease percent in the revenue derived from it ?
Options: a ) 12 % , b ) 14 % , c ) 16 % , d ) 20 % , e ) 23 %
Rationale: "explanation : 100 * 100 = 10000 70 * 110 = 7700 10000 - - - - - - - 2300 100 - - - - - - - ? = 23 % e )"
Answer: e
Python program:
a = 100 + 10 
b = 100 - 30
c = a * b
d = c / 100
e = 100 - d