euclaise/mathqa_programs huggingface dataset:
Problem: if the average of 10 x and 8 y is greater than 70 , and x is twice y , what is the least integer value of x ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 10 , e ) 20
Rationale: "substitution can be used in the following way : always start with the equation : x = 2 y . it is more straight forward to manage as compared to the inequality . substitute y = x / 2 , not the other way because you need to find the minimum value of x . so you can get rid of y . now go on to the inequality . so 8 y = 8 x / 2 = 4 x now average of 10 x and 4 x is greater than 70 . average of 10 x and 4 x is 7 x . so , 7 x > 70 x > 10 answer : d"
Answer: d
Python program:
a = 10 * 2
Problem: when processing flower - nectar into honey bees ' extract , a considerable amount of water gets reduced . how much flower - nectar must be processed to yield 1 kg of honey , if nectar contains 50 % water , and the honey obtained from this nectar contains 35 % water ?
Options: a ) 1.3 kg , b ) 1.5 kg , c ) 1.7 kg , d ) 1.9 kg , e ) none of these
Rationale: explanation : flower - nectar contains 50 % of non - water part . in honey this non - water part constitutes 65 % ( 100 - 35 ) . therefore 0.5 x amount of flower - nectar = 0.65 x amount of honey = 0.65 x 1 kg therefore amount of flower - nectar needed = ( 0.65 / 0.51 ) kg = 1.3 kgs answer : a
Answer: a
Python program:
a = 100 - 35
b = a / 100
c = 50 / 100
d = b / c
Problem: a sum of money is put out at compound interest for 2 years at 20 % . it would fetch rs . 1205 more if the interest were payable half - yearly , then it were pay able yearly . find the sum .
Options: a ) 22200 , b ) 31897 , c ) 48799 , d ) 50000 , e ) 52782
Rationale: "p ( 11 / 10 ) ^ 4 - p ( 6 / 5 ) ^ 2 = 1205 p = 50000 answer : d"
Answer: d
Python program:
a = 20 + 1 
b = 20 + 1 
c = a * b
d = 20 + 1 
e = c + d
Problem: cindy has her eye on a sundress but thinks it is too expensive . it goes on sale for 15 % less than the original price . before cindy can buy the dress , however , the store raises the new price by 25 % . if the dress cost $ 61.2 after it went on sale for 15 % off , what is the difference between the original price and the final price ?
Options: a ) $ 0.00 , b ) $ 4.50 , c ) $ 3.40 , d ) $ 5.00 , e ) $ 6.80
Rationale: "0.85 * { original price } = $ 61.2 - - > { original price } = $ 72 . { final price } = $ 61.2 * 1.25 = $ 76.5 . the difference = $ 76.5 - $ 72 = $ 4.5 answer : b ."
Answer: b
Python program:
a = 100 + 25 
b = a / 100
c = 61 * 2
d = 100 - 15
e = d / 100
f = 61 / 2
g = c - f
Problem: the smallest number which when diminished by 12 , is divisible 12 , 24 , 36 , 48 and 56 is :
Options: a ) 1008 , b ) 1015 , c ) 1020 , d ) 1032 , e ) 1048
Rationale: "required number = ( l . c . m . of 12 , 24 , 36 , 48,56 ) + 12 = 1008 + 12 = 1020 answer : option c"
Answer: c
Python program:
a = 3 ** 2
b = 2 ** 0
c = a * b
d = 3 + 4 
e = c * d
f = e + 12
Problem: there are 100 students in 3 sections a , b and c of a class . the average marks of all the 3 sections was 84 . the average of b and c was 87.5 and the average marks of students in a section was ?
Options: a ) 20 , b ) 99 , c ) 28 , d ) 27 , e ) 12
Rationale: numbers of students in section a = x numbers of students in section b and c = ( 100 – x ) x 70 + ( 100 – x ) 87.5 = 84 100 70 x + 87.5 100 – 87.5 x = 8400 8750 – 17.5 x = 8400 17.5 x = 8750 – 8400 = > x = 20 . answer : a
Answer: a
Python program:
a = 100 * 87
b = 100 * 84
c = a - b
d = 4 + 3 
e = d * 10
f = 87 - 5
g = c / f
Problem: a trader bought a car at 5 % discount on its original price . he sold it at a 60 % increase on the price he bought it . what percent of profit did he make on the original price ?
Options: a ) 17 % , b ) 62 % , c ) 52 % , d ) 19 % , e ) 22 %
Rationale: original price = 100 cp = 95 s = 95 * ( 160 / 100 ) = 152 100 - 152 = 52 % answer : c
Answer: c
Python program:
a = 100 - 5
b = 100 + 60 
c = a * b
d = c / 100
e = d / 100
f = e - 1
g = f * 100
Problem: the mean daily profit made by a shopkeeper in a month of 30 days was rs . 350 . if the mean profit for the first fifteen days was rs . 275 , then the mean profit for the last 15 days would be
Options: a ) rs . 200 , b ) rs . 350 , c ) rs . 275 , d ) rs . 425 , e ) none of these
Rationale: "average would be : 350 = ( 275 + x ) / 2 on solving , x = 425 . answer : d"
Answer: d
Python program:
a = 30 * 350
b = 15 * 275
c = a - b
d = c / 15
Problem: two trains of length 100 m and 200 m are 100 m apart . they start moving towards each other on parallel tracks , at speeds 18 kmph and 72 kmph . in how much time will the trains cross each other ?
Options: a ) 8 , b ) 16 , c ) 11 , d ) 12 , e ) 21
Rationale: "relative speed = ( 18 + 72 ) * 5 / 18 = 25 mps . the time required = d / s = ( 100 + 100 + 200 ) / 25 = 400 / 25 = 16 sec . answer : b"
Answer: b
Python program:
a = 18 + 72 
b = a * const_0_2778
c = 100 / b
Problem: if x : y = 1 : 3 , find the value of ( 2 x + 3 y ) : ( 5 x – y )
Options: a ) 11 : 3 , b ) 11 : 2 , c ) 3 : 2 , d ) 7 : 2 , e ) 9 : 5
Rationale: "explanation : given : x / y = 1 / 3 ( 2 x + 3 y ) / ( 3 x – y ) = ( 2 * 1 + 3 * 3 ) : ( 5 * 1 – 3 ) = 11 : 2 answer : b"
Answer: b
Python program:
a = 2 ** 3
b = a + 3 
c = 1 + 3 
d = c + 3 
e = b / d
Problem: if x # y is defined to equal x ^ 3 / y for all x and y , then ( - 1 # 2 ) # 3 =
Options: a ) 4 / 3 , b ) 1 / 3 , c ) 1 / 12 , d ) - 1 / 12 , e ) 1 / 24
Rationale: "( - 1 ) ^ 3 / 2 = 1 / 2 ( 1 / 2 ) ^ 3 / 3 = 1 / 24 so e is my answer"
Answer: e
Python program:
a = negate ** (
b = a / 3
c = b ** 3
d = c / 3
Problem: in a restaurant , the profit is 150 % of the cost . if the cost increases by 12 % but the selling price remains constant , approximately what percentage of the selling price is the profit ?
Options: a ) 30 % , b ) 55 % , c ) 90 % , d ) 100 % , e ) none of these
Rationale: "explanation : let c . p . = rs . 100 . then , profit = rs . 150 , s . p . = rs . 250 . new c . p . = 112 % of rs . 100 = rs . 112 new s . p . = rs . 250 . profit = rs . ( 250 - 112 ) = rs . 138 . required percentage = ( 138 / 250 * 100 ) % = 55 % appox answer : b"
Answer: b
Python program:
a = 150 / 100
b = 100 * a
c = b + 100 
d = 12 / 100
e = 1 + d 
f = 100 * e
g = c - f
h = 150 / 100
i = 100 * h
j = i + 100 
k = g / j
l = 100 * k
Problem: a can contains a mixture of liquids a and b is the ratio 7 : 5 . when 9 litres of mixture are drawn off and the can is filled with b , the ratio of a and b becomes 7 : 9 . how many liter e of liquid a was contained by the can initially ?
Options: a ) 10 , b ) 20 , c ) 21 , d ) 25 , e ) 27
Rationale: "as a : b : : 7 : 5 - - - > only option c is a multiple of 7 and hence it is a good place to start . also a : b : : 7 : 5 means that , a = ( 712 ) * total and b = ( 5 / 12 ) * total if a = 21 , b = 15 - - - > remove 9 litres - - - > you remove ( 7 / 12 ) * 9 of a - - - > a remaining = 21 - ( 7 / 12 ) * 9 = 63 / 4 similarly , for b , you remove ( 5 / 12 ) * 9 - - - > b remaining = 15 - ( 5 / 12 ) * 9 = 45 / 4 and then add 9 more litres of b - - - > 9 + 45 / 4 = 81 / 4 thus a / b ( final ratio ) = ( 45 / 4 ) / ( 81 / 4 ) = 7 : 9 , the same as the final ratio mentioned in the question . hence c is the correct answer . a / b = 7 / 9 = ( 7 x - ( 7 / 12 ) * 9 ) / ( 5 x - ( 5 / 12 ) * 9 + 9 ) , where 7 x and 5 x are initial quantities of a and b respectively . thus , 7 / 9 = ( 7 x - ( 7 / 12 ) * 9 ) / ( 5 x - ( 5 / 12 ) * 9 + 9 ) - - - > giving you x = 3 . thus a ( original ) e = 7 * 3 = 21 . c"
Answer: c
Python program:
a = 7 + 9 
b = 7 + 5 
c = 5 / b
d = c * 9
e = 9 - d
f = a * e
g = 9 * 7
h = 7 * 5
i = g - h
j = f / i
k = 7 * j
Problem: a can do a piece of work in 14 days . when he had worked for 2 days b joins him . if the complete work was finished in 8 days . in how many days b alone can finish the work ?
Options: a ) 18 , b ) 77 , c ) 66 , d ) 55 , e ) 14
Rationale: "8 / 14 + 6 / x = 1 x = 14 days answer : e"
Answer: e
Python program:
a = 1 / 8
b = 1 / 14
c = 2 * b
d = 1 - c
e = a * d
f = 1 / 14
g = e - f
h = 1/(g)
i = 14 + 8 
j = h - i
Problem: 8 chess players take part in a tournament . every player plays twice with each of his opponents . how many games are to be played ?
Options: a ) 66 , b ) 52 , c ) 58 , d ) 55 , e ) 56
Rationale: "though 2 * ( 8 c 2 ) is the correct approcah to do this , but for people like me who find perm , comb n prob a nightmare , an easy approach can be used . the first guy has to play 2 matches with the rest of 7 , so he ' ll play 14 matches . similarly , second guy has to play with the rest of 6 as his 2 games with the first guy are already played . so he plays 12 matches . this continues like this and the total matches are 14 + 12 + 10 . . . + 2 14 + 12 + . . . + 2 = 2 ( 7 + 6 + . . . + 1 ) = 2 ( ( 7 * 8 ) / 2 ) = 7 * 8 = 56 . answer : e"
Answer: e
Python program:
a = 8 - 1
b = 8 * a
Problem: a small college reduced its faculty by approximately 14 percent to 195 professors . what was the original number of faculty members ?
Options: a ) 182 , b ) 208 , c ) 227 , d ) 254 , e ) 302
Rationale: if x is the original number of faculty members , then after 14 % reduction in faculty members number is . 86 x but we are given . 86 x = 195 x = 227 so the original number of faculty members is 227 correct answer - c
Answer: c
Python program:
a = 100 - 14
b = a / 100
c = 195 / b
Problem: one fourth of one third of two fifth of a number is 16 . what will be 40 % of that number
Options: a ) 140 , b ) 150 , c ) 180 , d ) 192 , e ) 250
Rationale: "explanation : ( 1 / 4 ) * ( 1 / 3 ) * ( 2 / 5 ) * x = 16 then x = 16 * 30 = 480 40 % of 480 = 192 answer : option d"
Answer: d
Python program:
a = 1 / 4
b = 1 / 3
c = a * b
d = 2 + 3 
e = 2 / d
f = c * e
g = 16 / f
h = g * 40
i = h / 100
Problem: hree number are in the ratio of 3 : 4 : 5 and their l . c . m . is 2400 . their h . c . f . is :
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: let the numbers be 3 x , 4 x and 5 x . then , their l . c . m . = 60 x . so , 60 x = 2400 or x = 40 . the numbers are ( 3 x 40 ) , ( 4 x 40 ) and ( 5 x 40 ) . hence , required h . c . f . = 40 . answer : a
Answer: a
Python program:
a = 3 * 4
b = a * 5
c = 2400 / b
Problem: the length of a rectangle is two - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 625 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 10 units ?
Options: a ) 140 , b ) 99 , c ) 100 , d ) 72 , e ) 12
Rationale: "given that the area of the square = 625 sq . units = > side of square = √ 625 = 25 units the radius of the circle = side of the square = 25 units length of the rectangle = 2 / 5 * 25 = 10 units given that breadth = 10 units area of the rectangle = lb = 10 * 10 = 100 sq . units answer : c"
Answer: c
Python program:
a = math.sqrt(625)
b = 10 / 2
c = a / b
d = 2 * c
e = 10 * d
Problem: if x + y = 250 , x - y = 200 , for integers of x and y , y = ?
Options: a ) 200 , b ) 225 , c ) 50 , d ) 115 , e ) 150
Rationale: "x + y = 250 x - y = 200 2 x = 50 x = 25 y = 225 answer is b"
Answer: b
Python program:
a = 250 + 200 
b = a / 2
Problem: to fill a tank , 42 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 two - fifths of its present ?
Options: a ) 102 , b ) 103 , c ) 104 , d ) 105 , e ) 106
Rationale: "let the capacity of 1 bucket = x . then , the capacity of tank = 42 x . new capacity of bucket = 2 / 5 x therefore , required number of buckets = ( 42 x ) / ( 2 x / 5 ) = ( 42 x ) x 5 / 2 x = 210 / 2 = 105 answer is d ."
Answer: d
Python program:
a = 4 + 1 
b = 42 * a
c = b / 2
Problem: a factory produces 1 defective bulb out of 10 bulbs a yr . if it produces 870 bulbs a yr , how many defective bulbs are produced ?
Options: a ) 84 , b ) 85 , c ) 86 , d ) 87 , e ) 88
Rationale: 10 out of 1 is defective 20 out of 2 is defective 100 out of 10 is defective and so on 800 out of 80 is defective 70 out of 7 is defective 80 + 7 = 87 answer : d
Answer: d
Python program:
a = 870 / 10
Problem: find the principal which yields a simple interest of rs . 20 and compound interest of rs . 25 in two years , at the same percent rate per annum ?
Options: a ) s . 40 , b ) s . 48 , c ) s . 49 , d ) s . 20 , e ) s . 60
Rationale: "explanation : si in 2 years = rs . 20 , si in 1 year = rs . 10 ci in 2 years = rs . 25 % rate per annum = [ ( ci – si ) / ( si in 1 year ) ] * 100 = [ ( 25 – 20 ) / 20 ] * 100 = 25 % p . a . let the principal be rs . x time = t = 2 years % rate = 25 % p . a . si = ( prt / 100 ) 20 = ( x * 25 * 2 ) / 100 x = rs . 40 answer : a"
Answer: a
Python program:
a = 25 - 20
b = a * 100
c = b / 2
Problem: a shopkeeper sells 400 metres of cloth for $ 18000 at a loss of rs . 5 per metre . find his cost price for one metre of cloth ?
Options: a ) $ 20 , b ) $ 43 , c ) $ 50 , d ) $ 70 , e ) $ 40
Rationale: "c $ 50 sp per metre = 18000 / 400 = $ 45 loss per metre = $ 5 cp per metre = 45 + 5 = $ 50"
Answer: c
Python program:
a = 18000 / 400
b = a + 5
Problem: 36 * 36 * 36 = 6 ^ ?
Options: a ) 3 , b ) 2 , c ) 6 , d ) 1 , e ) 5
Rationale: "6 ^ 2 * 6 ^ 2 * 6 ^ 2 = 6 ^ ( 2 + 2 + 2 ) = 6 ^ 6 answer : 6 answer : c"
Answer: c
Python program:
a = 36 * 36
Problem: what is the least number which when divided by 5 , 9 , 12 and 18 leaves remainder 4 in each care ?
Options: a ) 130 , b ) 140 , c ) 136 , d ) 184 , e ) 196
Rationale: "explanation : lcm of 5 , 9 , 12 and 18 is 180 required number = 180 + 4 = 184 answer : option d"
Answer: d
Python program:
a = math.lcm(5, 9)
b = math.lcm(12, 18)
c = math.lcm(a, b)
d = c + 4
Problem: abhinav and bhupathi together have rs . 1210 . if 4 / 15 of abhinav ' s amount is equal to 2 / 5 of bhupathi ' s amount , how much amount does bhupathi have ?
Options: a ) rs 460 , b ) rs 484 , c ) rs 550 , d ) rs 664 , e ) none of these
Rationale: explanation : let a = abhinav , b = bhupathi . 4 / 15 a = 2 / 5 b = > a = ( 2 / 515 / 4 ) b = > a = 3 / 2 b = > a / b = 3 / 2 = > a : b = 3 : 2 b ' s share = rs . ( 12102 / 5 ) = rs . 484 . answer : b
Answer: b
Python program:
a = 1210 / 5
b = 1210 / 5
c = a + b
Problem: difference of two numbers is 1620 . if 7.5 % of the number is 12.5 % of the other number , find the number ?
Options: a ) 2660 , 1000 , b ) 3660 , 2000 , c ) 3000 , 4160 , d ) 2430 , 4050 , e ) 4660 , 3000
Rationale: "let the numbers be x and y . then , 7.5 % of x = 12.5 % of y x = 125 * y / 75 = 5 * y / 3 . now , x - y = 1620 5 * y / 3 – y = 1620 2 * y / 3 = 1620 y = [ ( 1620 * 3 ) / 2 ] = 2430 . one number = 2430 , second number = 5 * y / 3 = 4050 . answer d ."
Answer: d
Python program:
a = 7 / 5
b = 7 / 5
c = 1 - b
d = 1620 / c
e = a * d
Problem: a shirt goes on sale for 60 % of its original price . one week later , the sale price is marked down 10 % . the final price is what percent of the original price ?
Options: a ) 72 % , b ) 70 % , c ) 52 % , d ) 50 % , e ) 28 %
Rationale: "just assume original price is 100 . sale price = 60 then it is marked down by 10 % = 60 - 6 = 52 . hence it is 52 % od the original price . hence answer is c ."
Answer: c
Python program:
a = 60 / 100
b = a * 10
c = 60 - b
Problem: two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 9 hours and 16 hours respectively the ratio of their speeds is
Options: a ) 2 : 3 , b ) 4 : 3 , c ) 6 : 7 , d ) 9 : 16 , e ) none
Rationale: "solution let us name the trains as a and b . = ( a ' s speed ) : ( b ' s speed ) = √ b : √ a = √ 16 : √ 9 = 4 : 3 answer b"
Answer: b
Python program:
a = math.sqrt(16)
b = math.sqrt(9)
c = a / b
Problem: 61 small identical cubes are used to form a large cube . how many more cubes are needed to add one top layer of small cube all over the surface of the large cube ?
Options: a ) 64 , b ) 128 , c ) 152 , d ) 155 , e ) 256
Rationale: "61 small cube will make a large cube with 4 cubes in each line i . e . adding one layer will require one cube at each end and hence new cube will have 6 cubes in each line . total number of small cubes in new cube = 6 ^ 3 = 216 extra cube required = 216 - 61 = 155 hence , d is the answer ."
Answer: d
Python program:
a = cube_edge_by_volume + ( 
b = volume_cube - (
Problem: pipe a can fill a tank in 5 hr , pipe b in 10 hr and pipe c in 30 hr . if all the pipes are open in how many hours will tank be filled ?
Options: a ) 1 hr , b ) 2 hr , c ) 3 hr , d ) 4 hr , e ) 5 hr
Rationale: "part filled by ( a + b + c ) in 1 hour = 1 / 5 + 1 / 10 + 1 / 30 = 1 / 3 all the 3 pipes together will fill the tank in 3 hours answer is c"
Answer: c
Python program:
a = 5 / 5
b = 5 / 10
c = a + b 
d = 5 / 30
e = c + d 
f = e * 5
Problem: a pipe takes a hours to fill the tank . but because of a leakage it took 5 times of its original time . find the time taken by the leakage to empty the tank
Options: a ) 50 min , b ) 60 min , c ) 90 min , d ) 80 min , e ) 75 min
Rationale: "pipe a can do a work 60 min . lets leakage time is x ; then 1 / 60 - 1 / x = 1 / 300 x = 75 min answer : e"
Answer: e
Python program:
a = 1 * 5
b = 10 * a
Problem: the average weight of 19 students is 15 kg . by the admission of a new student the average weight is reduced to 14.7 kg . the weight of the new student is ?
Options: a ) 10.6 kg , b ) 10.8 kg , c ) 11 kg , d ) 14.9 kg , e ) none
Rationale: "answer weight of new student = total weight of all 20 students - total weight of initial 19 students = ( 20 x 14.7 - 19 x 15 ) kg = 9 kg . correct option : e"
Answer: e
Python program:
a = 19 + 1 
b = a * 14
c = 19 * 15
d = b - c
Problem: sandy walked 20 meters towards south . then sandy turned to her left and walked 20 meters . she then turned to her left and walked 20 meters . she then turned to her right and walked 20 meters . what distance is she from the starting point and in which direction ?
Options: a ) 20 m east , b ) 40 m north , c ) 30 m west , d ) 40 m east , e ) 20 m west
Rationale: "the net distance is 20 + 20 = 40 meters to the east . the answer is d ."
Answer: d
Python program:
a = 20 + 20
Problem: the following questions are based on the information given . choose the appropriate answer that suits the question based on the information . a cube is cut in two equal parts along a plane parallel to one of its faces . one piece is then colored red on the two larger faces and green on remaining . while the other is colored green on two smaller adjacent faces and red on the remaining . each is then cut into 32 cubes of same size and mixed up . 21 . how many cubes have only one colored face each ?
Options: a ) 32
b ) 8
c ) 16
d ) 24
e ) 0
Rationale: 16 = 2 ^ 3 each cube will have 2 ^ 3 cubes painted 1 side . answer : c
Answer: c
Python program:
a = 32 / 4
b = a * 2
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 2 years ?
Options: a ) 3277 , b ) 2977 , c ) 22500 , d ) 6077 , e ) 17112
Rationale: explanation : 40,000 * ( 3 / 4 ) ^ 2 answer : c
Answer: c
Python program:
a = 100 * 100
b = 4 * a
c = 3 / 4
d = c ** 2
e = b * d
Problem: a committee is reviewing a total of 20 x black - and - white films and 6 y color films for a festival . if the committee selects y / x % of the black - and - white films and all of the color films , what fraction e of the selected films are in color ?
Options: a ) 1 / 130 , b ) 1 / 5 , c ) 3 / 13 , d ) 10 / 13 , e ) 30 / 31
Rationale: "it ' s y / xpercentnot y / x . if x = 20 and y = 10 . then : 20 x = 400 black - and - white films ; 6 y = 60 color films . y / x % = 10 / 20 % = 0.5 % of the black - and - white films , so 2 black - and - white films and all 60 color films , thus total of 62 films were selected . color films thus compose e = 60 / 62 = 30 / 31 of the selected films . answer : e ."
Answer: e
Python program:
a = 20 / 100
b = a + 6 
c = 6 / b
Problem: a wooden box of dimensions 8 m x 7 m x 6 m is to carry rectangularboxes of dimensions 4 cm x 7 cm x 6 cm . the maximum number ofboxes that can be carried in the wooden box , is
Options: a ) 9800000 , b ) 1000000 , c ) 7500000 , d ) 2000000 , e ) none of these
Rationale: explanation : number = ( 800 * 700 * 600 ) / 8 * 7 * 6 = 2000000 answer : d
Answer: d
Python program:
a = 4 * 100
b = 2 * 0
c = a * b
d = 8 * 100
e = c * d
f = 4 * 0
g = f * 7
h = e / g
Problem: a searchlight on top of the watch - tower makes 3 revolutions per minute . what is the probability that a man appearing near the tower will stay in the dark for at least 10 seconds ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4
Rationale: "3 revolutions per minute = 1 revolution every 20 seconds so no matter what anybody appearing at the tower can not stay in the dark for more than 20 seconds . this will be our total number of possibilities i . e the denominator . p ( man in dark for at least 5 seconds ) = 1 - p ( man in dark for max of 10 seconds ) = 1 - 10 / 20 = 1 - 1 / 2 = 1 / 2 or the other way would be : p ( man in dark for at least 5 seconds ) is like saying he can be in dark for 5 , 6,7 . . . all the way to 20 seconds because that is the max . in this approach it would be 10 / 20 seconds = 1 / 2 . answer is c"
Answer: c
Python program:
a = const_60 * 1
b = a / 3
c = 10 / b
d = 1 - c
Problem: the time it took car p to travel 750 miles was 2 hours less than the time it took car r to travel the same distance . if car p ’ s average speed was 10 miles per hour greater than that of car r , what was car r ’ s average speed , in miles per hour ?
Options: a ) 40 , b ) 56 , c ) 60 , d ) 70 , e ) 80
Rationale: let speed of car r be = x then speed of car p = x + 10 a / q , ( 750 / x ) - ( 750 / ( x + 10 ) ) = 2 solving for x = 56 miles \ hr . b
Answer: b
Python program:
a = negate + ( 
b = negate ** (
c = b - 2
d = 750 * 10
e = d / 2
f = 4 * negate
g = math.sqrt(c)
h = a / g
Problem: if 5 % more is gained by selling an book for $ 350 than by selling it for $ 340 , the cost of the book is :
Options: a ) 500 , b ) 400 , c ) 200 , d ) 300 , e ) 100
Rationale: "c 200 let c . p . be $ x . then , 5 % of x = 350 - 340 = 10 x / 20 = 10 = > x = 200"
Answer: c
Python program:
a = 350 - 340
b = 5 / 100
c = a / b
Problem: find the number which when added to itself 13 times , gives 112 .
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "let the number be x . then , x + 13 x = 112 14 x = 112 x = 8 . answer : b"
Answer: b
Python program:
a = 13 - 1
b = 112 / a
Problem: there are 6 red shoes & 4 green shoes . if two of red shoes are drawn what is the probability of getting red shoes
Options: a ) 1 / 3 , b ) 1 / 4 , c ) 1 / 2 , d ) 1 / 5 , e ) 1 / 6
Rationale: "taking 2 red shoe the probablity is 6 c 2 from 10 shoes probablity of taking 2 red shoe is 6 c 2 / 10 c 2 = 1 / 3 answer : a"
Answer: a
Python program:
a = math.comb(6, 2)
b = 6 + 4 
c = math.comb(b, 2)
d = a / c
Problem: a batsman makes a score of 200 runs in the 17 th inning and thus increases his averages by 10 what is his average after 17 th inning ?
Options: a ) 39 , b ) 35 , c ) 42 , d ) 40 , e ) 41.5
Rationale: "let the average after 16 th inning = x then total run after 16 th inning = 16 x then total run after 17 th inning = 16 x + 200 then average run after 17 th inning = ( 16 x + 200 ) / 17 ( 16 x + 200 ) / 17 = x + 10 = > 16 x + 200 = 17 x + 170 x = 30 ; average after 17 th inning = 30 + 10 = 40 answer : d"
Answer: d
Python program:
a = 17 * 10
b = 200 - a
c = b + 10
Problem: if w and y are both odd prime numbers and w < y , how many distinct positive integer factors does 2 wy have ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 12
Rationale: since 2 wy prime factors are w ^ 1 * y ^ 1 * 2 ^ 1 , its total number or factors must be ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 2 ^ 3 = 8 . thus , i think d would be the correct answer . d
Answer: d
Python program:
a = 3 + 2 
b = a + 3