euclaise/mathqa_programs huggingface dataset:
Problem: p , q and r have $ 5000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ?
Options: a ) 2400 , b ) 2403 , c ) 3998 , d ) 2539 , e ) 2000
Rationale: "e 2000 let the amount with r be $ r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 5000 - r ) = > 3 r = 10000 - 2 r = > 5 r = 10000 = > r = 2000 ."
Answer: e
Python program:
a = 2 * 2
b = 5000 * a
c = 2 * 2
d = c / 3
e = d * 3
f = 1 * 3
g = e + f 
h = 1 * 3
i = g + h 
j = b / i
Problem: a , b , c can do a piece of work in 20 days , 30 days and 40 days respectively , working alone . how soon can the work be done if a is assisted by b and c on alternate days ?
Options: a ) 3 days , b ) 1 day , c ) 5 days , d ) 10 days , e ) 7 days
Rationale: "a + b 1 day work = 1 / 20 + 1 / 30 = 1 / 12 a + c 1 day work = 1 / 20 + 1 / 40 = 3 / 40 work done in 2 days = 1 / 12 + 3 / 40 = 19 / 120 19 / 120 work is done by a in 2 days whole work will be done in 2 * 19 / 120 = 3 days approximately answer is a"
Answer: a
Python program:
a = 1 / 20
b = 1 / 30
c = a + b 
d = 1 / 20
e = 1 / 40
f = d + e 
g = c + f 
h = 2 / g
Problem: a $ 500 investment and a $ 1,500 investment have a combined yearly return of 16 percent of the total of the two investments . if the $ 500 investment has a yearly return of 7 percent , what percent yearly return does the $ 1,500 investment have ?
Options: a ) 9 % , b ) 10 % , c ) 105 / 8 % , d ) 11 % , e ) 19 %
Rationale: "the equation we can form the question : return on total investment = sum of individual investments ( 500 + 1500 ) ( 16 ) = ( 500 â ˆ — 7 ) + ( 1500 x ) , where x is the return on investment of 1500 . solving the equation , we get x = 19 % ( option e ) answer : e"
Answer: e
Python program:
a = 3 * 500
b = 500 + a 
c = 16 / 100
d = b * c
e = 7 / 100
f = 500 * e
g = d - f
h = 3 * 500
i = g / h
j = i * 100
Problem: an investment yields an interest payment of $ 216 each month . if the simple annual interest rate is 9 % , what is the amount of the investment ?
Options: a ) $ 28,300 , b ) $ 30,400 , c ) $ 28,800 , d ) $ 32,500 , e ) $ 35,100
Rationale: "let the principal amount = p simple annual interest = 9 % simple monthly interest = ( 9 / 12 ) = ( 3 / 4 ) % ( 3 / 4 ) * ( p / 100 ) = 216 = > p = ( 216 * 4 * 10 ^ 2 ) / 3 = 72 * 4 * 10 ^ 2 = 288 * 10 ^ 2 = 28800 answer c"
Answer: c
Python program:
a = 3 * 4
b = 9 / a
c = 216 / b
d = c * 100
Problem: you have a 6 - sided cube and 6 cans of paint , each a different color . you may not mix colors of paint . how many distinct ways can you paint the cube using a different color for each side ? ( if you can reorient a cube to look like another cube , then the two cubes are not distinct . )
Options: a ) 24 , b ) 30 , c ) 48 , d ) 60 , e ) 120
Rationale: paint one of the faces red and make it the top face . 5 options for the bottom face . now , four side faces can be painted in ( 4 - 1 ) ! = 3 ! = 6 ways ( circular arrangements of 4 colors ) . total = 5 * 6 = 30 . answer : b .
Answer: b
Python program:
a = 6 / 2
b = math.factorial(a)
c = 6 - 1
d = b * c
Problem: one half of a two digit number exceeds its one third by 8 . what is the sum of the digits of the number ?
Options: a ) a ) 3 , b ) b ) 5 , c ) c ) 12 , d ) d ) 9 , e ) e ) 11
Rationale: "x / 2 – x / 3 = 8 = > x = 48 4 + 8 = 12 answer : c"
Answer: c
Python program:
a = 8 * 4
b = reminder + (
Problem: one night 18 percent of the female officers on a police force were on duty . if 144 police officers were on duty that night and half of these were female officers , how many female officers were on the police force ?
Options: a ) 300 , b ) 400 , c ) 500 , d ) 600 , e ) 700
Rationale: "let x be the number of female police officers on the police force . the number of female police officers on duty was 72 . 0.18 x = 72 x = 400 the answer is b ."
Answer: b
Python program:
a = 144 / 2
b = 18 / 100
c = a / b
Problem: a shirt goes on sale for 70 % 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 ) 63 % , b ) 70 % , c ) 62 % , d ) 50 % , e ) 28 %
Rationale: just assume original price is 100 . sale price = 70 then it is marked down by 10 % = 70 - 7 = 63 . hence it is 63 % od the original price . hence answer is a .
Answer: a
Python program:
a = 70 / 100
b = a * 10
c = 70 - b
Problem: a 250 m long train running at the speed of 120 km / hr crosses another train running in opposite direction at the speed of 80 km / hr in 9 sec . what is the length of the other train ?
Options: a ) 250 , b ) 245 , c ) 240 , d ) 235 , e ) 230
Rationale: "relative speed = 120 + 80 = 200 km / hr . = 200 * 5 / 18 = 500 / 9 m / sec . let the length of the other train be x m . then , ( x + 250 ) / 9 = 500 / 9 = > x = 250 . answer : option a"
Answer: a
Python program:
a = 120 + 80 
b = a * const_0_2778
c = b * 9
d = c - 250
Problem: 3 candidates in an election and received 2500 , 5000 and 15000 votes respectively . what % of the total votes did the winningcandidate got in that election ?
Options: a ) 45 % , b ) 50 % , c ) 57 % , d ) 66.6 % , e ) 65.6 %
Rationale: "total number of votes polled = ( 2500 + 5000 + 15000 ) = 22500 so , required percentage = 11628 / 20400 * 100 = 66.6 % d"
Answer: d
Python program:
a = 2500 + 5000 
b = a + 15000 
c = 15000 / b
d = c * 100
Problem: an auction house charges a commission of 15 % on the first $ 50000 of the sale price of an item , plus 10 % on the amount of of the sale price in excess of $ 50000 . what was the price of a painting for which the house charged a total commission of $ 24000 ?
Options: a ) $ 115,000 , b ) $ 160,000 , c ) $ 215,000 , d ) $ 240,000 , e ) $ 365,000
Rationale: say the price of the house was $ x , then 0.15 * 50,000 + 0.1 * ( x - 50,000 ) = 24,000 - - > x = $ 215,000 ( 15 % of $ 50,000 plus 10 % of the amount in excess of $ 50,000 , which is x - 50,000 , should equal to total commission of $ 24,000 ) . answer : c
Answer: c
Python program:
a = 15 / 100
b = 50000 * a
c = 24000 - b
d = 10 / 100
e = c / d
f = e + 50000 
g = f - 50000
h = g / 1000
Problem: laura took out a charge account at the general store and agreed to pay 4 % simple annual interest . if she charges $ 35 on her account in january , how much will she owe a year later , assuming she does not make any additional charges or payments ?
Options: a ) $ 36.4 , b ) $ 37.10 , c ) $ 37.16 , d ) $ 38.10 , e ) $ 38.80
Rationale: "principal that is amount taken by laura at year beginning = 35 $ rate of interest = 4 % interest = ( 4 / 100 ) * 35 = 1.4 $ total amount that laura owes a year later = 35 + 1.4 = 36.4 $ answer a"
Answer: a
Python program:
a = 4 / 100
b = a * 35
c = b + 35
Problem: a boat running up stram takes 6 hours to cover a certain distance , while it takes 10 hours to cover the same distance running down stream . what is the ratio between the speed of the boat and the speed of water current respectively ?
Options: a ) 2 : 3 , b ) 5 : 6 , c ) 4 : 1 , d ) 7 : 1 , e ) 8 : 1
Rationale: explanation : let speed of boat is x km / h and speed stream is y km / hr 6 ( x + y ) = 10 ( x - y ) 6 x + 6 y = 10 x - 10 y 16 y = 4 x 4 y = x x / y = 4 / 1 4 : 1 answer : option c
Answer: c
Python program:
a = 10 - 6
Problem: how many of the integers between 10 and 40 are even ?
Options: a ) 21 , b ) 20 , c ) 15 , d ) 10 , e ) 9
Rationale: "number start between 10 to 40 is 30 numbers half of them is even . . which is 15 answer : c"
Answer: c
Python program:
a = 40 - 10
b = a / 2
Problem: for a race a distance of 224 meters can be covered by p in 28 seconds and q in 32 seconds . by what distance does p defeat q eventually ?
Options: a ) 26 m , b ) 32 m , c ) 24 m , d ) 28 m , e ) none of these
Rationale: "explanation : this is a simple speed time problem . given conditions : = > speed of p = 224 / 28 = 8 m / s = > speed of q = 224 / 32 = 7 m / s = > difference in time taken = 4 seconds therefore , distance covered by p in that time = 8 m / s x 4 seconds = 32 metres answer : b"
Answer: b
Python program:
a = 28 * speed
b = 224 - a
Problem: jackie has two solutions that are 2 percent sulfuric acid and 12 percent sulfuric acid by volume , respectively . if these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 10 percent sulfuric acid , approximately how many liters of the 12 percent solution will be required ?
Options: a ) 18 , b ) 20 , c ) 48 , d ) 36 , e ) 42
Rationale: "let a = amount of 2 % acid and b = amount of 12 % acid . now , the equation translates to , 0.02 a + . 12 b = . 1 ( a + b ) but a + b = 60 therefore . 02 a + . 12 b = . 1 ( 60 ) = > 2 a + 12 b = 600 but b = 60 - a therefore 2 a + 12 ( 60 - a ) = 600 = > 10 a = 120 hence a = 12 . b = 60 - 12 = 48 . answer : c"
Answer: c
Python program:
a = 60 / 10
b = 3 * a
Problem: in a class of 35 students , 2 students did not borrow any books from the library , 12 students each borrowed 1 book , 10 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?
Options: a ) 3 , b ) 5 , c ) 8 , d ) 13 , e ) 15
Rationale: "total # of students = 35 avg # of books per student = 2 total # of books = 35 * 2 = 70 # of student borrowed at least 3 books = 35 - 2 - 12 - 10 = 11 # of books borrowed by above 11 students = 70 - ( 12 * 1 ) + ( 10 * 2 ) = 38 considering that 10 out of above 11 students borrowed only 3 books , # of books borrowed = 10 * 3 = 30 so maximum # of books borrowed by any single student = 38 - 30 = 8 option c"
Answer: c
Python program:
a = 35 * 2
b = 12 * 1
c = b + 10 
d = c + 2 
e = 35 - d
f = e - 1
g = f * 3
h = 12 * 1
i = 10 * 2
j = h + i 
k = g + j 
l = a - k
Problem: find avrg speed if a man travels at speed of 24 km / hr up and 36 km / hr dawn at an altitude of 200 m .
Options: a ) 25.8 , b ) 26.8 , c ) 27.8 , d ) 28.8 , e ) 29.8
Rationale: avg speed = 2 * x * y / ( x + y ) = 2 * 24 * 36 / ( 24 + 36 ) = 28.8 answer : d
Answer: d
Python program:
a = 2 * 24
b = a * 36
c = 24 + 36 
d = b / c
Problem: a watch was sold at a loss of 36 % . if it was sold for rs . 140 more , there would have been a gain of 4 % . what is the cost price ?
Options: a ) 350 , b ) 288 , c ) 799 , d ) 778 , e ) 901
Rationale: "64 % 104 % - - - - - - - - 40 % - - - - 140 100 % - - - - ? = > rs . 350 answer : a"
Answer: a
Python program:
a = 140 * 100
b = 100 + 4 
c = 100 - 36
d = b - c
e = a / d
Problem: what is the probability that jamie and tom will get selected for a job they both applied for in a company , given that their chances of getting selected is 2 / 3 and 5 / 7 respectively ?
Options: a ) 13 / 25 , b ) 2 / 5 , c ) 9 / 20 , d ) 11 / 20 , e ) 10 / 21
Rationale: explanation : p ( jamie ) = 2 / 3 p ( tom ) = 5 / 7 e = { jamie and tom both get selected } p ( e ) = p ( jamie ) * p ( tom ) = 2 / 3 * 5 / 7 = 10 / 21 answer : e
Answer: e
Python program:
a = 2 / 3
b = 5 / 7
c = a * b
Problem: weights of two friends ram and shyam are in the ratio 4 : 5 . if ram ' s weight is increased by 10 % and total weight of ram and shyam become 82.8 kg , with an increases of 15 % . by what percent did the weight of shyam has to be increased ?
Options: a ) 19 % , b ) 10 % , c ) 21 % , d ) 16 % , e ) none
Rationale: "solution : given ratio of ram and shayam ' s weight = 4 : 5 hence , ( x - 15 ) / ( 15 - 10 ) = 4 / 5 or , x = 19 % . answer : option a"
Answer: a
Python program:
a = 15 - 10
b = 4 / 5
c = a * b
d = 15 + c
Problem: a man invests in a 16 % stock at 128 . the interest obtained by him is :
Options: a ) 12.9 % , b ) 92.5 % , c ) 12.5 % , d ) 12.6 % , e ) 12.7 %
Rationale: "explanation : by investing rs 128 , income derived = rs . 16 by investing rs . 100 , income derived = = rs . 12.5 interest obtained = 12.5 % answer : c ) rs . 12.5 %"
Answer: c
Python program:
a = 16 / 128
b = a * 100
Problem: if a certain computer is capable of printing 4900 monthly credit card bills per hour , while a new model is capable of printing at a rate of 6600 per hour , the old model will take approximately how much longer than the new model to print 10000 bills ?
Options: a ) 31 , b ) 76 , c ) 88 , d ) 26 , e ) 81
Rationale: "explanation : old model is capable of printing at a rate of 4900 per hour new model is capable of printing at a rate of 6600 per hour old model time taken to print 10000 cards = 10000 / 4900 = 100 / 49 new model time taken to print 10000 cards = 10000 / 6600 = 100 / 66 old model – new model : 100 / 49 - 100 / 66 = 1700 / ( 49 × 66 ) = 850 / ( 49 × 33 ) = 0.525 hrs = > 31 mins therefore , the old model will take approximately 31 mins longer than the new model to print 10000 bills answer : a"
Answer: a
Python program:
a = 10000 / 4900
b = 10000 / 6600
c = a - b
d = c * const_60
Problem: the difference of two numbers is 1385 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder . what is the smaller number ?
Options: a ) 274 , b ) 270 , c ) 295 , d ) 360 , e ) 252
Rationale: "let the smaller number be x . then larger number = ( x + 1385 ) . x + 1385 = 6 x + 15 5 x = 1370 x = 274 smaller number = 274 . answer a"
Answer: a
Python program:
a = 1385 + 15 
b = 6 - 1
c = a / b
Problem: if a book is sold at 8 % profit instead of 8 % loss , it would have brought rs 12 more . find out the cost price of the book
Options: a ) rs 75 , b ) rs 72 , c ) rs 60 , d ) rs 70 , e ) rs 80
Rationale: "let c . p . of the book be rs . ’ x ’ given , 1.08 x - 0.92 x = 12 = > 0.16 x = 12 = 12 / 0.16 = rs 75 answer : a"
Answer: a
Python program:
a = 8 / 2
b = 100 * a
c = b / 8
Problem: if a is the smallest positive integer such that 3150 multiplied by a is the square of an integer , then a must be
Options: a ) 2 , b ) 5 , c ) 6 , d ) 7 , e ) 14
Rationale: solution : this problem is testing us on the rule that when we express a perfect square by its unique prime factors , every prime factor ' s exponent is an even number . let ’ s start by prime factorizing 3150 . 3150 = 315 x 10 = 5 x 63 x 10 = 5 x 7 x 3 x 3 x 5 x 2 3150 = 2 ^ 1 x 3 ^ 2 x 5 ^ 2 x 7 ^ 1 ( notice that the exponents of both 2 and 7 are not even numbers . this tells us that 3150 itself is not a perfect square . ) we also are given that 3150 multiplied by a is the square of an integer . we can write this as : 2 ^ 1 x 3 ^ 2 x 5 ^ 2 x 7 ^ 1 x a = square of an integer according to our rule , we need all unique prime factors ' exponents to be even numbers . thus , we need one more 2 and one more 7 . therefore , a = 7 x 2 = 14 answer is e .
Answer: e
Python program:
a = 1 + 4 
b = 1 + 4 
c = a * b
d = 3150 / c
e = d / 2
f = e / 3
g = f / 3
h = 2 * g
Problem: calculate how long it will take a swimmer to swim a distance of 3 km against the current of a river which flows at 1.7 km / hr , given that he can swim in still water at 3 km / h
Options: a ) 2.31 , b ) 9.31 , c ) 1.31 , d ) 4.31 , e ) 3.31
Rationale: "swim in still water at = 3 speed of river = 1.7 us = 3 - 1.7 = 1.3 distance = 3 t = 3 / 1.3 = 2.31 answer : a"
Answer: a
Python program:
a = 3 - 1
b = 3 / a
Problem: crazy eddie has a key chain factory . eddie managed to decrease the cost of manufacturing his key chains while keeping the same selling price , and thus increased the profit from the sale of each key chain from 35 % of the selling price to 50 % of the selling price . if the manufacturing cost is now $ 50 , what was it before the decrease ?
Options: a ) $ 20 , b ) $ 65 , c ) $ 50 , d ) $ 80 , e ) $ 100
Rationale: "deargoodyear 2013 , i ' m happy to help . this is a relatively straightforward problem , not very challenging . btw , crazy eddiewas the actually name of an electronics chain on the east coast of the usa back in the 1970 s . manufacturing now is $ 50 . they now are making a 50 % profit , so the selling price must be $ 100 . they had this same selling price , $ 100 , before they made the change , and had a profit of 35 % , so the manufacturing must have been $ 65 . answer = ( b ) ."
Answer: b
Python program:
a = 50 / 100
b = 50 / a
c = 50 / 100
d = 50 / c
e = 35 / 100
f = d * e
g = b - f
Problem: find a two digit number , given that the sum of the digits is 13 and the difference of the digits is 5 . ?
Options: a ) 74 , b ) 82 , c ) 95 , d ) 76 , e ) 94
Rationale: "using elimination method find which of the options fit the description of the number . . . from the option only 94 meets this description sum of digits - - - 9 + 4 = 13 difference of digits - - - 9 - 4 = 5 answer e ."
Answer: e
Python program:
a = 5 * 5
b = 5 + 4 
c = a * b
Problem: a can do a work in 24 days and b can do it in 16 days . in how many days a and b can do the work ?
Options: a ) 20 days , b ) 10 days , c ) 6 days , d ) 9 3 / 5 days , e ) 7 days
Rationale: "explanation : a ' s 1 day ' s work = 1 / 24 b ' s 1 day ' s work = 1 / 16 they work together = 1 / 24 + 1 / 16 = 5 / 48 = 48 / 5 = 9 3 / 5 days answer : option d"
Answer: d
Python program:
a = 1 / 16
b = 1 / 24
c = a - b
d = 1 / c
Problem: mike earns $ 14 per hour and phil earns $ 7 per hour . approximately how much less , as a percentage , does phil earn than mike per hour ?
Options: a ) 25 % , b ) 32.5 % , c ) 37 % , d ) 50 % , e ) 40 %
Rationale: what % less of 14 is 7 let it be x % less , then = 14 ( 1 - x / 100 ) = 7 1 - x / 100 = 7 / 14 x = 100 / 2 x = 50 % ans d
Answer: d
Python program:
a = 7 / 14
b = a * 100
Problem: albert is 2 times mary ’ s age and 4 times as old as betty . mary is 8 years younger than albert . how old is betty ?
Options: a ) 4 , b ) 6 , c ) 10 , d ) 16 , e ) 18
Rationale: a = 2 m = m + 8 m = 8 a = 16 a = 4 b , and so b = 4 the answer is a .
Answer: a
Python program:
a = 2 * 8
b = a / 4
Problem: a manufacturer is using glass as the surface for the multi - touch screen of its smartphone . the glass on the manufactured phone has a 4 % probability of not passing quality control tests . the quality control manager bundles the smartphone in groups of 10 . if that bundle has any smartphone that does not pass the quality control test , the entire bundle of 10 is rejected . what is the probability that a smartphone bundle that will be rejected by quality control ?
Options: a ) 0.25 , b ) . 05 ^ 10 , c ) 1 - 0.95 ^ 10 , d ) 1 - 0.05 ^ 10 , e ) 1 - 0.96 ^ 10
Rationale: find the probability of the opposite event and subtract from 1 . the opposite event is that bundle will not be rejected by quality control , which will happen if all 10 phones pass the test , so p ( all 10 phones pass test ) = 0.96 ^ 10 . p ( at least one phone do not pass the test ) = 1 - p ( all 10 phones pass test ) = 1 - 0.96 ^ 10 . answer : e .
Answer: e
Python program:
a = 4 / 100
b = 1 - a
c = b ** 10
d = 1 - c
Problem: the ratio between the perimeter and the width of a rectangle is 5 : 1 . if the area of the rectangle is 150 sq . cm , what is the length of the rectangle ?
Options: a ) 12 cm
b ) 15 cm
c ) 18 cm
d ) 21 cm
e ) 24 cm
Rationale: 2 l + 2 w = 5 w l = 3 w / 2 w * l = 150 3 w ^ 2 / 2 = 150 w ^ 2 = 100 w = 10 l = 3 ( 10 ) / 2 = 15 the answer is b .
Answer: b
Python program:
a = 150 / 10
Problem: in a village there are 150 men and 90 women in present time . if in next year population will be p = ( a ^ 2 + b ^ 2 ) ^ 1 / 2 , and in every year men are reduces 6 % . what is population of after 2 year .
Options: a ) 140 , b ) 141 , c ) 142 , d ) 143 , e ) 145
Rationale: "next year total population = [ 150 ^ 2 + 90 ^ 2 ] ^ . 5 = 174.92 = 175 man decreased by 6 % so total man = 150 * . 94 = 141 women will be = 175 - 141 = 34 so population after two years = [ 135 ^ 2 + 34 ^ 2 ] ^ . 5 = 145.04 = 145 so population after two year = 145 answer : e"
Answer: e
Python program:
a = 1 / 6
b = 1 - a
c = b * 150
d = c ** 2
e = 150 ** 2
f = 90 ** 2
g = e + f 
h = 1 / 2
i = g ** h
j = 1 / 6
k = 1 - j
l = k * 150
m = i - l
n = m ** 2
o = d + n 
p = 1 / 2
q = o ** p
Problem: crazy eddie has a key chain factory . eddie managed to decrease the cost of manufacturing his key chains while keeping the same selling price , and thus increased the profit from the sale of each key chain from 30 % of the selling price to 50 % of the selling price . if the manufacturing cost is now $ 50 , what was it before the decrease ?
Options: a ) $ 20 , b ) $ 40 , c ) $ 50 , d ) $ 70 , e ) $ 100
Rationale: "deargoodyear 2013 , i ' m happy to help . this is a relatively straightforward problem , not very challenging . btw , crazy eddiewas the actually name of an electronics chain on the east coast of the usa back in the 1970 s . manufacturing now is $ 50 . they now are making a 50 % profit , so the selling price must be $ 100 . they had this same selling price , $ 100 , before they made the change , and had a profit of 30 % , so the manufacturing must have been $ 70 . answer = ( d ) ."
Answer: d
Python program:
a = 50 / 100
b = 50 / a
c = 50 / 100
d = 50 / c
e = 30 / 100
f = d * e
g = b - f
Problem: if ( 1 / 2 ) ^ 16 ( 1 / 81 ) ^ k = 1 / 18 ^ 16 , then k =
Options: a ) 8 , b ) 12 , c ) 16 , d ) 24 , e ) 36
Rationale: "i ' m going to focus on denominator only . . ( 2 ^ 16 ) . ( ( 3 ^ 4 ) ^ k = 18 ^ 16 ( 2 ^ 16 ) . ( ( 3 ^ 4 k ) = ( 2 . 3 ^ 2 ) ^ 16 ( 2 ^ 16 ) . ( ( 3 ^ 4 k ) = ( 2 ^ 24 ) . ( 3 ^ 2 ) ^ 16 hence 4 k = 32 k = 8 answer a i hope it ' s quite clear"
Answer: a
Python program:
a = 16 * 2
b = a / 4
Problem: excluding stoppages , the speed of a bus is 50 kmph and including stoppages , it is 35 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 17 minutes , b ) 18 minutes , c ) 19 minutes , d ) 16 minutes , e ) none of these
Rationale: "explanation : in one hour due to stoppages , it covers 15 km less . time taken to cover 15 km = [ 15 / 50 * 60 ] min = 18 min answer : b"
Answer: b
Python program:
a = 50 - 35
b = a / 50
c = const_60 * b
Problem: in triangle pqr , the angle q = 90 degree , pq = 3 cm , qr = 8 cm . x is a variable point on pq . the line through x parallel to qr , intersects pr at y and the line through y , parallel to pq , intersects qr at z . find the least possible length of xz
Options: a ) 3.6 cm , b ) 2.4 cm , c ) 4.8 cm , d ) 2.16 cm , e ) 3.2 cm
Rationale: "look at the diagram below : now , in case when qy is perpendicular to pr , two right triangles pqr and pqy are similar : qy : qp = qr : pr - - > qy : 3 = 8 : 10 - - > qy = 2.4 . answer : b ."
Answer: b
Python program:
a = 3 * 8
b = a / 10
Problem: an engineer undertakes a project to build a road 15 km long in 300 days and employs 40 men for the purpose . after 100 days , he finds only 2.5 km of the road has been completed . find the ( approximate ) number of extra men he must employ to finish the work in time .
Options: a ) a . 43 , b ) b . 45 , c ) c . 55 , d ) d . 68 , e ) e . 60
Rationale: "40 workers working already let x be the total men required to finish the task in next 200 days 2.5 km done hence remaining is 12.5 km also , work has to be completed in next 200 days ( 300 - 100 = 200 ) we know that , proportion of men to distance is direct proportion and , proportion of men to days is inverse proportion hence , x = ( 40 * 12.5 * 100 ) / ( 2.5 * 200 ) thus , x = 100 thus , more men needed to finish the task = 100 - 40 = 60 hence answer is e"
Answer: e
Python program:
a = 15 - 2
b = 40 * a
c = b * 100
d = 300 - 100
e = 2 * 5
f = c / e
g = f - 40
Problem: the average age of 25 students of a class is 25 years . out of these , the average age of 10 students is 22 years and that of the other 14 students is 28 years . the age of the 25 th student is ?
Options: a ) 10 , b ) 15 , c ) 13 , d ) 11 , e ) 9
Rationale: "age of the 25 th student = 25 * 25 - ( 10 * 22 + 14 * 28 ) = 625 - 612 = 13 years answer is c"
Answer: c
Python program:
a = 25 * 25
b = 10 * 22
c = 14 * 28
d = b + c 
e = a - d
Problem: how many numbers between 1000 and 5000 are exactly divisible by 225 ?
Options: a ) 16 , b ) 18 , c ) 19 , d ) 12 , e ) 21
Rationale: explanation : first multiple of 225 after 1000 is 1125 ( 225 ã — 5 ) and last multiple of 225 before 5000 is 4950 ( 225 ã — 22 ) total number are l + a / d = 4950 - 1125 / 225 + 1 = 18 answer is b
Answer: b
Python program:
a = 5000 - 1000
b = a / 225