euclaise/mathqa_programs huggingface dataset:
Problem: right triangle abc is to be drawn in the xy - plane so that the right angle is at a and ab is parallel to the y - axis . if the x - and y - coordinates of a , b , and c are to be integers that are consistent with the inequalities - 6 ≤ x ≤ 2 and 4 ≤ y ≤ 9 , then how many different triangles can be drawn that will meet these conditions ?
Options: a ) 54 , b ) 432 , c ) 2,160 , d ) 2,916 , e ) 148,824
Rationale: "we have the rectangle with dimensions 9 * 6 ( 9 horizontal dots and 6 vertical ) . ab is parallel to y - axis and ac is parallel to x - axis . choose the ( x , y ) coordinates for vertex a : 9 c 1 * 6 c 1 ; choose the x coordinate for vertex c ( as y coordinate is fixed by a ) : 8 c 1 , ( 9 - 1 = 8 as 1 horizontal dot is already occupied by a ) ; choose the y coordinate for vertex b ( as x coordinate is fixed by a ) : 5 c 1 , ( 6 - 1 = 5 as 1 vertical dot is already occupied by a ) . 9 c 1 * 6 c * 8 c 1 * 5 c 1 = 2160 . answer : c ."
Answer: c
Python program:
a = 6 - 1
b = 6 * a
c = 9 * 6
d = b * c
Problem: the market value of a 10.5 % stock , in which an income of rs . 756 is derived by investing rs . 6000 , brokerage being 1 / 4 % , is :
Options: a ) 83.08 , b ) 114 , c ) 114.75 , d ) 124 , e ) 124.75
Rationale: face value = rs . 6000 . dividend = 10.5 % . annual income = rs . 756 . brokerage per rs . 100 = rs . 0.25 . dividend is always paid on the face value of a share . face value * dividend / ( market value + brokerage per rs . 100 ) = annual income . = 6000 * 10.5 / 756 = market value of rs . 100 stock + brokerage per rs . 100 . = market value of rs . 100 stock + brokerage per rs . 100 = rs . 83.33 . = market value of rs . 100 stock = rs . 83.33 - re . 0.25 . = market value of rs . 100 stock = rs . 83.08 answer : a
Answer: a
Python program:
a = 6000 / 756
b = a * 10
c = 1 / 4
d = b - c
Problem: the curved surface of a sphere is 64 pi cm 2 . find its radius ?
Options: a ) 1 cm , b ) 4 cm , c ) 2 cm , d ) 3 cm , e ) 5 cm
Rationale: "4 ï € r 2 = 64 = > r = 4 answer b"
Answer: b
Python program:
a = 64 / 4
b = math.sqrt(a)
Problem: a shopping cart contains only apples , oranges , and pears . if there are 3 times as many oranges as apples , and 4 times as many pears as oranges , then the apples are equivalent to what fraction of the pears ?
Options: a ) 1 / 6 , b ) 1 / 8 , c ) 1 / 12 , d ) 1 / 4 , e ) 3 / 4
Rationale: o = 3 a p = 4 o = 12 a a = p / 12 the answer is c .
Answer: c
Python program:
a = 4 * 3
b = 1 / a
Problem: the compound interest earned by sunil on a certain amount at the end of two years at the rate of 6 % p . a . was rs . 370.80 . find the total amount that sunil got back at the end of two years in the form of principal plus interest earned .
Options: a ) rs . 3360.80 , b ) rs . 3370.80 , c ) rs . 3320.70 , d ) rs . 3230.80 , e ) rs . 3130.80
Rationale: let the sum be rs . p p { [ 1 + 6 / 100 ] 2 - 1 } = 370.80 p ( 6 / 100 ) ( 2 + 6 / 100 ) = 370.80 [ a 2 - b 2 = ( a - b ) ( a + b ) ] p = 246 / ( 0.05 ) ( 2.05 ) = 3000 . amount = rs . 3370.80 . answer : b
Answer: b
Python program:
a = 6 / 100
b = 1 + a 
c = b ** 2
d = c - 1
e = 370 / 8
f = e + 370
Problem: q ' = 3 q - 3 , what is the value of ( 3 ' ) ' ?
Options: a ) 0 , b ) 10 , c ) 20 , d ) 30 , e ) 40
Rationale: "( 3 ' ) ' = ( 3 * 3 - 3 ) ' = 6 ' = 6 * 6 - 6 = 30 answer d"
Answer: d
Python program:
a = 3 * 3
b = a - 3
c = b * 3
d = c - 3
e = 3 - 1
f = d * e
Problem: five equal cubes , each of side 5 cm , are placed adjacent to each other . the volume of the new solid formed will be
Options: a ) 125 cm 3
b ) 625 cm 3
c ) 15525 cm 3
d ) 1225 cm 3
e ) none
Rationale: solution the new solid formed is a cuboid of length 25 cm , breadth 5 cm and height 5 cm ∴ volume = ( 25 x 5 x 5 ) cm 3 ‹ = › 625 cm 3 answer b
Answer: b
Python program:
a = volume_cube * (
Problem: a watch was sold at a loss of 10 % . if it was sold for rs . 180 more , there would have been a gain of 5 % . what is the cost price ?
Options: a ) rs . 1200 , b ) rs . 1100 , c ) rs . 1300 , d ) rs . 1400 , e ) rs . 1000
Rationale: "90 % 105 % - - - - - - - - 15 % - - - - 180 100 % - - - - ? = > rs . 1200 answer : a"
Answer: a
Python program:
a = 180 * 100
b = 100 + 5 
c = 100 - 10
d = b - c
e = a / d
Problem: a train 80 m in length crosses a telegraph post in 6 seconds . the speed of the train is ?
Options: a ) 16 kmph , b ) 88 kmph , c ) 54 kmph , d ) 48 kmph , e ) 19 kmph
Rationale: "s = 80 / 6 * 18 / 5 = 48 kmph answer : d"
Answer: d
Python program:
a = 80 / 6
b = const_3_6 * a
Problem: a man can row upstream at 7 kmph and downstream at 33 kmph , and then find the speed of the man in still water ?
Options: a ) 11 , b ) 77 , c ) 30 , d ) 20 , e ) 34
Rationale: "us = 7 ds = 33 m = ( 33 + 7 ) / 2 = 20 answer : d"
Answer: d
Python program:
a = 7 + 33 
b = a / 2
Problem: in a class of 150 students 55 speak english ; 85 speak telugu and 30 speak neither english nor telugu how many speak both english and telugu ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: total = 150 english = 55 telugu = 85 none / neither english nor telugu = 30 no . of students who speak only one or both = 150 - 30 = 120 so , 120 stud ' s can speak english or telugu or both . then , no . of stud ' s speak only english = 120 - 85 ( telugu ) = 35 ` ` ` ` ` ` ` ` ` ` telugu = 120 - 55 = 65 remaining 120 - ( 65 + 35 ) = 20 stud ' s can speak both . b )
Answer: b
Python program:
a = 55 + 85 
b = 150 - 30
c = a - b
Problem: of the goose eggs laid at a certain pond , 2 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year . if 110 geese survived the first year and if no more than one goose hatched from each egg , how many goose eggs were laid at the pond ?
Options: a ) 280 , b ) 400 , c ) 540 , d ) 550 , e ) 840
Rationale: "of the goose eggs laid at a certain pond , 2 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month : 2 / 3 * 3 / 4 = 1 / 2 survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year : ( 1 - 3 / 5 ) * 1 / 2 = 1 / 5 survived the first year . 110 geese survived the first year : 1 / 5 * ( total ) = 110 - - > ( total ) = 550 . answer : d ."
Answer: d
Python program:
a = 3 / 5
b = 1 - a
c = 110 / b
d = 3 / 4
e = c / d
f = 2 / 3
g = e / f
Problem: a library has an average of 510 visitors on sundays and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is :
Options: a ) 250 , b ) 276 , c ) 280 , d ) 285 , e ) 295
Rationale: "explanation : since the month begins with a sunday , to there will be five sundays in the month . required average = ( 510 × 5 + 240 × 25 / 30 ) = 8550 / 30 = 285 answer : d"
Answer: d
Python program:
a = 3 + 4 
b = 30 / a
c = math.floor(b)
d = c + 1 
e = d * 510
f = 3 + 4 
g = 30 / f
h = math.floor(g)
i = h + 1 
j = 30 - i
k = j * 240
l = e + k 
m = l / 30
Problem: the price of a t . v . set worth rs . 15000 is to be paid in 20 installments of rs . 1500 each . if the rate of interest be 6 % per annum , and the first installment be paid at the time of purchase , then the value of the last installment covering the interest as well will be ?
Options: a ) 29997 , b ) 28088 , c ) 13500 , d ) 19000 , e ) 2799
Rationale: "money paid in cash = rs . 1500 balance payment = ( 15000 - 1500 ) = rs . 13500 . answer : c"
Answer: c
Python program:
a = 15000 - 1500
Problem: a cheese factory sells its cheese in rectangular blocks . a normal block has a volume of 5 cubic feet . if a large block has three times the width , twice the depth , and half the length of a normal block , what is the volume of cheese in a large block in cubic feet ?
Options: a ) 10 , b ) 30 , c ) 15 , d ) 20 , e ) 25
Rationale: "volume of cube = lbh = 5 new cube l , b , h are increases of 3 b , 2 h and a decrease of . 5 l new volume of cube = . 5 l * 3 b * 2 h = 3 * lbh = 3 * 5 = 15 answer : c"
Answer: c
Python program:
a = 2 * 2
b = a * 2
c = b * 5
Problem: after a storm deposits 120 billion gallons of water into the city reservoir , the reservoir is 60 % full . if the original contents of the reservoir totaled 240 billion gallons , the reservoir was approximately what percentage full before the storm ?
Options: a ) 40 % , b ) 48 % , c ) 54 % , d ) 58 % , e ) 65 %
Rationale: "when the storm deposited 120 billion gallons , volume of water in the reservoir = 240 + 120 = 360 billion gallons if this is only 60 % of the capacity of the reservoir , the total capacity of the reservoir = 360 / 0.6 = 600 billion gallons therefore percentage of reservoir that was full before the storm = ( 240 / 600 ) * 100 = 40 % option c"
Answer: c
Python program:
a = 120 + 240 
b = 60 / 100
c = a / b
d = 240 / c
e = d * 100
Problem: the average of first six prime numbers greater than 65 is ?
Options: a ) 55 , b ) 77 , c ) 56 , d ) 67 , e ) 98
Rationale: "67 + 71 + 73 + 79 + 83 + 89 = 462 / 6 = 77 answer : b"
Answer: b
Python program:
a = 65 + 1
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 25 % 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 ) $ 75 , b ) $ 40 , 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 25 % , so the manufacturing must have been $ 75 . answer = ( a ) ."
Answer: a
Python program:
a = 50 / 100
b = 50 / a
c = 50 / 100
d = 50 / c
e = 25 / 100
f = d * e
g = b - f
Problem: ' a ' and ' b ' are positive integers such that their lcm is 20 and their hcf is 1 . what is the addition of the maximum and minimum possible values of ' a + b ' ?
Options: a ) 28 , b ) 30 , c ) 22 , d ) 20 , e ) 32
Rationale: "possible values of a and b can be 5,4 ; 4,5 ( which are same for a + b ) and 1,20 ; 20,1 ( same result for a + b ) so 21 + 9 = 30 . ans b ."
Answer: b
Python program:
a = 20 / 4
b = a + 4 
c = 20 / 4
d = c + 4 
e = b - d
Problem: speed of a boat in standing water is 9 kmph and speed of the stream is 1.5 kmph . a man can rows to a place at a distance of 105 km and comes back to the starting point . the total time taken by him is ?
Options: a ) 12 hours , b ) 24 hours , c ) 36 hours , d ) 10 hours , e ) 15 hours
Rationale: "speed upstream = 7.5 kmph speed downstream = 10.5 kmph total time taken = 105 / 7.5 + 105 / 10.5 = 24 hours answer is b"
Answer: b
Python program:
a = 9 + 1 
b = 9 - 1
c = a + b 
d = c * 105
e = 9 + 1 
f = 105 / e
g = 9 - 1
h = 105 / g
i = f + h 
j = 9 + 1 
k = 9 - 1
l = j + k 
m = i - l
n = m * const_60
o = d + n
Problem: the speed at which a man can row a boat in still water is 15 kmph . if he rows downstream , where the speed of current is 3 kmph , what time will he take to cover 30 metres ?
Options: a ) 6 , b ) 8 , c ) 12 , d ) 4 , e ) 13
Rationale: "speed of the boat downstream = 15 + 3 = 18 kmph = 18 * 5 / 18 = 5 m / s hence time taken to cover 60 m = 30 / 5 = 6 seconds . answer : a"
Answer: a
Python program:
a = 15 + 3 
b = a * const_0_2778
c = 30 / b
Problem: a money lender finds that due to a fall in the annual rate of interest from 8 % to 7 3 / 4 % his yearly income diminishes by rs . 62.50 , his capital is ?
Options: a ) 24,602 , b ) 25,000 , c ) 24,600 , d ) 24,628 , e ) 24,6012
Rationale: "let the capital be rs . x . then , ( x * 8 * 1 ) / 100 - ( x * 31 / 4 * 1 / 100 ) = 62.50 32 x - 31 x = 6250 * 4 x = 25,000 . answer : b"
Answer: b
Python program:
a = 4 / 4
b = 62 / 50
Problem: harkamal purchased 8 kg of grapes 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 ) 1055 , b ) b ) 1075 , c ) c ) 1145 , d ) d ) 1070 , e ) e ) 1080
Rationale: "cost of 8 kg grapes = 70 × 8 = 560 . cost of 9 kg of mangoes = 65 × 9 = 585 . total cost he has to pay = 560 + 585 = 1145 . c )"
Answer: c
Python program:
a = 8 * 70
b = 9 * 65
c = a + b
Problem: it was calculated that 75 men could complete a piece of work in 20 days . when work was scheduled to commence , it was found necessary to send 25 men to another project . how much longer will it take to complete the work ?
Options: a ) 10 , b ) 30 , c ) 20 , d ) 15 , e ) 40
Rationale: "before : one day work = 1 / 20 one man ’ s one day work = 1 / ( 20 * 75 ) now : no . of workers = 50 one day work = 50 * 1 / ( 20 * 75 ) the total no . of days required to complete the work = ( 75 * 20 ) / 50 = 30 answer : b"
Answer: b
Python program:
a = 75 / 25
b = 20 * a
Problem: the number of diagonals of a polygon of n sides is given by the formula z = n ( n - 3 ) / 2 . if a polygon has twice as many diagonals as sides , how many sides does it have ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "z = n ( n - 3 ) z = 2 * n 2 n = n ( n - 3 ) = > 2 = n - 3 = > n = 5 answer b"
Answer: b
Python program:
a = 3 + 2
Problem: divide rs . 32000 in the ratio 3 : 9 ?
Options: a ) 12000 , 20000 , b ) 12000 , 200098 , c ) 12000 , 20007 , d ) 12000 , 20006 , e ) 8000 , 24000
Rationale: "3 / 12 * 32000 = 8000 9 / 12 * 32000 = 24000 answer : e"
Answer: e
Python program:
a = 9 - 2
b = 9 - 2
c = 3 + b 
d = 32000 / c
e = a * d
Problem: what will be the remainder if 2 ^ 300 is divided by 4 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: d 4 now if you go on calculating 2 ^ 300 , you will lose so much time and it might not even be feasible to carry out so long of calculations . thus we will make use of a trick here . we will calculate the remainder of each power of 2 till we come across a pattern . 2 ^ 1 divided by 4 leaves the remainder 2 . 2 ^ 2 divided by 4 leaves the remainder 0 . 2 ^ 3 divided by 4 leaves the remainder 0 . 2 ^ 4 divided by 4 leaves the remainder 0 . you can see that all the following powers of two will be divisible by 4 . therefore the remainder when 2 ^ 300 is divided by 4 will be 0 only .
Answer: d
Python program:
a = 2 ** 2
Problem: a movie buff owns movies on dvd and on blu - ray in a ratio of 7 : 2 . if she buys 5 more blu - ray movies , that ratio would change to 13 : 4 . if she owns movies on no other medium , what was the original number of movies in her library before the extra purchase ?
Options: a ) 22 , b ) 28 , c ) 77 , d ) 99 , e ) 351
Rationale: if u can just keep an eye on the options 99 is the only multiple of 9 in options given . . so you can mark it wid in seconds . now coming to the process m ( d ) = 7 x and b ( d ) = 2 x now from the next line the new eqn becomes 7 x / ( 2 x + 6 ) = 13 / 4 solving it 28 x = 26 x + 78 x = 39 which means m ( d ) = 273 and b ( d ) = 78 so total initially is m ( d ) + b ( d ) = 351 e
Answer: e
Python program:
a = 5 + 1 
b = 13 * a
c = 4 * 7
d = 13 * 2
e = c - d
f = b / e
g = 7 + 2 
h = f * g
Problem: three numbers are in the ratio 1.5 : 2 : 3.5 and their h . c . f is 18 . the numbers are :
Options: a ) 22,36 , 63 , b ) 27,45 , 63 , c ) 27,54 , 63 , d ) 54 , 45 , 36 , e ) 27,36 , 63
Rationale: "let the required numbers be 1.5 x , 2 x and 3.5 x . then , their h . c . f = x . so , x = 18 . the numbers are 27,36 , 63 . answer : e"
Answer: e
Python program:
a = 1 * 5
b = a * 100
c = 2 * 3
d = b + c
Problem: 10 % people of a village in sri lanka died by bombardment , 20 % of the remainder left the village on account of fear . if now the population is reduced to 4500 , how much was it in the beginning ?
Options: a ) 5999 , b ) 6788 , c ) 6250 , d ) 4559 , e ) 6989
Rationale: "x * ( 90 / 100 ) * ( 80 / 100 ) = 4500 x = 6250 answer : c"
Answer: c
Python program:
a = 100 - 10
b = a / 100
c = 100 - 20
d = c / 100
e = b * d
f = 4500 / e
g = math.floor(f)
Problem: the tax on a commodity is diminished by 25 % 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 ) 17.5 %
Rationale: "explanation : 100 * 100 = 10000 75 * 110 = 8250 10000 - - - - - - - 1750 100 - - - - - - - ? = 17.5 % e )"
Answer: e
Python program:
a = 100 + 10 
b = 100 - 25
c = a * b
d = c / 100
e = 100 - d
Problem: the sum of the first 60 positive even integers is 3,750 . what is the sum of the odd integers from 101 to 200 , inclusive ?
Options: a ) 4,700 , b ) 7,500 , c ) 10,500 , d ) 15,000 , e ) 19,600
Rationale: "101 + 103 + . . . . . . . 199 if we remove 100 from each of these it will be sum of 1 st 100 odd numbers . so 101 + 103 + . . . . . . . 199 = 60 * 100 + ( 1 + 3 + 5 + 7 + . . . . . . ) sum of 1 st 100 natural numbers = ( 100 * 101 ) / 2 = 5050 sum of 1 st 60 positive even integers = 3750 sum of 1 st 100 odd numbers = 5050 - 3750 = 1300 so 101 + 103 + . . . . . . . 199 = 60 * 100 + ( 1 + 3 + 5 + 7 + . . . . . . ) = 6000 + 1300 = 4700 a is the answer ."
Answer: a
Python program:
a = 200 + 101 
b = a / 2
c = 200 - 101
d = c / 2
e = d + 1 
f = b * e
Problem: a wooden cube whose edge length is 6 inches is composed of smaller cubes with edge lengths of one inch . the outside surface of the large cube is painted red and then it is split up into its smaller cubes . if one cube is randomly selected from the small cubes , what is the probability that the cube will have at least one red face ?
Options: a ) 54.9 %
b ) 58.7 %
c ) 62.5 %
d ) 66.3 %
e ) 70.4 %
Rationale: there are a total of 6 * 6 * 6 = 216 cubes . all the exterior cubes will have at least one face painted red . the interior is formed by 4 * 4 * 4 = 64 cubes . the number of cubes with at least one side painted red is 216 - 64 = 152 cubes the probability that a cube has at least one side painted red is 152 / 216 which is about 70.4 % the answer is e .
Answer: e
Python program:
a = 1 * 4
b = volume_cube / (
c = 1 - b
d = 100 * c
Problem: ages of two persons differ by 18 years . if 6 year ago , the elder one be 3 times as old the younger one , find their present age
Options: a ) 12,28 , b ) 15,33 , c ) 16,32 , d ) 18,34 , e ) 19,34
Rationale: "explanation : let the age of younger person is x , then elder person age is ( x + 18 ) = > 3 ( x - 6 ) = ( x + 18 - 6 ) [ 6 years before ] = > 3 x - 18 = x + 12 = > x = 15 . so other person age is x + 18 = 33 answer : option b"
Answer: b
Python program:
a = 6 * 6
b = a + 18 
c = b - 6
d = 6 - 1
e = c / d
f = e - 1
Problem: the h . c . f . of two numbers is 28 and the other two factors of their l . c . m . are 12 and 15 . the larger of the two numbers is
Options: a ) 420 , b ) 430 , c ) 312 , d ) 322 , e ) none
Rationale: "solution clearly , the numbers are ( 28 x 12 ) and ( 28 x 15 ) . larger number = ( 28 x 15 ) = 420 . answer a"
Answer: a
Python program:
a = 28 * 15
Problem: in the first 8 overs of a cricket game , the run rate was only 2.3 what should be the rate in the remaining 20 overs to reach the target of 260 runs ?
Options: a ) 12.08 , b ) 12.18 , c ) 12.0 , d ) 6.19 , e ) 6.21
Rationale: "required run rate = [ 260 - ( 2.3 * 8 ) ] / 20 = 241.60 / 20 = 12.08 answer : a"
Answer: a
Python program:
a = 8 * 2
b = 260 - a
c = b / 20
Problem: in the first 20 overs of a cricket game , the run rate was only 4.3 . what should be the run rate in the remaining 30 overs to reach the target of 264 runs ?
Options: a ) 5.93 , b ) 6.5 , c ) 6.75 , d ) 7 , e ) 8
Rationale: "explanation : required run rate = ( 264 - ( 4.3 x 20 ) ) / 30 = 178 / 30 = 5.93 answer : a"
Answer: a
Python program:
a = 20 * 4
b = 264 - a
c = b / 30
Problem: at what price must an article costing rs . 150 be marked in order that after deducting 10 % from the list price . it may be sold at a profit of 30 % on the cost price ?
Options: a ) 62.5 , b ) 62.0 , c ) 62.6 , d ) 216.67 , e ) 62.2
Rationale: "cp = 150 sp = 150 * ( 130 / 100 ) = 195 mp * ( 90 / 100 ) = 195 mp = 216.67 answer : d"
Answer: d
Python program:
a = 150 * 30
b = a / 100
c = 150 + b 
d = c * 100
e = 100 - 10
f = d / e
Problem: a man can row 8 kmph in still water . when the river is running at 2 kmph , it takes him 1 hour to row to a place and black . what is the total distance traveled by the man ?
Options: a ) 5.75 , b ) 5.7 , c ) 7.5 , d ) 5.74 , e ) 5.71
Rationale: "m = 8 s = 2 ds = 10 us = 6 x / 10 + x / 6 = 1 x = 3.75 d = 3.75 * 2 = 7.5 answer : c"
Answer: c
Python program:
a = 8 + 2 
b = 8 - 2
c = a * b
d = 8 + 2 
e = 8 - 2
f = d + e 
g = c / f
h = g * 2
Problem: all the faces of cubes are painted with red colour . it is then cut into 64 equal small cubes . find how many small cubes are there whose three faces are coloured ?
Options: a ) 4
b ) 8
c ) 16
d ) 24
e ) 2
Rationale: there are 64 small cubes , hence one side side of the big cube is 3 √ 64 = 4 cm number of small cubes having three faces coloured = no . of corners = 8 answer : b
Answer: b
Python program:
a = 64 / 4
b = a / 2
Problem: an association of mathematics teachers has 1,260 members . only 525 of these members cast votes in the election for president of the association . what percent of the total membership voted for the winning candidate if the winning candidate received 60 percent of the votes cast ?
Options: a ) 75 % , b ) 58 % , c ) 42 % , d ) 34 % , e ) 25 %
Rationale: "total number of members = 1260 number of members that cast votes = 525 since , winning candidate received 60 percent of the votes cast number of votes for winning candidate = ( 60 / 100 ) * 525 = 315 percent of total membership that voted for winning candidate = ( 315 / 1260 ) * 100 = 25 % answer e"
Answer: e
Python program:
a = 60 / 100
b = a * 525
c = 4 ** 2
d = 100 * c
e = b / d
f = e * 100
Problem: if the sides of a square are doubled in length , the area of the original square is now how many times as large as the area of the resultant square ?
Options: a ) 25 % , b ) 50 % , c ) 100 % , d ) 200 % , e ) 400 %
Rationale: let the original square have sides of length l and the new square have sides of length 2 l . the resulting areas are l ^ 2 for the original square and 4 l ^ 2 for the new square ( as the length of the side is square to get the area ) . the original square ' s area is l ^ 2 / 4 l ^ 2 or 25 % of the new square ' s area . choice a
Answer: a
Python program:
a = 1 / 2
b = a ** 2
c = b * 100
Problem: there are 16 bees in the hive , then 10 more fly . how many bees are there in all ?
Options: a ) 7 , b ) 33 , c ) 12 , d ) 17 , e ) 26
Rationale: 16 + 10 = 26 . answer is e .
Answer: e
Python program:
a = 16 + 10
Problem: the banker ' s gain on a sum due 6 years hence at 12 % per annum is rs . 612 . what is the banker ' s discount ?
Options: a ) 1240 , b ) 1120 , c ) 1190 , d ) 1462 , e ) none of these
Rationale: "explanation : td = ( bg × 100 ) / tr = ( 612 × 100 ) / ( 6 × 12 ) = rs . 850 bg = bd – td = > 612 = bd - 850 = > bd = 612 + 850 = 1462 answer : option d"
Answer: d
Python program:
a = 612 * 100
b = 12 * 6
c = a / b
d = 612 + c
Problem: if remainder is 19 , quotient is 61 and dividend is 507 then what is divisor ?
Options: a ) 8 , b ) 18 , c ) 10 , d ) 12 , e ) 14
Rationale: "we know dividend = divisor * quotient + remainder = = = > 507 = divisor * 61 + 19 = = = = = > 488 / 61 = divisor = = = > divisor = 8 ans - a"
Answer: a
Python program:
a = 507 - 19
b = a / 61
Problem: the average salary of raj and roshan is rs . 4000 but the average salary of raj , roshan and thomas is rs . 5000 . what is the salary of thomas ?
Options: a ) 4000 , b ) 5000 , c ) 6000 , d ) 7000 , e ) 8000
Rationale: total salary of raj and roshan = 2 x 4000 = 8000 total salary of raj roshan and thomas = 3 x 5000 = 15000 salary of thomas = 15000 - 8000 = rs . 7000 answer : d
Answer: d
Python program:
a = 5000 + 4000 
b = 1000 * 2
c = a - b