euclaise/mathqa_programs huggingface dataset:
Problem: a volunteer organization is recruiting new members . in the fall they manage to increase their number by 6 % . by the spring however membership falls by 19 % . what is the total change in percentage from fall to spring ?
Options: a ) - 16.16 % , b ) - 15.15 % , c ) - 14.14 % , d ) - 13.13 % , e ) - 12.12 %
Rationale: "( 100 % + 6 % ) * ( 100 % - 19 % ) = 1.06 * . 81 = 0.8586 . 1 - 0.8586 = 14.14 % lost = - 14.14 % the answer is c the organization has lost 14.14 % of its total volunteers from fall to spring ."
Answer: c
Python program:
a = 6 / 100
b = 1 + a 
c = 19 / 100
d = 1 - c
e = b * d
f = e * 100
g = 100 - f
Problem: one hour after yolanda started walking from x to y , a distance of 31 miles , bob started walking along the same road from y to x . if yolanda â s walking rate was 1 miles per hour and bob â s was 2 miles per hour , how many miles had bob walked when they met ?
Options: a ) 19 , b ) 20 , c ) 22 , d ) 21 , e ) 19.5
Rationale: "let t be the number of hours that bob had walked when he met yolanda . then , when they met , bob had walked 4 t miles and yolanda had walked ( t + 1 ) miles . these distances must sum to 31 miles , so 2 t + ( t + 1 ) = 31 , which may be solved for t as follows 2 t + ( t + 1 ) = 31 2 t + t + 1 = 31 3 t = 30 t = 10 ( hours ) therefore , bob had walked 2 t = 2 ( 10 ) = 20 miles when they met . the best answer is b ."
Answer: b
Python program:
a = 31 - 1
b = 1 + 2 
c = a / b
d = c * 2
Problem: the length of a rectangular plot is 20 metres more than its breadth . if the cost of fencing the plot @ rs . 26.50 per metre is rs . 5565 , what is the length of the plot in metres ?
Options: a ) 333 , b ) 200 , c ) 288 , d ) 210 , e ) 1999
Rationale: "let length of plot = l meters , then breadth = l - 20 meters and perimeter = 2 [ l + l - 20 ] = [ 4 l - 40 ] meters [ 4 l - 40 ] * 26.50 = 5565 [ 4 l - 40 ] = 5565 / 26.50 = 210 4 l = 250 l = 250 / 4 = 62.5 meters . answer : d"
Answer: d
Python program:
a = 5565 / 26
b = a / 2
c = 2 * 20
d = b - c
Problem: if the perimeter of δ acd is 9 + 3 √ 3 , what is the perimeter of equilateral triangle δ abc ?
Options: a ) 9
b ) 18 − 3 √ 3
c ) 18
d ) 18 + 3 √ 3
e ) 27
Rationale: the altitude of an equilateral triangle is side * √ 3 / 2 . as perimeter of triangle acd is 9 + 3 √ 3 , ac + cd + ad = ( side + side / 2 + side * √ 3 / 2 ) = 9 + 3 √ 3 or side = 6 . perimeter of equilateral triangle , abc is 3 ( side ) or 18 . answer : ( optionc )
Answer: c
Python program:
a = 3 * 2
b = math.sqrt(3)
c = 3 - b
d = a * c
e = math.sqrt(3)
f = 3 - e
g = d / f
h = 3 * g
Problem: if 8 boys meet at a reunion and each boy shakes hands exactly once with each of the others , then what is the total number of handshakes
Options: a ) 41 , b ) 28 , c ) 43 , d ) 44 , e ) 45
Rationale: "n ( n - 1 ) / 2 = 8 * 7 / 2 = 28 answer : b"
Answer: b
Python program:
a = math.factorial(8)
b = 8 - 2
c = math.factorial(b)
d = math.factorial(2)
e = c * d
f = a / e
Problem: a man ' s basic pay for a 40 hour week is rs . 20 . overtime is paid for at 25 % above the basic rate . in a certain week he worked overtime and his total wage was rs . 25 . he therefore worked for a total of :
Options: a ) 45 hours , b ) 47 hours , c ) 48 hours , d ) 50 hours , e ) none
Rationale: explanation : basic rate per hour = rs . ( 20 / 40 ) = rs . 1 / 2 overtime per hour = 125 % of rs . 1 / 2 = 125 / 100 × 1 / 2 = rs . 5 / 8 suppose he worked x hours overtime . then , 20 + 5 / 8 x = 25 or 5 / 8 x = 5 x = 5 × 8 / 5 = 8 hours so he worked in all for ( 40 + 8 ) hours = 48 hours . correct option : c
Answer: c
Python program:
a = 25 - 20
b = 20 / 40
c = 100 + 25 
d = c / 100
e = b * d
f = a / e
g = f + 40
Problem: a can complete a work in 15 days and b can do the same work in 7 days . if a after doing 3 days , leaves the work , find in how many days b will do the remaining work ?
Options: a ) 2 days , b ) 5 1 / 2 days , c ) 6 1 / 2 days , d ) 7 1 / 2 days , e ) 10 days
Rationale: "the required answer = ( 15 - 3 ) * 7 / 15 = 84 / 15 = 5 1 / 2 days answer is b"
Answer: b
Python program:
a = 15 * 3
b = 15 / 3
c = a + b
Problem: how many positive integers less than 60 have a reminder 01 when divided by 3 ?
Options: a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 20
Rationale: "1 also gives the remainder of 1 when divided by 3 . so , there are total of 20 numbers . answer : e ."
Answer: e
Python program:
a = 4 + 1 
b = a - 1
c = math.factorial(b)
d = math.factorial(1)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: it takes six minutes to load a certain video on a cellphone , and fifteen seconds to load that same video on a laptop . if the two devices were connected so that they operated in concert at their respective rates , how many seconds would it take them to load the video ?
Options: a ) 13.8 , b ) 14.1 , c ) 14.4 , d ) 14.6 , e ) 14.8
Rationale: "the laptop can load the video at a rate of 1 / 15 of the video per second . the phone can load the video at a rate of 1 / ( 60 * 6 ) = 1 / 360 of the video per second . the combined rate is 1 / 15 + 1 / 360 = 25 / 360 of the video per second . the time required to load the video is 360 / 25 = 14.4 seconds . the answer is c ."
Answer: c
Python program:
a = 2 + 3 
b = a + 4 
c = b * const_60
d = 1/(c)
e = 3 * 4
f = e + 3 
g = 1/(f)
h = d + g 
i = 1/(h)
j = 4 * 4
k = j * 3
l = k - 2
m = 100 * 100
n = l / m
o = i - n
Problem: a computer store offers employees a 10 % discount off the retail price . if the store purchased a computer from the manufacturer for $ 1200 dollars and marked up the price 10 % to the final retail price , how much would an employee save if he purchased the computer at the employee discount ( 10 % off retail price ) as opposed to the final retail price .
Options: a ) 122 , b ) 132 , c ) 142 , d ) 152 , e ) 162
Rationale: "cost price = 1200 profit = 10 % = 10 % of 1200 = 120 selling price = cp + profit sp = 1320 a discount of 10 % to employees means 10 % off on 1320 so 10 % of 1320 = 132 ans b"
Answer: b
Python program:
a = 1200 * 10
b = a / 100
c = b + 1200 
d = 1200 / 100
e = d * 2
f = c / e
Problem: for all real numbers v , an operation is defined by the equation v * = v - v / 3 . if ( v * ) * = 12 , then v =
Options: a ) 15 , b ) 18 , c ) 21 , d ) 24 , e ) 27
Rationale: ( v * ) * = ( v - v / 3 ) - ( v - v / 3 ) / 3 12 = 2 v / 3 - 2 v / 9 = 4 v / 9 v = 27 the answer is e .
Answer: e
Python program:
a = 1 / 3
b = 1 - a
c = 12 / b
d = 1 / 3
e = 1 - d
f = c / e
Problem: the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 500 resolutions .
Options: a ) 287 m , b ) 704 m , c ) 168 m , d ) 278 m , e ) 107 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 500 resolutions . = 500 * 2 * 22 / 7 * 22.4 = 70400 cm = 704 m answer : b"
Answer: b
Python program:
a = 3 + 4 
b = a * 3
c = b + 1 
d = 3 + 4 
e = c / d
f = e * 22
g = f * 2
h = g * 500
i = h / 100
Problem: 20 percent of the women in a college class are science majors , and the non - science majors make up 60 % of the class . what percentage of the men are science majors if 40 % of the class are men ?
Options: a ) 40 % , b ) 50 % , c ) 60 % , d ) 70 % , e ) 80 %
Rationale: science majors make up 0.4 of the class . 60 % of the class are women and 0.2 * 0.6 = 0.12 of the class are female science majors . then 0.28 of the class are male science majors . 0.4 x = 0.28 x = 0.7 = 70 % the answer is d .
Answer: d
Python program:
a = 100 - 20
b = a / 100
c = 100 - 40
d = b * c
e = 60 - d
f = 40 - e
g = f / 40
h = g * 100
Problem: a grocer has a sale of rs . 8435 , rs . 8927 , rs . 8855 , rs . 9230 and rs . 8562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 8500 ?
Options: a ) s . 1991 , b ) s . 2991 , c ) s . 3991 , d ) s . 4991 , e ) s . 6991
Rationale: "explanation : total sale for 5 months = rs . ( 8435 + 8927 + 8855 + 9230 + 8562 ) = rs . 44009 . required sale = rs . [ ( 8500 x 6 ) â € “ 44009 ] = rs . ( 51000 â € “ 44009 ) = rs . 6991 . answer e"
Answer: e
Python program:
a = 5 + 1 
b = a * 8500
c = 8435 + 8927 
d = c + 8855 
e = d + 9230 
f = e + 8562 
g = b - f
Problem: two stations a and b are 110 km apart on a straight line . one train starts from a at 5 a . m . and travels towards b at 20 kmph . another train starts from b at 8 a . m . and travels towards a at a speed of 25 kmph . at what time will they meet ?
Options: a ) 11 , b ) 10 , c ) 8 , d ) 12 , e ) 15
Rationale: "suppose they meet x hours after 5 a . m . distance covered by a in x hours = 20 x km . distance covered by b in ( x - 1 ) hours = 25 ( x - 1 ) km . therefore 20 x + 25 ( x - 1 ) = 110 45 x = 135 x = 3 . so , they meet at 8 a . m . answer : c"
Answer: c
Python program:
a = 110 - 20
b = 25 + 20 
c = a / b
d = 8 + c
Problem: a circular ground whose diameter is 40 metres , has a garden of area 1100 m ^ 2 around it . what is the wide of the path of the garden ?
Options: a ) 8.07 , b ) 7.07 , c ) 6.07 , d ) 7.0 , e ) 8.5
Rationale: "req . area = ï € [ ( 20 ) 2 â € “ ( r ) 2 ] = 22 â  „ 7 ã — ( 400 - r ^ 2 ) [ since a 2 - b 2 = ( a + b ) ( a - b ) ] ie ) 22 / 7 ( 400 - r ^ 2 ) = 1100 , ie ) r ^ 2 = 50 , r = 7.07 m answer b"
Answer: b
Python program:
a = 40 / 1100
b = a + 1100 
c = circle_area - (
Problem: in a manufacturing plant , it takes 36 machines 4 hours of continuous work to fill 4 standard orders . at this rate , how many hours of continuous work by 72 machines are required to fill 12 standard orders ?
Options: a ) 3 , b ) 6 , c ) 8 , d ) 9 , e ) 12
Rationale: "the choices give away the answer . . 36 machines take 4 hours to fill 4 standard orders . . in next eq we aredoubling the machines from 36 to 72 , but thework is not doubling ( only 1 1 / 2 times ) , = 4 * 48 / 72 * 12 / 4 = 6 ans b"
Answer: b
Python program:
a = 36 * 12
b = a * 4
c = b / 72
d = c / 4
Problem: a man gains 20 % by selling an article for a certain price . if he sells it at double the price , the percentage of profit will be .
Options: a ) 130 % , b ) 140 % , c ) 150 % , d ) 160 % , e ) 170 %
Rationale: "explanation : let the c . p . = x , then s . p . = ( 120 / 100 ) x = 6 x / 5 new s . p . = 2 ( 6 x / 5 ) = 12 x / 5 profit = 12 x / 5 - x = 7 x / 5 profit % = ( profit / c . p . ) * 100 = > ( 7 x / 5 ) * ( 1 / x ) * 100 = 140 % option b"
Answer: b
Python program:
a = 20 / 100
b = 1 + a 
c = b * 2
d = c - 1
e = d * 100
f = e + 100
Problem: if the cost price is 90 % of the selling price , then what is the profit percent ?
Options: a ) 5 % , b ) 11 % , c ) 13 % , d ) 21 % , e ) 19 %
Rationale: "let s . p . = $ 100 c . p . = $ 90 profit = $ 10 profit % = 10 / 90 * 100 = 25 / 6 = 11 % approximately answer is b"
Answer: b
Python program:
a = 100 - 90
b = a / 90
c = b * 100
Problem: marginal cost is the cost of increasing the quantity produced ( or purchased ) by one unit . if the fixed cost for n products is $ 10,000 and the marginal cost is $ 200 , and the total cost is $ 40,000 , what is the value of n ?
Options: a ) 30 , b ) 50 , c ) 60 , d ) 80 , e ) 150
Rationale: "total cost for n products = fixed cost for n products + n * marginal cost - - > $ 40,000 = $ 10,000 + n * $ 200 - - > n = 150 . answer : e ."
Answer: e
Python program:
a = 200 / 10
Problem: 7 does not occur in 1000 . so we have to count the number of times it appears between 1 and 999 . any number between 1 and 999 can be expressed in the form of xyz where 0 < x , y , z < 9 .
Options: a ) 200 , b ) 300 , c ) 400 , d ) 500 , e ) 470
Rationale: 1 . the numbers in which 7 occurs only once . e . g 7 , 17 , 78 , 217 , 743 etc this means that 7 is one of the digits and the remaining two digits will be any of the other 9 digits ( i . e 0 to 9 with the exception of 7 ) you have 1 * 9 * 9 = 81 such numbers . however , 7 could appear as the first or the second or the third digit . therefore , there will be 3 * 81 = 243 numbers ( 1 - digit , 2 - digits and 3 - digits ) in which 7 will appear only once . in each of these numbers , 7 is written once . therefore , 243 times . 2 . the numbers in which 7 will appear twice . e . g 772 or 377 or 747 or 77 in these numbers , one of the digits is not 7 and it can be any of the 9 digits ( 0 to 9 with the exception of 7 ) . there will be 9 such numbers . however , this digit which is not 7 can appear in the first or second or the third place . so there are 3 * 9 = 27 such numbers . in each of these 27 numbers , the digit 7 is written twice . therefore , 7 is written 54 times . 3 . the number in which 7 appears thrice - 777 - 1 number . 7 is written thrice in it . therefore , the total number of times the digit 7 is written between 1 and 999 is 243 + 54 + 3 = 300 option b
Answer: b
Python program:
a = 9 * 9
b = 3 * a
c = 3 * 9
d = c * 2
e = b + d 
f = e + 3
Problem: a person can swim in still water at 4 km / h . if the speed of water 2 km / h , how many hours will the man take to swim back against the current for 16 km ?
Options: a ) 3 , b ) 6 , c ) 8 , d ) 9 , e ) 7
Rationale: "m = 4 s = 2 us = 4 - 2 = 2 d = 16 t = 16 / 2 = 8 answer : c"
Answer: c
Python program:
a = 4 - 2
b = 16 / a
Problem: in 1982 and 1983 , company b ’ s operating expenses were $ 12.0 million and $ 15.0 million , respectively , and its revenues were $ 15.6 million and $ 18.8 million , respectively . what was the percent increase in company b ’ s profit ( revenues minus operating expenses ) from 1982 to 1983 ?
Options: a ) 3 % , b ) 5 5 / 9 % , c ) 25 % , d ) 33 1 / 3 % , e ) 60 %
Rationale: profit in 1982 = 15.6 - 12 = 3.6 million $ profit in 1983 = 18.8 - 15 = 3.8 million $ percentage increase in profit = ( 3.8 - 3.6 ) / 3.6 * 100 % = 5 5 / 9 % answer b
Answer: b
Python program:
a = 15 - 12
b = a * 100
c = 18 - 8
d = b / c
e = 100 - d
Problem: peter can cover a certain distance in 1 hr . 24 min . by covering two - third of the distance at 4 kmph and the rest at 5 kmph . find the total distance .
Options: a ) 4 km , b ) 5 km , c ) 6 km , d ) 7 km , e ) 8 km
Rationale: time = distance / speed let total distance travelled be x in 84 / 60 hrs 2 / 3 rd of x travelled in 4 km / hr 1 / 3 rd of distance travelled in 5 km / hr 2 x / ( 3 * 4 ) + x / ( 3 * 5 ) = 84 / 60 x = 6 km answer : c
Answer: c
Python program:
a = 4 * 10
b = 100 - a
c = 24 / b
d = 1 + c 
e = 1 / 3
f = e / 5
g = 2 / 3
h = g / 4
i = f + h 
j = d / i
Problem: if the area of a circle decreases by 20 % , then the radius of a circle decreases by
Options: a ) 20 %
b ) 18 %
c ) 36 %
d ) 11 %
e ) none of these
Rationale: if area of a circle decreased by x % then the radius of a circle decreases by ( 100 − 10 √ 100 − x ) % = ( 100 − 10 √ 100 − 20 ) % = ( 100 − 10 √ 80 ) % = 100 - 89 = 11 % answer d
Answer: d
Python program:
a = 100 - 20
b = a / 100
c = math.sqrt(b)
d = 1 - c
e = d * 100
Problem: if n is a natural number , then ( 6 n ^ 2 + 6 n ) is always divisible by ?
Options: a ) 6 only , b ) 6 and 12 , c ) 12 only , d ) by 18 only , e ) none of these
Rationale: "( 6 n ^ 2 + 6 n ) = 6 n ( n + 1 ) , which is always divisible by 6 and 12 both , since n ( n + 1 ) is always even . correct option : b"
Answer: b
Python program:
a = 6 * 100
b = 2 * 6
c = a + b
Problem: two trains 140 m and 180 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
Options: a ) 11.52 sec , b ) 10.1 sec , c ) 10.6 sec , d ) 10.8 sec , e ) 10.2 sec
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 140 + 180 = 320 m . required time = 320 * 9 / 250 = 11.52 sec . answer : a"
Answer: a
Python program:
a = 140 + 180 
b = 60 + 40 
c = b * const_0_2778
d = a / c
Problem: the average of first seven multiples of 8 is :
Options: a ) 9 , b ) 16 , c ) 15 , d ) 32 , e ) 10
Rationale: "explanation : ( 8 ( 1 + 2 + 3 + 4 + 5 + 6 + 7 ) / 7 = 8 x 28 / 7 = 32 answer : d"
Answer: d
Python program:
a = 8 + 1
Problem: a box contains 100 balls , numbered from 1 to 100 . if 3 balls are selected at random and with replacement from the box . if the 3 numbers on the balls selected contain two odd and one even . what is the probability j that the first ball picked up is odd numbered ?
Options: a ) 0 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 1
Rationale: "answer - d selecting the balls either even or odd is having probability 50 / 100 = 1 / 2 we have already selected 3 balls with 2 odd numbers and 1 even number . so we have 3 combinations ooe , oeo , eoo . we have 3 outcomes and 2 are favourable as in 2 cases 1 st number is odd . so probability j is 2 / 3 . d"
Answer: d
Python program:
a = 2 / 3
Problem: the ratio between the perimeter and the width of a rectangle is 5 : 1 . if the area of the rectangle is 54 square centimeters , what is the length of the rectangle in centimeters ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "perimeter = 2 ( w + l ) = 5 w 3 w = 2 l w = 2 l / 3 wl = 54 2 l ^ 2 / 3 = 54 l ^ 2 = 81 l = 9 cm the answer is d ."
Answer: d
Python program:
a = 54 / 10
Problem: carol and jordan draw rectangles of equal area . if carol ' s rectangle measures 5 inches by 24 inches and jordan ' s rectangle is 3 inches long , how wide is jordan ' s rectangle , in inches ?
Options: a ) 25 , b ) 43 , c ) 42 , d ) 40 , e ) 18
Rationale: "area of carol ' s rectangle = 24 * 5 = 120 let width of jordan ' s rectangle = w since , the areas are equal 3 w = 120 = > w = 40 answer d"
Answer: d
Python program:
a = rectangle_area / (
Problem: dacid obtained 76 , 65 , 82 , 67 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 98 , b ) 78 , c ) 76 , d ) 87 , e ) 75
Rationale: "average = ( 76 + 65 + 82 + 67 + 85 ) / 5 = 375 / 5 = 75 . answer : e"
Answer: e
Python program:
a = 76 + 65 
b = a + 82 
c = b + 67 
d = c + 85 
e = 10 / 2
f = d / e
Problem: 16 ltr of water is added with 24 ltr of a solution containing 90 % of alcohol in the water . the % of alcohol in the new mixture is ?
Options: a ) 48 % , b ) 52 % , c ) 54 % , d ) 60 % , e ) 70 %
Rationale: "we have a 24 litre solution containing 90 % of alcohol in the water . = > quantity of alcohol in the solution = 24 ã — 90 / 100 now 16 litre of water is added to the solution . = > total quantity of the new solution = 24 + 16 = 40 percentage of alcohol in the new solution = 24 ã — 90 / 100 40 ã — 100 = 24 ã — 9010040 ã — 100 = 24 ã — 2.25 / 100 = 54 % c"
Answer: c
Python program:
a = 90 / 100
b = a * 24
c = 16 + 24 
d = b / c
e = 100 * d
Problem: a bag contains 3 white marbles and 3 black marbles . if each of 3 girls and 3 boys randomly selects and keeps a marble , what is the probability that all of the girls select the same colored marble ?
Options: a ) 1 / 35 , b ) 1 / 10 , c ) 1 / 15 , d ) 1 / 20 , e ) 1 / 25
Rationale: first , total ways to select for all boys and girls , i . e 6 ! / ( 3 ! * 3 ! ) = 6 * 5 * 4 * 3 * 2 * 1 / 3 * 2 * 1 * 3 * 2 * 1 = 20 then there are one two way girls can have all same colors , either white or black . the number of ways in which 3 girls can select 3 white balls = 3 c 3 = 1 the number of ways in which 3 girls can select 3 black balls = 3 c 3 = 1 therefore , total favorable outcomes / total outcomes = 2 / 20 = 1 / 10 b
Answer: b
Python program:
a = 3 + 3 
b = math.comb(a, 3)
c = 2 / b
Problem: a cube has four of its faces painted half red and half white . the other faces are completely painted white . what is the ratio between the red painted areas and the white painted areas of the cube ?
Options: a ) 1 : 4 , b ) 1 : 3 , c ) 1 : 2 , d ) 2 : 5 , e ) 2 : 11
Rationale: "let x be the area of each face of the cube . the area painted red is 4 ( x / 2 ) = 2 x the area painted white is 4 ( x / 2 ) + 2 x = 4 x the ratio of red to white is 2 x : 4 x which is 1 : 2 . the answer is c ."
Answer: c
Python program:
a = 1 + 4 
b = 1 / 2
c = a * b
d = c * 2
e = 1 + 4 
f = 1 / 2
g = e * f
h = g + 1 
i = h * 2
j = d / i
Problem: if a book is sold at 5 % profit instead of 5 % loss , it would have brought rs 13 more . find out the cost price of the book
Options: a ) 75 , b ) 72 , c ) 130 , d ) 70 , e ) 80
Rationale: "let c . p . of the book be rs . ’ x ’ given , 1.05 x - 0.95 x = 13 = > 0.1 x = 13 = 13 / 0.1 = rs 130 answer : c"
Answer: c
Python program:
a = 5 / 2
b = 100 * a
c = b / 5
Problem: if 4 and 8 are factors of 60 n , what is the minimum value of n ?
Options: a ) 2 , b ) 3 , c ) 8 , d ) 14 , e ) 56
Rationale: 60 n / 4 * 8 should be integer = > 2 * 2 * 3 * 5 * n / 2 * 2 * 2 * 2 * 2 = 3 * 5 * n / 8 must be an integer for this to be true n must multiple of 8 , thus min of n = 8 hence c
Answer: c
Python program:
a = math.lcm(4, 8)
Problem: if 3 ^ 8 x 3 ^ 7 = 3 ^ n what is the value of n ?
Options: a ) 20 , b ) 18 , c ) 17 , d ) 16 , e ) 15
Rationale: "3 ^ 8 * 3 ^ 7 = 3 ^ n or 3 ^ 8 + 7 = 3 ^ n n = 15 e"
Answer: e
Python program:
a = 3 ** 7
b = 3 ** 8
c = a * b
d = math.log(c)
e = math.log(3)
f = d / e
Problem: in karthik ' s opinion , his weight is greater than 55 kg but less than 62 kg . his brother does not agree with karthik and he thinks that karthik ' s weight is greater than 50 kg but less than 60 kg . his father ' s view is that his weight can not be greater than 58 kg . if all of them are correct in their estimation , what is the average of different probable weights of karthik ?
Options: a ) 54.5 , b ) 56.5 , c ) 59.2 , d ) 61 , e ) 62
Rationale: explanation : solution : assume karthik ' s weight be x kg . according to karthik , 55 < x < 62 according to karthik ; s brother , 50 < x < 60 . according to karthik ' s mother , x < 58 . the values satisfying all the above conditions are 56 and 57 . . ' . required average = ( 56 + 57 ) / 2 = 56.5 . answer : b
Answer: b
Python program:
a = 55 + 58 
b = a / 2
Problem: two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post . if the length of each train be 200 m , in what time will they cross other travelling in opposite direction ?
Options: a ) 17 sec , b ) 12 sec , c ) 16 sec , d ) 15 sec , e ) 20 sec
Rationale: "speed of the first train = 120 / 10 = 12 m / sec . speed of the second train = 120 / 5 = 8 m / sec . relative speed = 12 + 8 = 20 m / sec . required time = ( 200 + 200 ) / 20 = 20 sec . answer : e"
Answer: e
Python program:
a = 200 * 2
b = speed + ( 
c = a / b
Problem: if 20 men can build a wall 66 metres long in 8 days , what length of a similar can be built by 86 men in 8 days ?
Options: a ) 283.8 mtrs , b ) 378.4 mtrs , c ) 478.4 mtrs , d ) 488.4 mtrs , e ) 578.4 mtrs
Rationale: "if 20 men can build a wall 66 metres long in 8 days , length of a similar wall that can be built by 86 men in 8 days = ( 66 * 86 * 8 ) / ( 8 * 20 ) = 283.8 mtrs answer : a"
Answer: a
Python program:
a = 86 * 8
b = 20 * 8
c = a / b
d = 66 * c
Problem: how many odd numbers between 10 and 1,300 are the squares of integers ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 17
Rationale: "the square of an odd number is an odd number : 10 < odd < 1,000 10 < odd ^ 2 < 1,000 3 . something < odd < 31 . something ( by taking the square root ) . so , that odd number could be any odd number from 5 to 31 , inclusive : 5 , 7 , 9 , 11 , 13 , 15 , 17 , 19 , 21 , 23 , 25 , 27 , 29 , and 31 . 17 numbers . answer : e ."
Answer: e
Python program:
a = 10 + 4
Problem: the l . c . m of two numbers is 2310 and their h . c . f is 30 . if one number is 770 the other is
Options: a ) 330 , b ) 90 , c ) 270 , d ) 250 , e ) 350
Rationale: "the other number = l . c . m * h . c . f / given number = 2310 * 30 / 770 = 90 answer is b ."
Answer: b
Python program:
a = 30 * 2310
b = a / 770
Problem: a garden center sells a certain grass seed in 5 - pound bags at $ 13.85 per bag , 10 - pound bags at $ 20.43 per bag , and 25 - pound bags $ 32.20 per bag . if a customer is to buy at least 65 pounds of the grass seed , but no more than 80 pounds , what is the least possible cost of the grass seed that the customer will buy ?
Options: a ) $ 94.03 , b ) $ 96.75 , c ) $ 98.68 , d ) $ 102.07 , e ) $ 105.3
Rationale: "there can be 2 cases 1 ) 25 + 25 + 10 + 5 = $ 98.68 or 2 ) 25 + 25 + 25 = $ 96.60 c"
Answer: c
Python program:
a = 2 * 32
b = 1 * 20
c = a + b 
d = 1 * 13
e = c + d