euclaise/mathqa_programs huggingface dataset:
Problem: the distance between west - town to east - town is 15 kilometers . two birds start flying simultaneously towards one another , the first leaving from west - town at a speed of 2 kilometers per minute and the second bird , leaving from east - town , at a speed of 1 kilometers per minute . what will be the distance , in kilometers , between the meeting point and west - town ?
Options: a ) 3 . , b ) 7 . , c ) 10 . , d ) 12 . , e ) 15 .
Rationale: "time taken by the birds to meet = 15 / ( 2 + 1 ) = 5 mins distance traveled by the bird traveling from west - town = 2 * 5 = 10 answer : c"
Answer: c
Python program:
a = 2 * 2
Problem: a certain clock marks every hour by striking a number of times equal to the hour , and the time require for a stroke is exactly equal to the time interval between strokes . at 6 : 00 the time lapse between the beginning of the first stoke and the end of the last stroke is 22 seconds . at 10 : 00 , how many seconds elapse between the beginning of the first stroke and the end of the last stroke ?
Options: a ) 42 , b ) 36 , c ) 46 , d ) 38 , e ) 40
Rationale: "at 6 ' o clock , there would be 6 strikes . first strike , then a short interval , the second strike , then a short interval and so on till the 6 th strike . so there would be in all 5 intervals between 6 strikes . similarly , between 10 strikes , there would be 9 intervals . according to the question , the time spent in the strike and the interval is same . at 6 ' o clock , the 6 strikes and the 5 intervals together take 22 sec so each strike and each interval takes 2 secs . at 12 ' o clock , the 10 strikes and 9 intervals will take 2 * ( 10 + 9 ) = 38 secs d d"
Answer: d
Python program:
a = 10 - 1
b = a + 10 
c = 6 - 1
d = c + 6 
e = 22 / d
f = b * e
Problem: two trains , each 100 m long , moving in opposite directions , cross other in 20 sec . if one is moving twice as fast the other , then the speed of the faster train is ?
Options: a ) 22 , b ) 98 , c ) 60 , d ) 88 , e ) 24
Rationale: "let the speed of the slower train be x m / sec . then , speed of the train = 2 x m / sec . relative speed = ( x + 2 x ) = 3 x m / sec . ( 100 + 100 ) / 20 = 3 x = > x = 10 / 3 . so , speed of the faster train = 20 / 3 = 20 / 3 * 18 / 5 = 24 km / hr . answer : e"
Answer: e
Python program:
a = 100 + 100 
b = 1 + 2 
c = 20 * b
d = a / c
e = d * 2
f = e * 3600
g = f / 1000
Problem: if a and b get profits of rs . 6,000 and rs . 4,000 respectively at the end of year then ratio of their investments are
Options: a ) 4 : 1 , b ) 1 : 4 , c ) 3 : 2 , d ) 2 : 3 , e ) 2 : 5
Rationale: "suppose a and b is ratio of investment . so a : b = 6000 + 4000 a : b = 10000 a / ( a + b ) * 10000 = 6000 2 a = 3 b a / b = 3 / 2 i . e 3 : 2 answer : c"
Answer: c
Python program:
a = 3 * 2
b = a * 100
c = b * 100
d = 3 * 2
e = d * 100
f = e * 100
g = 2 + 3 
h = g * 2
i = f / h
j = c / i
Problem: on dividing 171 by a number , the quotient is 8 and the remainder is 3 . find the divisor .
Options: a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: "d = ( d - r ) / q = ( 171 - 3 ) / 8 = 168 / 8 = 21 d"
Answer: d
Python program:
a = 171 / 8
b = math.floor(a)
Problem: 40 men shake hands with each other . maximum no of handshakes without cyclic handshakes .
Options: a ) 780 , b ) 200 , c ) 210 , d ) 220 , e ) 230
Rationale: "or , if there are n persons then no . of shakehands = nc 2 = 40 c 2 = 780 answer : a"
Answer: a
Python program:
a = 40 - 1
b = 40 / 2
c = a * b
Problem: a , b and c enter into partnership . a invests some money at the beginning , b invests double the amount after 6 months , and c invests thrice the amount after 8 months . if the annual gain be rs . 21000 . a ' s share is ?
Options: a ) 2999 , b ) 2778 , c ) 7000 , d ) 2889 , e ) 6612
Rationale: "x * 12 : 2 x * 6 : 3 x * 4 1 : 1 : 1 1 / 3 * 21000 = 7000 answer : c"
Answer: c
Python program:
a = 1 * 12
b = 1 * 12
c = 12 - 6
d = c * 2
e = b + d 
f = 12 - 8
g = f * 3
h = e + g 
i = 21000 / h
j = a * i
Problem: a box has exactly 100 balls , and each ball is either red , blue , or white . if the box has 15 more blue balls than white balls , and thrice as many red balls as blue balls , how many white balls does the box has ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "x = the number of red balls y = the number of blue balls z = the number of white balls from the first sentence we have equation # 1 : x + y + z = 100 . . . the box has 15 more blue balls than white balls . . . equation # 2 : y = 15 + z . . . thrice as many red balls as blue balls . . . equation # 3 : x = 3 y solve equation # 2 for z : z = y - 15 now , we can replace both x and z with y in equation # 1 3 y + y + ( y - 15 ) = 100 5 y - 15 = 100 5 y = 115 y = 23 there are 23 blue balls . this is 15 more than the number of white balls , so z = 8 . that ' s the answer . just as a check , x = 69 , and 69 + 23 + 8 = 100 . answer = 8 , ( a )"
Answer: a
Python program:
a = 15 * 3
b = 100 - a
c = b / 4
Problem: how long does a train 150 m long traveling at 36 kmph takes to cross a signal post ?
Options: a ) 8 sec , b ) 15 sec , c ) 20 sec , d ) 10 sec , e ) 22 sec
Rationale: d = 150 m s = 36 * 5 / 18 = 10 t = 150 * 1 / 10 = 15 sec answer : b
Answer: b
Python program:
a = 36 * const_0_2778
b = 150 / a
Problem: a car dealership has 40 cars on the lot , 20 % of which are silver . if the dealership receives a new shipment of 80 cars , 50 % of which are not silver , what percentage of total number of cars are silver ?
Options: a ) 30 % , b ) 35 % , c ) 40 % , d ) 45 % , e ) 50 %
Rationale: "the number of silver cars is 0.2 * 40 + 0.5 * 80 = 48 the percentage of cars which are silver is 48 / 120 = 40 % the answer is c ."
Answer: c
Python program:
a = 20 / 100
b = 40 * a
c = 50 / 100
d = 80 * c
e = b + d 
f = 40 + 80 
g = e / f
h = g * 100
Problem: the two lines y = x and x = - 7 intersect on the coordinate plane . what is the value of the area of the figure formed by the intersecting lines and the x - axis ?
Options: a ) 18.5 , b ) 21.5 , c ) 24.5 , d ) 27.5 , e ) 30.5
Rationale: "the point of intersection is ( - 7 , - 7 ) . the triangle has a base of length 7 and a height of 7 . area = ( 1 / 2 ) * base * height = ( 1 / 2 ) * 7 * 7 = 24.5 the answer is c ."
Answer: c
Python program:
a = 7 * 7
b = a / 2
Problem: a train 125 m long passes a man , running at 3 km / hr in the same direction in which the train is going , in 10 sec . the speed of the train is ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 79 , e ) 48
Rationale: "speed of the train relative to man = 125 / 10 = 25 / 2 m / sec . = 25 / 2 * 18 / 5 = 45 km / hr let the speed of the train be x km / hr . then , relative speed = ( x - 3 ) km / hr . x - 3 = 45 = > x = 48 km / hr . answer : option e"
Answer: e
Python program:
a = 3 * const_0_2778
b = a * 3
c = 125 - b
d = c / 10
e = d / const_0_2778
Problem: if 16 ^ y = 4 ^ 14 , what is y ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 7
Rationale: 16 ^ y = 4 ^ 2 y = 4 ^ 14 2 y = 14 y = 7 the answer is e .
Answer: e
Python program:
a = 14 / 2
Problem: if each participant of a chess tournament plays exactly one game with each of the remaining participants , then 105 games will be played during the tournament . find the number of participants .
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: "let p be the number of participants . pc 2 = 105 ( p ) ( p - 1 ) = 210 = 15 * 14 p = 15 the answer is a ."
Answer: a
Python program:
a = 105 * 2
b = a * 4
c = b + 1 
d = math.sqrt(c)
e = d + 1 
f = e / 2
Problem: a train running at the speed of 90 km / hr crosses a pole in 6 seconds . find the length of the train .
Options: a ) 150 meter , b ) 100 meter , c ) 105 meter , d ) 120 meter , e ) 130 meter
Rationale: "speed = 90 * ( 5 / 18 ) m / sec = 25 m / sec length of train ( distance ) = speed * time ( 25 ) * 6 = 150 meter answer : a"
Answer: a
Python program:
a = 90 * 1000
b = a / 3600
c = b * 6
Problem: jen has a jar of jam , and she ate 1 / 3 of the jam for lunch . if jen ate 1 / 7 of the remaining jam for dinner , what fraction of the jam was left after dinner ?
Options: a ) 2 / 7 , b ) 3 / 7 , c ) 4 / 7 , d ) 9 / 14 , e ) 11 / 14
Rationale: let x be the amount of jam at the beginning . after lunch , the remaining jam was ( 2 / 3 ) x . after dinner , the remaining jam was ( 6 / 7 ) ( 2 / 3 ) x = ( 4 / 7 ) x . the answer is c .
Answer: c
Python program:
a = 7 - 3
b = a / 7
Problem: a garden center sells a certain grass seed in 5 - pound bags at $ 13.85 per bag , 10 - pound bags at $ 20.42 per bag , and 25 - pound bags $ 32.25 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 ) $ 98.78 , d ) $ 98.77 , e ) $ 105.3
Rationale: "there can be 2 cases 1 ) 25 + 25 + 10 + 5 = $ 98.77 or 2 ) 25 + 25 + 25 = $ 96.75 d"
Answer: d
Python program:
a = 2 * 32
b = 1 * 20
c = a + b 
d = 1 * 13
e = c + d
Problem: the radius of the two circular fields is in the ratio 3 : 7 the area of the first field is what percent less than the area of the second ?
Options: a ) 82.9 % , b ) 84.2 % , c ) 81.0 % , d ) 80.6 % , e ) 81.6 %
Rationale: "r = 3 ï € r 2 = 9 r = 7 ï € r 2 = 49 49 ï € â € “ 40 ï € 100 - - - - ? = > 81.6 % . answer : e"
Answer: e
Python program:
a = 7 ** 2
b = 3 ** 2
c = a - b
Problem: the distance between west - town to east - town is 20 kilometers . two birds start flying simultaneously towards one another , the first leaving from west - town at a speed of 4 kilometers per minute and the second bird , leaving from east - town , at a speed of 1 kilometers per minute . what will be the distance , in kilometers , between the meeting point and west - town ?
Options: a ) 3 . , b ) 7 . , c ) 10 . , d ) 16 . , e ) 15 .
Rationale: time taken by the birds to meet = 20 / ( 4 + 1 ) = 4 mins distance traveled by the bird traveling from west - town = 4 * 4 = 16 answer : d
Answer: d
Python program:
a = 4 * 4
Problem: angelo and isabella are both salespersons . in any given week , angelo makes $ 550 in base salary plus 8 percent of the portion of his sales above $ 6,000 for that week . isabella makes 10 percent of her total sales for any given week . for what amount of weekly sales would angelo and isabella earn the same amount of money ?
Options: a ) 3,500 , b ) 24,500 , c ) 25,500 , d ) 26,500 , e ) 27,500
Rationale: "official solution : the problem asks for the amount of weekly sales it takes for angelo and isabella to earn the same amount of money . you can write an equation that sets angelo ’ s and isabella ’ s weekly earnings equal to each other , with x representing weekly sales . weekly earnings for each salesperson equal base salary plus commission . so angelo ’ s earnings are 550 + ( 0.08 ) ( x – 6,000 ) , and isabella ’ s are 0.10 x . set up the equation and solve : 550 + ( 0.08 ) ( x – 6,000 ) = 0.10 x distribute the 0.08 : 550 + 0.08 x – 480 = 0.10 x combine terms and subtract 0.08 x from both sides : 70 = 0.02 x divide both sides by 0.02 : 3,500 = x your answer is a ."
Answer: a
Python program:
a = 8 / 100
b = 6 * 0
c = 550 - b
d = 10 / 100
e = 8 / 100
f = d - e
g = c / f
h = g / 6
i = math.floor(h)
Problem: if p ^ 2 – 13 p + 40 = s , and p is a positive integer between 1 and 10 , inclusive , what is the probability that s < 0 ?
Options: a ) 1 / 10 , b ) 1 / 5 , c ) 2 / 5 , d ) 3 / 5 , e ) 3 / 10
Rationale: p 2 – 13 p + 40 = s so ( p – 8 ) ( p – 5 ) = s for q to be negative , the expressions ( p – 8 ) and ( p – 5 ) must have opposite signs . which integers on the number line will yield opposite signs for the expressions ( p – 8 ) and ( p – 5 ) ? those integers in the range 5 < p < 8 ( notice 5 and 8 are not included because they would both yield a value of zero and zero is a nonnegative integer ) . that means that there are only two integer values for p , 6 and 7 , that would yield a negative q . with a total of 10 possible p values , only 2 yield a negative q , so the probability is 2 / 10 or 1 / 5 . the correct answer is b .
Answer: b
Python program:
a = 13 ** 2
b = 4 * 40
c = a - b
d = math.sqrt(c)
e = 13 + d 
f = e / 2
g = 13 ** 2
h = 4 * 40
i = g - h
j = math.sqrt(i)
k = 13 + j 
l = k / 2
m = 13 - l
n = f - m
o = n - 1
p = o / 10
Problem: a and b complete a work in 6 days . a alone can do it in 10 days . if both together can do the work in how many days ?
Options: a ) 3.75 days , b ) 3.78 days , c ) 3.25 days , d ) 3.15 days , e ) 2.75 days
Rationale: "1 / 6 + 1 / 10 = 8 / 30 = 4 / 15 15 / 4 = 3.75 days answer : a"
Answer: a
Python program:
a = 1/(6)
b = 1/(10)
c = a + b 
d = 1/(c)
Problem: 5 * 2 is a 3 digit number with * is a missing digit . if the number is divisible by 6 , the missing digit is
Options: a ) 0 , b ) 2 , c ) 5 , d ) 7 , e ) 9
Rationale: sol . let the number be 5 x 2 . clearly , it is divisible by 2 . now , 5 + x + 2 = ( 7 + x ) must be divisible by 3 . so , x = 2 . answer b
Answer: b
Python program:
a = 5 * 100
b = a + 2 
c = 1 * 10
d = b + c 
e = 1 * 10
f = d + e 
g = 5 * 100
h = g + 2 
i = f - h
j = 1 * 10
k = i / j
Problem: how many pounds of salt at 50 cents / lb must be mixed with 40 lbs of salt that costs 38 cents / lb so that a merchant will get 20 % profit by selling the mixture at 48 cents / lb ?
Options: a ) 2 , b ) 5 , c ) 8 , d ) 15 , e ) 25
Rationale: selling price is 48 cents / lb for a 20 % profit , cost price should be 40 cents / lb ( cp * 6 / 5 = 48 ) basically , you need to mix 38 cents / lb ( salt 1 ) with 50 cents / lb ( salt 2 ) to get a mixture costing 40 cents / lb ( salt avg ) weight of salt 1 / weight of salt 2 = ( salt 2 - saltavg ) / ( saltavg - salt 1 ) = ( 50 - 40 ) / ( 40 - 38 ) = 5 / 1 we know that weight of salt 1 is 40 lbs . weight of salt 2 must be 8 lbs . answer ( c )
Answer: c
Python program:
a = 48 * 40
b = 100 + 20 
c = b / 100
d = 38 * 40
e = c * d
f = a - e
g = 100 + 20 
h = g / 100
i = 50 * h
j = i - 48
k = f / j
Problem: in a certain animal population , for each of the first 3 months of life , the probability that an animal will die during that month is 1 / 10 . for a group of 600 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ?
Options: a ) 438 , b ) 446 , c ) 452 , d ) 462 , e ) 470
Rationale: "number of newborns that can die in first month = 1 / 10 * 600 = 60 survived = 540 number of newborns that can die in second month = 1 / 10 * 540 = 54 survived = 486 number of newborns that can die in third month = 1 / 10 * 486 = 48 survived = 438 answer : a"
Answer: a
Python program:
a = 1 / 10
b = 1 - a
c = 600 * b
d = 1 / 10
e = 1 - d
f = c * e
g = 1 / 10
h = 1 - g
i = f * h
Problem: three interviewers , a , b , and c are interviewing 40 applicants . only with three interviewers ' admission can an applicant be admitted . if interviewer b admitted 15 applicants , a admitted 17 applicants , and c admitted 20 applicants , at least how many applicants get the admission ?
Options: a ) 8
b ) 2
c ) 6
d ) 0
e ) 12
Rationale: if b admitted 15 are overlapping with a admission of 17 but c does not overlap with anybody . then no student will get nod from all the 3 . hence 0 student will get admission . answer : d
Answer: d
Python program:
a = 15 + 17 
b = a + 20 
c = b - 40
Problem: 0 , 1 , 5 , 14 , 30 , ____
Options: a ) 25 , b ) 35 , c ) 45 , d ) 65 , e ) 55
Rationale: "0 , 1,5 , 14 , 30 , . . . . . 0 + 1 * 1 = 1 1 + 2 * 2 = 5 5 + 3 * 3 = 14 14 + 4 * 4 = 30 so 30 + 5 * 5 = 55 answer : e"
Answer: e
Python program:
a = negate - (
Problem: the security gate at a storage facility requires a 4 - digit lock code . if the lock code must consist only of digits from 1 through 7 , inclusive , with no repeated digits , and the first and last digits of the code must be odd , how many lock codes are possible ?
Options: a ) 120 , b ) 240 , c ) 360 , d ) 720 , e ) 1440
Rationale: x - x - x - x - x - - > there are 4 odd digits from 1 to 7 , inclusive thus options for the first and the last x ' s are : 4 - x - x - 3 . other x ' s can take following values : 4 - 5 - 4 - 3 - - > 4 * 5 * 4 * 3 = 240 . answer : b .
Answer: b
Python program:
a = 4 * 3
b = 4 + 1 
c = math.factorial(b)
d = math.factorial(3)
e = c / d
f = a * e
Problem: if [ [ x ] ] = x ^ 2 + 2 x + 4 , what is the value of [ [ 4 ] ] ?
Options: a ) 3 , b ) 9 , c ) 15 , d ) 19 , e ) 28
Rationale: "[ [ x ] ] = x ^ 2 + 2 x + 4 [ [ 4 ] ] = 4 ^ 2 + 2 * 4 + 4 = 28 . option e"
Answer: e
Python program:
a = 4 ** 2
b = 2 * 2
c = a + b 
d = c + 4
Problem: in a forest 110 deer were caught , tagged with electronic markers , then released . a week later , 50 deer were captured in the same forest . of these 50 deer , it was found that 5 had been tagged with the electronic markers . if the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest , and if no deer had either left or entered the forest over the preceding week , what is the approximate number of deer in the forest ?
Options: a ) 150 , b ) 750 , c ) 1,250 , d ) 1,500 , e ) 2,500
Rationale: "the percentage of tagged deer in the second sample = 5 / 50 * 100 = 10 % . so , 150 tagged deers comprise 10 % of total # of deers - - > total # of deers = 110 * 10 = 1,100 . answer : d ."
Answer: d
Python program:
a = 50 * 5
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 . 4240 , what is the length of the plot in metres ?
Options: a ) 20 , b ) 200 , c ) 50 , d ) 400 , e ) 140
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 = 4240 [ 4 l - 40 ] = 4240 / 26.50 = 160 4 l = 200 l = 200 / 4 = 50 meters . answer : c"
Answer: c
Python program:
a = 4240 / 26
b = a / 2
c = 2 * 20
d = b - c
Problem: in the new budget the price of milk rose by 20 % . by how much percent must a person reduce his consumption so that his expenditure on it does not increase ?
Options: a ) 7.5 % , b ) 9.1 % , c ) 10.9 % , d ) 16.67 % , e ) 15 %
Rationale: reduce in consumption = r / ( 100 + r ) * 100 % = 20 / 120 * 100 = 16.67 % answer is d
Answer: d
Python program:
a = 20 + 100 
b = 20 / a
c = b * 100
Problem: evaluate 64 / . 08
Options: a ) 800 , b ) 500 , c ) 505 , d ) none of these , e ) 506
Rationale: "explanation : 64 / . 08 = 6400 / 8 = 800 option a"
Answer: a
Python program:
a = 8 / 64
b = 100 / 0
Problem: two airplanes take off from one airfield at noon . one flies due east at 206 miles per hour while the other flies directly northeast at 283 miles per hour . approximately how many miles apart are the airplanes at 2 p . m . ?
Options: a ) 412 , b ) 332 , c ) 400 , d ) 483 , e ) 566
Rationale: "a in two hours : the plane flying east will be 412 miles away from airport . the other plane will be 566 miles away from airport . 566 / 412 = ~ 1.4 = ~ sqrt ( 2 ) this means that planes formed a right isocheles triangle = > sides of such triangles relate as 1 : 1 : sqrt ( 2 ) = > the planes are 412 miles apart . a"
Answer: a
Python program:
a = 283 * 2
b = a ** 2
c = 206 * 2
d = c ** 2
e = b - d
f = math.sqrt(e)
Problem: 96 % of 5 / 8 =
Options: a ) 0.2 , b ) 0.5 , c ) 0.6 , d ) 0.75 , e ) 1.0
Rationale: "should be simple . 0.96 * 5 / 8 = 4.8 / 8 = 0.6 correct option : c"
Answer: c
Python program:
a = 8 * 5
b = a / 100
c = b * 96
d = c / 100
Problem: a man goes downstream at 14 kmph , and upstream 8 kmph . the speed of the stream is
Options: a ) 0 kmph , b ) 4 kmph , c ) 16 kmph , d ) 2.5 kmph , e ) 3 kmph
Rationale: speed of the stream = 1 / 2 ( 14 - 8 ) kmph = 3 kmph . correct option : e
Answer: e
Python program:
a = 14 - 8
b = a / 2
Problem: the ratio of radius of a circle and the side of a square is 2 : 11 . find the ratio of their areas :
Options: a ) 2 : 1 , b ) 4 : 7 , c ) 8 : 77 , d ) 4 : 121 , e ) none
Rationale: "radius / side = 2 / 11 ⇒ area of circle / area of square = 4 / 121 answer : d"
Answer: d
Python program:
a = 2 / 11
b = a ** 2
Problem: a train overtakes two person who are walking in the same direction in which the train is going , at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively . the length of the train is :
Options: a ) 45 m , b ) 50 m , c ) 54 m , d ) 72 m , e ) none of these
Rationale: let actual speed of train = s m / sec and length of train = l m . then , s - 2 × 5 / 18 = l 9 ⇒ 9 s = l + 5 . . . … ( i ) and s - 4 × 5 ⁄ 18 = l ⁄ 10 ⇒ 90 s = 9 l + 100 . . . . . ( ii ) by ( i ) & ( ii ) , we get l = 50 m . answer b
Answer: b
Python program:
a = 4 * const_0_2778
b = a * 10
c = 2 * const_0_2778
d = 9 * c
e = b - d
f = 2 * const_0_2778
g = e - f
h = 9 * g
Problem: a is twice as good a workman as b and together they finish a piece in 18 days . in how many days will a alone finish the work ?
Options: a ) 25 days , b ) 26 days , c ) 23 days , d ) 45 days , e ) 27 days
Rationale: "sol . ( a ’ s 1 day ’ s work ) : ) ( b ’ s 1 days work ) = 2 : 1 . ( a + b ) ' s 1 day ' s work = 1 / 18 divide 1 / 18 in the ratio 2 : 1 . : . a ’ s 1 day ' s work = ( 1 / 18 * 2 / 3 ) = 1 / 27 hence , a alone can finish the work in 27 days . ans : e"
Answer: e
Python program:
a = 1 + 2 
b = a * 18
Problem: on dividing a number by 56 , we get 26 as remainder . on dividing the same number by 8 , what will be the remainder ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "number = 56 x + 26 ( ∵ since the number gives 26 as remainder on dividing by 56 ) = ( 7 × 8 × x ) + ( 3 × 8 ) + 2 hence , if the number is divided by 8 , we will get 2 as remainder . answer : a"
Answer: a
Python program:
a = 26 ** 2
b = a / 56
c = 26 ** 2
d = c / 56
e = math.floor(d)
f = b - e
g = f * 56
Problem: if the wheel is 12 cm then the number of revolutions to cover a distance of 1240 cm is ?
Options: a ) 11 , b ) 14 , c ) 16 , d ) 12 , e ) 19
Rationale: "2 * 22 / 7 * 12 * x = 1240 = > x = 16 answer : c"
Answer: c
Python program:
a = 3 * 100
b = 1 * 10
c = a + b 
d = c + 4 
e = d / 100
f = 2 * e
g = f * 12
h = 1240 / g
Problem: ( ab ) x − 2 = ( ba ) x − 7 . what is the value of x ?
Options: a ) 1.5 , b ) 4.5 , c ) 7.5 , d ) 9.5 , e ) 8.7
Rationale: explanation : ( a / b ) x − 2 = ( b / a ) x − 7 ⇒ ( a / b ) x − 2 = ( a / b ) − ( x − 7 ) ⇒ x − 2 = − ( x − 7 ) ⇒ x − 2 = − x + 7 ⇒ x − 2 = − x + 7 ⇒ 2 x = 9 ⇒ x = 92 = 4.5 option b
Answer: b
Python program:
a = 2 + 7 
b = a / 2
Problem: a and b together can do a piece of work in 6 days and a alone can do it in 10 days . in how many days can b alone can do it ?
Options: a ) 12 days , b ) 18 days , c ) 15 days , d ) 21 days , e ) 22 days
Rationale: "explanation : a and b can do work 1 / 6 in 1 day a alone can do 1 / 10 work in 1 day b alone can do ( 1 / 6 - 1 / 10 ) = 1 / 15 work in 1 day = > complete work can be done in 15 days by b answer : option c"
Answer: c
Python program:
a = 1/(6)
b = 1/(10)
c = a - b
d = 1/(c)
Problem: jerry ’ s average ( arithmetic mean ) score on the first 3 of 4 tests is 94 . if jerry wants to raise his average by 2 points , what score must he earn on the fourth test ?
Options: a ) 87 , b ) 89 , c ) 90 , d ) 93 , e ) 102
Rationale: total score on 3 tests = 94 * 3 = 282 jerry wants the average to be = 96 hence total score on 4 tests should be = 96 * 4 = 384 score required on the fourth test = 384 - 282 = 102 option e
Answer: e
Python program:
a = 94 + 2 
b = 4 * a
c = 94 * 3
d = b - c
Problem: in the biology lab of ` ` jefferson ' ' high school there are 0.036 * 10 ^ 5 germs , equally divided among 18000 * 10 ^ ( - 3 ) petri dishes . how many germs live happily in a single dish ?
Options: a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) 500
Rationale: "0.036 * 10 ^ 5 can be written as 3600 18000 * 10 ^ ( - 3 ) can be written as 18 required = 3600 / 18 = 200 answer : b"
Answer: b
Python program:
a = 1000 * 100
b = a * 0
c = 18000 / 1000
d = b / c
Problem: an amount of money is to be divided between p , q and r in the ratio of 3 : 7 : 12 . if the difference between the shares of p and q is rs . 4400 , what will be the difference between q and r ' s share ?
Options: a ) 2788 , b ) 5500 , c ) 7282 , d ) 2782 , e ) 2729
Rationale: 4 - - - 4400 5 - - - ? = > 5500 answer : b
Answer: b
Python program:
a = 12 - 7
b = 7 - 3
c = 4400 / b
d = a * c