euclaise/mathqa_programs huggingface dataset:
Problem: two trains a and b starting from two points and travelling in opposite directions , reach their destinations 9 hours and 4 hours respectively after meeting each other . if the train a travels at 90 kmph , find the rate at which the train b runs .
Options: a ) 40 , b ) 60 , c ) 135 , d ) 80 , e ) 100
Rationale: "if two objects a and b start simultaneously from opposite points and , after meeting , reach their destinations in ‘ a ’ and ‘ b ’ hours respectively ( i . e . a takes ‘ a hrs ’ to travel from the meeting point to his destination and b takes ‘ b hrs ’ to travel from the meeting point to his destination ) , then the ratio of their speeds is given by : sa / sb = √ ( b / a ) i . e . ratio of speeds is given by the square root of the inverse ratio of time taken . sa / sb = √ ( 4 / 9 ) = 2 / 3 this gives us that the ratio of the speed of a : speed of b as 2 : 3 . since speed of a is 80 kmph , speed of b must be 80 * ( 3 / 2 ) = 135 kmph c"
Answer: c
Python program:
a = 9 / 4
b = math.sqrt(a)
c = 90 * b
Problem: a vessel of capacity 90 litres is fully filled with pure milk . nine litres of milk is removed from the vessel and replaced with water . nine litres of the solution thus formed is removed and replaced with water . find the quantity of pure milk in the final milk solution ?
Options: a ) 73.9 , b ) 72.9 , c ) 73.0 , d ) 73.5 , e ) 92.2
Rationale: "let the initial quantity of milk in vessel be t litres . let us say y litres of the mixture is taken out and replaced by water for n times , alternatively . quantity of milk finally in the vessel is then given by [ ( t - y ) / t ] n * t for the given problem , t = 90 , y = 9 and n = 2 . hence , quantity of milk finally in the vessel = [ ( 90 - 9 ) / 90 ] 2 ( 90 ) = 72.9 litres . answer : option b"
Answer: b
Python program:
a = 3 * 3
b = 90 - a
c = 3 * 3
d = 90 - c
e = d / 90
f = 3 * 3
g = e * f
h = b - g
Problem: 377 ÷ 13 ÷ 29 × 1 / 4 ÷ 2 = ?
Options: a ) 1 / 6 , b ) 1 / 8 , c ) 1 / 10 , d ) 1 / 12 , e ) 1 / 15
Rationale: explanation : 377 ÷ 13 ÷ 29 × 1 / 4 ÷ 2 = ? = > ? = ( 337 / ( 13 × 29 × 4 × 2 ) ) = 1 / 8 answer : option b
Answer: b
Python program:
a = 377 / 13
b = a / 29
c = b * 1
d = c / 4
e = d / 2
Problem: if x = 2 ^ 8 and x ^ x = 2 ^ k , what is k ?
Options: a ) 2 ^ 15 , b ) 2 ^ 14 , c ) 2 ^ 13 , d ) 2 ^ 12 , e ) 2 ^ 11
Rationale: "solution : we know that x = 2 ^ 8 which implies x ^ x = ( 2 ^ 8 ) ^ ( 2 ^ 8 ) = 2 ^ ( 8 * 2 ^ 8 ) [ because ( x ^ y ) ^ z = x ^ ( y * z ) ) ] so 2 ^ ( 2 ^ 3 * 2 ^ 8 ) = 2 ^ ( 2 ^ ( 3 + 8 ) ) [ because x ^ a * x ^ b = x ^ ( a + b ) ] therefore x ^ x = 2 ^ ( 2 ^ 11 ) given that x ^ x = 2 ^ k so 2 ^ ( 2 ^ 11 ) = 2 ^ k since the base is same the exponent will also be same therefore k = 2 ^ 11 answer : e"
Answer: e
Python program:
a = 2 ** 8
b = a * 8
Problem: if 11.25 m of a uniform steel rod weighs 42.75 kg . what will be the weight of 6 m of the same rod ?
Options: a ) 22.8 kg , b ) 25.6 kg , c ) 28 kg , d ) 26.5 kg , e ) none of these
Rationale: "explanation : let the required weight be x kg . then , less length , less weight ( direct proportion ) = > 11.25 : 6 : : 42.75 : x = > 11.25 x x = 6 x 42.75 = > x = ( 6 x 42.75 ) / 11.25 = > x = 22.8 answer : a"
Answer: a
Python program:
a = 6 * 42
b = a / 11
Problem: david obtained 70 , 60 , 78 , 60 and 65 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology what are his average marks ?
Options: a ) 75 , b ) 27.6 , c ) 66.6 , d ) 16.5 , e ) 11
Rationale: "explanation : average = ( 70 + 60 + 78 + 60 + 65 ) / 5 = 333 / 5 = 66.6 . answer : c"
Answer: c
Python program:
a = 70 + 60 
b = a + 78 
c = b + 60 
d = c + 65 
e = 2 + 3 
f = d / e
Problem: a car drives 60 miles on local roads at 30 mph , and 65 miles on the highway at 65 mph , what is the average speed of the entire trip ?
Options: a ) 36 mph , b ) 40 mph , c ) 44 mph , d ) 42 mph , e ) 58 mph
Rationale: "so the answer is plainly d . . . . we have a general relation for speed , time and distance : v ( velocity ) * t ( time ) = d ( distance ) for first part we have d = 60 miles , and v = 30 mph so we can obtain time : 30 * t = 60 or t = 60 / 30 = 2 hours the needed time to cover 60 miles in the same way we should divide 65 by 65 to find the needed time to cover 65 miles , so t = 1 hours so the total time for covering total distance would be 2 + 1 = 3 hours and total distance is 60 + 65 = 125 miles final stage : average speed is total distance divide to total time : 125 / 3 = 41.6 miles per hour that rounds up to 42 . . . ."
Answer: d
Python program:
a = 60 + 65 
b = 60 / 30
c = 65 / 65
d = b + c 
e = a / d
Problem: set a consists of the integers from 4 to 15 , inclusive , while set b consists of the integers from 7 to 20 , inclusive . how many distinct integers do belong to the both sets at the same time ?
Options: a ) 5 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "a = { 4 , 5,6 , 7,8 , 9,10 , 11,12 } b = { 6 , 7,8 , 9,10 , 11,12 . . . } thus we see that there are 9 distinct integers that are common to both . d is the correct answer ."
Answer: d
Python program:
a = 7 + 4
Problem: the length of a rectangle is halved while its width is also halved . what is the % change in area ?
Options: a ) 25 % , b ) 30 % , c ) 50 % , d ) 65 % , e ) 75 %
Rationale: "the original area is l * w the new area is 0.5 l * 0.5 w = 0.25 * l * w = l * w - 0.75 * l * w the area decreased by 75 % . the answer is e ."
Answer: e
Python program:
a = 1 / 2
b = 3 * a
c = b - 1
d = c / 1
e = d * 100
Problem: the floor of a rectangular room is 15 m long and 12 m wide . the room is surrounded by a verandah of width 2 m on all its sides . the area of the verandah is :
Options: a ) 124 m 2
b ) 120 m 2
c ) 108 m 2
d ) 58 m 2
e ) none of these
Rationale: area of the outer rectangle = 19 × 16 = 304 m 2 area of the inner rectangle = 15 × 12 = 180 m 2 required area = ( 304 – 180 ) = 124 m 2 answer a
Answer: a
Python program:
a = 2 * 2
b = a + 15 
c = 2 * 2
d = 12 + c 
e = rectangle_area - (
Problem: a , band c enter into partnership . a invests 3 times as much as b and b invests two - third of what c invests . at the end of the year , the profit earned is rs . 6600 . what is the share of b ?
Options: a ) 1100 , b ) 800 , c ) 1400 , d ) 1200 , e ) none of them
Rationale: "let c ' s capital = rs . x . then , b ' s capital = rs . ( 2 / 3 ) x a ’ s capital = rs . ( 3 x ( 2 / 3 ) . x ) = rs . 2 x . ratio of their capitals = 2 x : ( 2 / 3 ) x : x = 6 : 2 : 3 . hence , b ' s share = rs . ( 6600 x ( 2 / 11 ) ) = rs . 1200 . answer is d ."
Answer: d
Python program:
a = 2 * 3
b = 2 / 3
c = b * 3
d = a + c 
e = d + 3 
f = 2 / e
g = 6600 * f
Problem: a reduction of 40 % in the price of apples would enable a man to obtain 64 more for rs . 40 , what is reduced price per dozen ?
Options: a ) 1 , b ) 3 , c ) 6 , d ) 7 , e ) 10
Rationale: "b 40 * ( 40 / 100 ) = 16 - - - 64 ? - - - 12 = > rs . 3"
Answer: b
Python program:
a = 40 * 40
b = a / 100
c = b / 64
d = c * 12
Problem: a , b , c , d and e are 5 consecutive points on a straight line . if bc = 3 cd , de = 7 , ab = 5 and ac = 11 , what is the length of ae ?
Options: a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: ac = 11 and ab = 5 , so bc = 6 . bc = 3 cd so cd = 2 . the length of ae is ab + bc + cd + de = 5 + 6 + 2 + 7 = 20 the answer is c .
Answer: c
Python program:
a = 11 - 5
b = a / 3
c = 11 + b 
d = c + 7
Problem: a tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume . if 3,000 gallons of water evaporate from the tank , the remaining solution will be approximately what percent sodium chloride ?
Options: a ) 6.28 % , b ) 7.14 % , c ) 7.86 % , d ) 8.25 % , e ) 8.63 %
Rationale: "the amount of sodium chloride is 0.05 * 10,000 = 500 gallons 500 / 7000 = 1 / 14 which is about 7.14 % the answer is b ."
Answer: b
Python program:
a = 100 * 100
b = 5 / 100
c = a * b
d = 100 * 100
e = 2 + 3 
f = 2 + 3 
g = f * 2
h = g * 100
i = e * h
j = 2 + 3 
k = j * 100
l = i + k 
m = d - l
n = c / m
o = n * 100
Problem: if a : b : : 3 : 7 , then what is ( 5 a + 6 b ) : ( a - 4 b ) ?
Options: a ) 57 : 11 , b ) - 57 : 11 , c ) 11 : 10 , d ) - 57 : 25 , e ) - 1 : 10
Rationale: "a / b = 3 / 7 dividing numerator & denominator of ' ( 5 a + 6 b ) / ( a - 2 b ) ' by b , [ 5 ( a / b ) + 6 ] / [ ( a / b ) - 4 ] = [ 5 * ( 3 / 7 ) + 6 ] / [ ( 3 / 7 ) - 4 ] = - 57 / 25 answer : d"
Answer: d
Python program:
a = 5 * 3
b = 7 * 6
c = a + b 
d = 4 * 7
e = 3 - d
f = c / e
Problem: of 3 numbers , the third is 4 times the second and the second is two times the first . if their average is 165 , the second number of the 3 numbers is :
Options: a ) 18 , b ) 100 , c ) 90 , d ) 45 , e ) 120
Rationale: explanation : let first number be x . so , 2 nd no . = 2 x & 3 rd no . = 8 x . so , x + 2 x + 8 x = 165 × 3 = 495 11 x = 495 / 11 x = 495 / 11 hence , first number is x = 45 so , second number is = 2 x 45 = 90 answer : c
Answer: c
Python program:
a = 3 * 165
b = 4 * 2
c = b + 3 
d = c / 2
e = a / d
Problem: the side of a rhombus is 20 m and length of one of its diagonals is 16 m . the area of the rhombus is ?
Options: a ) 223.28 , b ) 293.28 , c ) 293.78 , d ) 291.28 , e ) 193.28
Rationale: "area of the rhombus = 1 / 2 * p * √ 4 ( a ) 2 - ( p ) 2 a = 20 ; p = 16 a = 1 / 2 * 16 * √ 4 ( 20 ) 2 - ( 16 ) 2 = 1 / 2 * 16 * √ 1600 - 256 = 1 / 2 * 16 * √ 1344 a = 293.28 answer : b"
Answer: b
Python program:
a = 2 * 20
b = a ** 2
c = 16 ** 2
d = b - c
e = math.sqrt(d)
f = 16 * e
g = f / 2
Problem: in a certain company , a third of the workers do not have a retirement plan . 20 % of the workers who do not have a retirement plan are women , and 50 % of the workers who do have a retirement plan are men . if 120 of the workers of that company are men , how many of the workers are women ?
Options: a ) 80 , b ) 95 , c ) 105 , d ) 120 , e ) 210
Rationale: "20 % of the workerswithoutretirement plan are women , this means 80 % of the workerswithoutretirement plan are men right ? makes 100 % = no retirement plan . then 40 % of those wo have a retirement plan are men , which means 60 % of those who have a retirement plan are women . these percentages are always refering to the subgroupsretirement plan = yesandno retirement plan . make the total workers equal x and work from there and it should be fine > x / 3 have no retirement plan at all . i struggled with the question a lot , it was hard for me although usually i have no problems with sets questions like this . i believe it must be a 700 + question . yes , you are right . i read the question incorrectly ! i glazed overnotfor some reason . if 20 % of the workers who do not have a retirement plan are women , 80 % who do not have retirement plan are men . also 40 % who do have retirement plan are men . since 1 / 3 do not have retirement plan and 2 / 3 do have , it becomes a simple weighted average question . cavg = ( 80 * 1 + 50 * 2 ) / 3 = 60 % are men total = 120 * 100 / 60 = 200 no . of women = 200 - 120 = 80 a"
Answer: a
Python program:
a = 1 / 3
b = 1 / 3
c = 20 / 100
d = b * c
e = a - d
f = 1 / 3
g = 1 - f
h = 50 / 100
i = g * h
j = e + i 
k = 120 / j
l = 1 / 3
m = 20 / 100
n = l * m
o = 1 / 3
p = 1 - o
q = 1 / 3
r = 1 - q
s = 50 / 100
t = r * s
u = p - t
v = n + u 
w = k * v
Problem: how many seconds will a train 70 meters long take to cross a bridge 80 meters long if the speed of the train is 36 kmph ?
Options: a ) 22 sec , b ) 27 sec , c ) 25 sec , d ) 15 sec , e ) 11 sec
Rationale: "explanation : d = 70 + 80 = 150 s = 36 * 5 / 18 = 10 mps t = 150 / 10 = 15 sec answer : option d"
Answer: d
Python program:
a = 80 + 70 
b = 36 * const_0_2778
c = a / b
Problem: for the past n days , the average ( arithmetic mean ) daily production at a company was 30 units . if today ' s production of 90 units raises the average to 35 units per day , what is the value of n ?
Options: a ) 30 , b ) 18 , c ) 10 , d ) 9 , e ) 3
Rationale: "( average production for n days ) * n = ( total production for n days ) - - > 30 n = ( total production for n days ) ; ( total production for n days ) + 90 = ( average production for n + 1 days ) * ( n + 1 ) - - > 30 n + 90 = 35 * ( n + 1 ) - - > n = 3 . answer : e ."
Answer: e
Python program:
a = 90 - 30
b = 35 - 30
c = a / b
d = c - 1
Problem: how many unique positive odd integers less than 80 are equal to the product of a positive multiple of 5 and an odd number ?
Options: a ) 4 , b ) 8 , c ) 11 , d ) 12 , e ) 15
Rationale: "the question basically asks how many positive odd integers less than 80 are odd multiples of 5 so we have 5,15 , 25,35 , 45,55 , 65,75 = 8 b"
Answer: b
Python program:
a = 80 / 5
b = a / 2
Problem: there were two candidates in an election . winner candidate received 70 % of votes and won the election by 280 votes . find the number of votes casted to the winning candidate ?
Options: a ) 228 , b ) 744 , c ) 490 , d ) 199 , e ) 231
Rationale: "w = 70 % l = 30 % 70 % - 30 % = 40 % 40 % - - - - - - - - 280 70 % - - - - - - - - ? = > 280 / 40 * 70 = 490 answer : c"
Answer: c
Python program:
a = 100 - 70
b = 70 - a
c = b / 100
d = 280 / c
e = d * 70
f = e / 100
Problem: add 16 % of 36 and 13 % of 45 .
Options: a ) 9.5 , b ) 8.5 , c ) 7.2 , d ) 7 , e ) 8
Rationale: "16 % of 36 + 13 % of 45 36 * 16 / 100 + 45 * 13 / 100 5.8 + 1.4 = 7.2 answer c"
Answer: c
Python program:
a = 16 * 36
b = a / 100
c = 13 * 45
d = c / 100
e = b + d
Problem: a is 30 % more efficient than b . how much time will they , working together , take to complete a job which a alone could have done in 23 days ?
Options: a ) 11 days , b ) 13 days , c ) 20 3 / 17 days , d ) 21 days , e ) none of these
Rationale: "explanation : ratio of times taken by a and b = 100 : 130 = 10 : 13 suppose b takes x days to do the work . x = ( 23 * 13 ) / 10 = 299 / 10 a ' s 1 day work = 1 / 23 ; b ' s 1 day work = 10 / 299 ( a + b ) ' s 1 day work = ( 1 / 23 + 10 / 299 ) = 1 / 13 a and b together can complete the job in 13 days . answer is b"
Answer: b
Python program:
a = 1 / 23
b = 30 / 100
c = b + 1 
d = c * 23
e = 1 / d
f = a + e 
g = 1/(f)
Problem: suresh started a business , investing rs . 18000 . after 3 months and 4 months respectively , rohan and sudhir joined him with capitals of 12000 and 9000 . at the end of the year the total profit was rs . 3850 . what is the difference between rohan ’ s and sudhir ’ s share in the profit ?
Options: a ) s . 345 , b ) s . 350 , c ) s . 352 , d ) s . 362 , e ) s . 368
Rationale: suresh : rohan : sudhir ratio of their investments = 18000 × 12 : 12000 × 9 : 9000 × 8 = 6 : 3 : 2 the difference between rohan ’ s and sudhir ’ s share = 1 share : . i . e . = rs . 3850 × 1 / 11 = rs . 350 . b
Answer: b
Python program:
a = 3 * 4
b = a - 3
c = 3 * 4
d = b / c
e = 12000 * d
f = 3 * 4
g = f - 4
h = 3 * 4
i = g / h
j = 9000 * i
k = e - j
l = 3 * 4
m = l - 3
n = 3 * 4
o = m / n
p = 12000 * o
q = 18000 + p 
r = 3 * 4
s = r - 4
t = 3 * 4
u = s / t
v = 9000 * u
w = q + v 
x = 3850 / w
y = k * x
Problem: a train passes a station platform in 36 sec and a man standing on the platform in 20 sec . if the speed of the train is 72 km / hr . what is the length of the platform ?
Options: a ) 229 , b ) 240 , c ) 288 , d ) 277 , e ) 320
Rationale: "speed = 72 * 5 / 18 = 20 m / sec . length of the train = 20 * 20 = 400 m . let the length of the platform be x m . then , ( x + 400 ) / 36 = 20 = > x = 320 m . answer : e"
Answer: e
Python program:
a = 72 * const_0_2778
b = 20 * a
Problem: in a certain city , 60 percent of the registered voters are democrats and the rest are republicans . in a mayoral race , if 75 percent of the registered voters who are democrats and 20 percent of the registered voters who are republicans are expected to vote for candidate a , what percent of the registered voters are expected to vote for candidate a ?
Options: a ) 50 % , b ) 53 % , c ) 54 % , d ) 55 % , e ) 57 %
Rationale: "registered voters = 100 d = 60 r = 40 75 % of d ( 60 ) = 45 20 % of r ( 40 ) = 8 total voter % of registered voters = 53 / 100 53 % answer : b"
Answer: b
Python program:
a = 75 / 100
b = 60 * a
c = 100 - 60
d = 20 / 100
e = c * d
f = b + e
Problem: a jogger running at 9 km / hr along side a railway track is 200 m ahead of the engine of a 210 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?
Options: a ) 89 , b ) 20 , c ) 36 , d ) 41 , e ) 34
Rationale: "speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 200 + 210 = 410 m . time taken = 410 / 10 = 41 sec . answer : option d"
Answer: d
Python program:
a = 200 + 210 
b = 45 - 9
c = 10 / 2
d = 45 - 9
e = d / 2
f = c / e
g = b * f
h = a / g
Problem: if 4 / p = 8 & 6 / q = 18 then p - q = ?
Options: a ) 5 / 24 , b ) 6 / 24 , c ) 7 / 24 , d ) 1 / 6 , e ) 9 / 24
Rationale: "p = 4 / 8 , q = 6 / 18 = > q = 1 / 3 therefore p - q = ( 1 / 2 ) - ( 1 / 3 ) = 1 / 6 answer : d"
Answer: d
Python program:
a = 6 / 8
b = 4 / 18
c = a - b
Problem: a box contain the number of balls which is as much greater than 20 is less than 30 . the number of balls is ?
Options: a ) 40 , b ) 25 , c ) 30 , d ) 50 , e ) 35
Rationale: "answer let the number be x . then , x - 20 = 30 - x â ‡ ’ 2 x = 30 + 20 = 50 â ‡ ’ 2 x = 50 â ˆ ´ x = 25 correct option : b"
Answer: b
Python program:
a = 30 + 20 
b = a / 2
Problem: if 10 typists can type 30 letters in 30 minutes , then how many letters will 40 typists working at the same rate complete in 1 hour ?
Options: a ) 200 , b ) 210 , c ) 205 , d ) 225 , e ) 240
Rationale: "no . of letters typing by 10 typists in 30 minutes = 30 no . of letters typing by 10 typists in 60 minutes = 30 * 2 = 60 no . of letters typing by 40 typists in 60 minutes = 60 / 10 * 40 = 240 answer : e"
Answer: e
Python program:
a = const_60 * 0
b = a / 10
c = b * 40
Problem: a car going at 20 miles per hour set out on an 80 - mile trip at 9 : 00 a . m . exactly 10 minutes later , a second car left from the same place and followed the same route . how fast , in miles per hour , was the second car going if it caught up with the first car at 10 : 30 a . m . ?
Options: a ) 40 , b ) 50 , c ) 53 , d ) 55 , e ) 60
Rationale: "let car a = car that starts at 9 am car b = car that starts at 9 : 10 am time for which car a travels at speed of 20 m per hour = 1.5 hours distance travelled by car a = 20 * 1.5 = 30 miles since car b catches up car a at 10 : 30 , time = 80 mins = 4 / 3 hour speed of car b = 30 / ( 4 / 3 ) = 40 miles per hour answer a"
Answer: a
Python program:
a = 10 - 9
b = a * const_60
c = 20 - 10
d = b + c 
e = d / const_60
f = 80 / e
Problem: the ratio of number of boys and girls in a school is 1 : 2 . if there are 90 students in the school , find the number of girls in the school ?
Options: a ) 45 , b ) 50 , c ) 60 , d ) 75 , e ) 90
Rationale: let the number of boys and girls be x and 2 x total students = 100 number of girls in the school = 2 * 90 / 3 = 60 answer is c
Answer: c
Python program:
a = 90 / 3
b = a * 2
Problem: an amount of rs . 1638 was divided among a , b and c , in the ratio 1 / 2 : 1 / 3 : 1 / 4 . find the share of c ?
Options: a ) 386 , b ) 378 , c ) 396 , d ) 395 , e ) 394
Rationale: "let the shares of a , b and c be a , b and c respectively . a : b : c = 1 / 2 : 1 / 3 : 1 / 4 let us express each term with a common denominator which is the last number divisible by the denominators of each term i . e . , 12 . a : b : c = 6 / 12 : 4 / 12 : 3 / 12 = 6 : 4 : 3 . share of c = 3 / 13 * 1638 = rs . 378 answer : b"
Answer: b
Python program:
a = 2 + 3 
b = a + 4 
c = 1638 / b
d = c * 4
Problem: a group of 3 investors and 3 clients recently frequented the chinese luyang restaurant . the total bill for the meal , including 20 % gratuity , came to $ 720 . on average , how much did the meal of each individual cost before gratuity ?
Options: a ) $ 160 , b ) $ 96 , c ) $ 90 , d ) $ 80 , e ) $ 100
Rationale: 3 investors and 3 clients - so total 6 people the bill $ 720 includes 20 % gratuity . . . so the actual cost of dinner was $ 600 now , the cost per person will be $ 600 / 6 which is $ 100 option e
Answer: e
Python program:
a = 20 + 100 
b = a / 100
c = 720 / b
d = 3 + 3 
e = c / d
Problem: a man can row a distance of 5 km in 60 min with the help of the tide . the direction of the tide reverses with the same speed . now he travels a further 30 km in 10 hours . how much time he would have saved if the direction of tide has not changed ?
Options: a ) 2 , b ) 8 , c ) 4 , d ) 6 , e ) 5
Rationale: "explanation : he covered 5 km in 1 hour , so he might cover 30 km in 6 hours . but he took 10 hours . he would have saved 10 â € “ 6 = 4 hours . answer : c"
Answer: c
Python program:
a = 30 / 5
b = 10 - a
Problem: a man cycling along the road noticed that every 10 minutes a bus overtakes him and every 4 minutes he meets an oncoming bus . if all buses and the cyclist move at a constant speed , what is the time interval between consecutive buses ?
Options: a ) 5 minutes , b ) 6 minutes , c ) 8 minutes , d ) 9 minutes , e ) 48 / 7 minutes
Rationale: "let ' s say the distance between the buses is d . we want to determine interval = \ frac { d } { b } , where b is the speed of bus . let the speed of cyclist be c . every 10 minutes a bus overtakes cyclist : \ frac { d } { b - c } = 10 , d = 10 b - 10 c ; every 4 minutes cyclist meets an oncoming bus : \ frac { d } { b + c } = 4 , d = 4 b + 4 c ; d = 10 b - 10 c = 4 b + 4 c , - - > b = 7 c / 3 , - - > d = 12 b - 12 b * 3 / 7 = 48 / 7 b . interval = \ frac { d } { b } = \ frac { 48 / 7 b } { b } = 48 / 7 answer : e ( 48 / 7 minutes ) ."
Answer: e
Python program:
a = 4 + 10 
b = 10 - 4
c = a / b
d = 10 / c
e = 10 - d
f = e / 1
Problem: the simple form of the ratio 4 / 2 : 2 / 5 is ?
Options: a ) 10 : 6 , b ) 5 : 1 , c ) 15 : 3 , d ) 25 : 3 , e ) 30 : 3
Rationale: "4 / 2 : 2 / 5 = 20 : 4 = 5 : 1 answer : b"
Answer: b
Python program:
a = 2 / 5
Problem: the average score of 35 students in a class is 37 . if every student is given 3 grace marks , the new average of the class is :
Options: a ) 33 , b ) 21 , c ) 38 , d ) 40 , e ) 92
Rationale: explanation : average score = 37 grace mark 3 is given to 35 student then its average will be 3 . hence new average = 37 + 3 = 40 answer : d
Answer: d
Python program:
a = 3 * 35
b = a / 35
c = 37 + b
Problem: chris mixed 3 pounds of raisins with 4 pounds of nuts . if a pound of nuts costs 2 times as much as a pound of raisins , then the total cost of the raisins was what fraction of the total cost of the mixture ?
Options: a ) 1 / 7 , b ) 1 / 5 , c ) 1 / 4 , d ) 1 / 3 , e ) 3 / 11
Rationale: 1 lbs of raisin = $ 1 3 lbs of raisin = $ 3 1 lbs of nuts = $ 2 4 lbs of nuts = $ 8 total value of mixture = 8 + 3 = 11 fraction of the value of raisin = 3 / 11 ans : e
Answer: e
Python program:
a = 4 * 2
b = a + 3 
c = 3 / b
Problem: 82 * 83 * 84 * . . 89 what is the digit in units place ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "in the product 82 * 83 * 84 * 85 * 86 . . . . . . * 89 last ( unit ) digit will be zero as 82 * 85 will give zero as last ( unit ) digit and further multiplication with any number will also give zero at unit place . answer : a"
Answer: a
Python program:
a = volume_rectangular_prism / (
Problem: a bag contains 20 red jellybeans and 20 blue jellybeans . if 3 jellybeans are removed one at a time , at random and are not replaced , what is the probability that all 3 jellybeans removed from the bag are blue ?
Options: a ) 9 / 100 , b ) 2 / 19 , c ) 1 / 8 , d ) 3 / 20 , e ) 3 / 10
Rationale: "method - 1 10 red jellybeans and 10 blue jellybeans total outcomes = no . of ways to choose 3 jelly bean at random out of a total 20 jellybeans = 20 c 3 = 1140 favourable outcomes = no . of ways to choose 3 jelly bean such that they are all blue out of 10 blue = 10 c 3 = 120 probability = favourable outcomes / total outcomes = 10 c 3 / 20 c 3 probability = 120 / 1140 = 2 / 19 answer : option b method - 2 probability of first jelly bean to be blue = 10 / 20 [ total 10 blue out of total 20 jellybeans ] probability of second jelly bean to be blue = 9 / 19 [ total 9 blue remaining out of total 19 jellybeans remaining ] probability of third jelly bean to be blue = 8 / 18 [ total 8 blue remaining out of total 18 jellybeans remaining ] required probability = ( 10 / 20 ) * ( 9 / 19 ) * ( 8 / 18 ) = 3 / 20 answer : option d"
Answer: d
Python program:
a = math.comb(20, 3)
b = 20 + 20 
c = math.comb(b, 3)
d = a / c