euclaise/mathqa_programs huggingface dataset:
Problem: what should be the least number to be added to the 1202 number to make it divisible by 4 ?
Options: a ) 12 , b ) 17 , c ) 18 , d ) 77 , e ) 2
Rationale: answer : 2 option : e
Answer: e
Python program:
a = 4 - reminder
Problem: a sum of money deposited at c . i . amounts to rs . 3250 in 2 years and to rs . 3830 in 3 years . find the rate percent ?
Options: a ) 30 % , b ) 10 % , c ) 20 % , d ) 17 % , e ) 50 %
Rationale: "3250 - - - 580 100 - - - ? = > 17 % answer : d"
Answer: d
Python program:
a = 3830 - 3250
b = a / 3250
c = b * 100
Problem: if | 20 x - 10 | = 150 , then find the product of the values of x ?
Options: a ) - 45 , b ) 56 , c ) - 62 , d ) 35 , e ) - 30
Rationale: "| 20 x - 10 | = 150 20 x - 10 = 150 or 20 x - 10 = - 150 20 x = 160 or 20 x = - 140 x = 8 or x = - 7 product = - 7 * 8 = - 56 answer is b"
Answer: b
Python program:
a = 150 - 10
b = 150 + 10 
c = a - b
d = c - 10
Problem: a certain car uses 12 gallons of gasoline in traveling 180 miles . in order for the car to travel the same distance using 10 gallons of gasoline , by how many miles per gallon must the car ’ s gas mileage be increased ?
Options: a ) 2 , b ) 3 , c ) 6 , d ) 8 , e ) 10
Rationale: "180 / 10 = 18 . the difference is 18 - 15 = 3 . answer b"
Answer: b
Python program:
a = 180 / 10
b = 180 / 12
c = a - b
Problem: a man is 24 years older than his son . in two years , his age will be twice the age of his son . what is the present age of his son ?
Options: a ) 23 years , b ) 22 years , c ) 21 years , d ) 20 years , e ) 30 years
Rationale: "let present age of the son = x years then present age the man = ( x + 24 ) years given that in 2 years man ' s age will be twice the age of his son x = 22 answer b"
Answer: b
Python program:
a = 2 * 2
b = a - 2
c = 24 - b
d = 2 - 1
e = c / d
Problem: in the hillside summer camp there are 60 children . 90 % of the children are boys and the rest are girls . the camp administrator decided to make the number of girls only 5 % of the total number of children in the camp . how many more boys must she bring to make that happen ?
Options: a ) 50 . , b ) 45 . , c ) 40 . , d ) 60 . , e ) 25 .
Rationale: "given there are 60 students , 90 % of 60 = 54 boys and remaining 6 girls . now here 90 % are boys and 10 % are girls . now question is asking about how many boys do we need to add , to make the girls percentage to 5 or 5 % . . if we add 60 to existing 54 then the count will be 114 and the girls number will be 6 as it . now boys are 95 % and girls are 5 % . ( out of 120 students = 114 boys + 6 girls ) . imo option d is correct ."
Answer: d
Python program:
a = 100 - 5
b = a / 100
c = b * 60
d = 5 / 100
e = d * 60
f = c + e
Problem: if x and y are integers such that x ^ 2 = 3 y and xy = 36 , then x – y = ?
Options: a ) - 30 , b ) - 20 , c ) - 5 , d ) 5 , e ) 0
Rationale: here x and y are integers . x ^ 2 = 3 y , xy = 36 . substitute ( x ^ 2 ) / 3 = y in xy = > x ^ 3 = 36 * 3 = > x ^ 3 = 108 . here x ^ 3 is positive , x is also positive . x = 6 then y = 6 . x - y = 0 so option e is correct
Answer: e
Python program:
a = 36 * 3
b = a ** const_0_33
c = 36 * 3
d = c ** const_0_33
e = 36 / d
f = b - e
Problem: 49 pumps can empty a reservoir in 13 / 2 days , working 8 hours a day . if 196 pumps are used for 5 hours each day , then the same work will be completed in :
Options: a ) 2 days , b ) 5 / 2 days , c ) 13 / 5 days , d ) 3 days , e ) none of these
Rationale: explanation : let the required number of days be x . then , more pumps , less days ( indirect proportion ) less working hrs / day , more days ( indirect proportion ) pumps 196 : 49 working hrs / day 5 : 8 : : 13 / 2 : x 96 x 5 x x = 49 x 8 x 13 / 2 x = 49 x 8 x 13 / 2 x 1 / ( 196 x 5 ) x = 13 / 5 answer c
Answer: c
Python program:
a = 49 / 196
b = 8 / 5
c = a * b
d = 13 / 2
e = c * d
Problem: a couple decides to have 3 children . if they succeed in having 4 children and each child is equally likely to be a boy or a girl , what is the probability that they will have exactly 2 girls and 1 boy ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 5 / 8 , e ) 4
Rationale: "sample space = 2 ^ 3 = 8 . favourable events = { bgg } , { bgb } , { bbb } , { ggg } , { gbg } probability = 5 / 8 = 5 / 8 . ans ( d ) ."
Answer: d
Python program:
a = math.factorial(3)
b = math.factorial(1)
c = a / b
d = 2 / 1
e = d ** 3
f = c * e
g = 2 - f
Problem: working together at their respective constant rates , machine a and machine b can produce 600 units in 8 hours . working alone , machine b would complete that same output in 50 % more time . if machine a were to work on its own for an 8 - hour shift , what percent of the 600 unit total would it produce ?
Options: a ) 25 , b ) 37 , c ) 50 , d ) 30 , e ) 75
Rationale: "1 / a + 1 / b = 1 / t 1 / a + 1 / 12 = 1 / 8 ( 50 % more of 8 is 12 ) 1 / a = 1 / 24 machine a can produce 600 units in 24 hrs , so it can produce 600 * 8 / 24 = 200 units is 8 hrs . 200 is 30 % of 600 . d is the answer"
Answer: d
Python program:
a = 4 * 4
b = a * 100
c = b / 8
d = 4 * 4
e = d * 100
f = 8 * 50
g = f / 100
h = 8 + g 
i = e / h
j = c - i
k = j * 8
l = 4 * 4
m = l * 100
n = k / m
o = n * 100
Problem: some of the 50 % solution of acid was removed and this was replaced with an equal amount of 30 % solution of acid . as a result , a 40 % solution of acid was obtained . what fraction of the original solution was replaced ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 2 / 3 , d ) 1 / 4 , e ) 2 / 5
Rationale: "let x be the fraction of the original solution that was replaced . 0.5 * ( 1 - x ) + 0.3 ( x ) = 0.4 0.2 x = 0.1 x = 1 / 2 the answer is a ."
Answer: a
Python program:
a = 50 + 30 
b = 40 / a
Problem: in a certain brick wall , each row of bricks above the bottom row contains one less brick than the row just below it . if there are 5 rows in all and a total of 200 bricks in the wall , how many bricks does the bottom row contain ?
Options: a ) 42 , b ) 35 , c ) 40 , d ) 33 , e ) 38
Rationale: "the bottom row has x bricks x + x - 1 + x - 2 + x - 3 + x - 4 = 200 5 x - 10 = 200 5 x = 190 x = 38 answer : e"
Answer: e
Python program:
a = 200 - 1
b = a - 2
c = b - 3
d = c - 4
e = d / 5
Problem: a certain business school has 500 students , and the law school at the same university has 800 students . among these students , there are 30 sibling pairs consisting of 1 business student and 1 law student . if 1 student is selected at random from both schools , what is the probability that a sibling pair is selected ?
Options: a ) 3 / 40000 , b ) 3 / 20000 , c ) 3 / 4000 , d ) 9 / 400 , e ) 6 / 130
Rationale: probability of selecting 1 student from harvard ' s business school - - - 1 / 500 probability of selecting 1 student from harvard ' s law school - - - - - - - - - 1 / 800 probability that these two students are siblings - - - - ( 1 / 500 * 1 / 800 ) since there are 30 siblings , hence ( 1 / 500 * 1 / 800 ) * 30 . 3 / 40000 answer : a
Answer: a
Python program:
a = 1 / 500
b = 1 / 800
c = a * b
d = c * 30
Problem: a number increased by 40 % gives 700 . the number is
Options: a ) 250 , b ) 500 , c ) 450 , d ) 500 , e ) 520
Rationale: "formula = total = 100 % , increse = ` ` + ' ' decrease = ` ` - ' ' a number means = 100 % that same number increased by 40 % = 140 % 140 % - - - - - - - > 700 ( 140 × 5 = 700 ) 100 % - - - - - - - > 700 ( 100 × 5 = 500 ) b )"
Answer: b
Python program:
a = 40 / 100
b = 1 + a 
c = 700 / b
Problem: the profits of qrs company rose 40 % from march to april , then dropped 20 % from april to may , then rose 50 % from may to june . what was the percent increase for the whole quarter , from march to june ?
Options: a ) 15 % , b ) 32 % , c ) 40 % , d ) 68 % , e ) 80 %
Rationale: "assume 100 in march , then 140 in april as 40 % increase , then 112 in may as 20 % decrease from april , and then 168 in june which is 150 % of 112 . so overall increase is from 100 to 168 is 68 % answer d"
Answer: d
Python program:
a = 50 / 100
b = 1 + a 
c = 40 / 100
d = 1 + c 
e = 20 / 100
f = 1 - e
g = d * f
h = b * g
i = h - 1
j = 100 * i
Problem: find the value of 4 x [ ( 3.6 x 0.48 x 2.50 ) / ( 0.12 x 0.09 x 0.5 ) ]
Options: a ) 800 , b ) 3200 , c ) 900 , d ) 1600 , e ) none
Rationale: "answer 4 x [ ( 3.6 x 0.48 x 2.50 ) / ( 0.12 x 0.09 x 0.5 ) ] = 4 x [ ( 36 x 48 x 250 ) / ( 12 x 9 x 5 ) ] = 4 x 4 x 4 x 50 = 3200 correct option : b"
Answer: b
Python program:
a = 3 * 6
b = a * 2
c = 0 * 12
d = c * 0
e = b / d
f = e * 4
Problem: an army ’ s recruitment process included n rounds of selection tasks . for the first a rounds , the rejection percentage was 60 percent per round . for the next b rounds , the rejection percentage was 50 percent per round and for the remaining rounds , the selection percentage was 70 percent per round . if there were 100000 people who applied for the army and 175 were finally selected , what was the value of n ?
Options: a ) 4 , b ) 9 , c ) 6 , d ) 8 , e ) 10
Rationale: "fastly i reduce 60 % till it gets closer to our required 2000 candidates step ( 1 ) 40000 accepted . step ( 2 ) another 40 % of 40000 = 16000 accepted . here it is quiet observable that if we further deduct candidate by 60 % it would change our probablity of easy going 2000 candidate . so i would get to second stage of recruitment where 50 % is accepted step ( 3 ) 50 % of 16000 = 8000 step ( 4 ) 50 % of 8000 = 4000 step ( 5 ) 50 % of 4000 = 2000 step ( 6 ) 50 % of 2000 = 1000 step ( 7 ) 50 % of 1000 = 500 step ( 8 ) 50 % of 500 = 250 step ( 9 ) 70 % of 350 = 175 ( our target ) total 9 steps required . ans b"
Answer: b
Python program:
a = 1 + 4 
b = 2 + a 
c = b + 2
Problem: from the sale of sleeping bags , a retailer made a gross profit of 12 % of the wholesale cost . if each sleeping bag was sold for $ 28 , what was the wholesale cost per bag ?
Options: a ) 3.0 , b ) 3.36 , c ) 24.64 , d ) 25.0 , e ) 31.36
Rationale: cost price * 1.12 = selling price - - > cost price * 1.12 = $ 28 - - > cost price = $ 25 . answer : d . actually even without any math only c and d make any sense , but since 24.64 * 1.12 wo n ' t be an integer ( $ 28 ) then only answer choice d remains .
Answer: d
Python program:
a = 28 * 100
b = 100 + 12 
c = a / b
Problem: there is enough provisions for 700 men in an army camp for 25 days . if there were 300 men less , how long will the provision last ?
Options: a ) 30 days , b ) 40 days , c ) 50 days , d ) 59 days , e ) 65 days
Rationale: "exp : we have , m 1 d 1 = m 2 d 2 700 * 25 = 300 * d 2 d 2 = 700 * 25 / 300 = 59 days . answer : d"
Answer: d
Python program:
a = 700 * 25
b = a / 300
Problem: the distance between delhi and mathura is 140 kms . a starts from delhi with a speed of 24 kmph at 7 a . m . for mathura and b starts from mathura with a speed of 46 kmph at 8 a . m . from delhi . when will they meet ?
Options: a ) 11 , b ) 23 3 / 4 , c ) 16 1 / 2 , d ) 9 1 / 2 , e ) 98
Rationale: "d = 140 – 24 = 116 rs = 46 + 24 = 70 t = 116 / 70 = 1.6 hours 8 a . m . + 1.6 = 9 1 / 2 a . m . . answer : d"
Answer: d
Python program:
a = 24 + 46 
b = 140 / a
c = 8 + b
Problem: 3 distinct single - digit numbers . a , b , c are in gp . if abs ( x ) for real x is the absolute value of x ( x if x is + ve or 0 and - x if x is - ve ) , then the number of different possible values of abs ( a + b + c ) is
Options: a ) 5 , b ) 6 , c ) 3 , d ) 4 , e ) 7
Rationale: a , b , c may be ( 1 , 2,4 ) & ( 4 , 2,1 ) ( 1 , 3,9 ) & ( 9 , 3,1 ) ( 2 , 4,8 ) & ( 8 , 4,2 ) ( 4 , 6,9 ) & ( 9 , 6,4 ) find abs ( a + b + c ) for these 8 gps 7,13 , 15,19 so , we get 4 different values answer : d
Answer: d
Python program:
a = 3 + 1
Problem: the charge for a single room at hotel p is 25 percent less than the charge for a single room at hotel r and 20 percent less than the charge for a single room at hotel g . the charge for a single room at hotel r is what percent greater than the charge for a single room at hotel g ?
Options: a ) 15 % , b ) 20 % , c ) 40 % , d ) 50 % , e ) 6 %
Rationale: "let rate in r = 100 x then p = 75 x g = 100 y p = 80 y thus 75 x = 80 y or x = 1.06 y ans r = 106 y so increase = 6 % answer : e"
Answer: e
Python program:
a = 100 - 25
b = 100 - 20
c = a / b
d = c * 100
e = 100 - d
f = 100 - 25
g = 100 - 20
h = f / g
i = h * 100
j = e / i
k = j * 100
Problem: if the average ( arithmetic mean ) of x , x + 2 , and x + 4 is 53 , what is the value of x ?
Options: a ) 52 , b ) 53 , c ) 54 , d ) 55 , e ) 51
Rationale: "am of x , x + 2 , and x + 4 = x + ( x + 2 ) + ( x + 4 ) / 3 = 3 x + 6 / 3 = x + 2 given that x + 2 = 53 x = 51 answer : e"
Answer: e
Python program:
a = 4 * 2
b = 2 * 2
c = a - b
Problem: a courtyard is 18 meter long and 12 meter board is to be paved with bricks of dimensions 12 cm by 6 cm . the total number of bricks required is :
Options: a ) 16000 , b ) 18000 , c ) 20000 , d ) 30000 , e ) none of these
Rationale: "explanation : number of bricks = courtyard area / 1 brick area = ( 1800 ã — 1200 / 12 ã — 6 ) = 30000 option d"
Answer: d
Python program:
a = 18 * 100
b = 12 * 100
c = a * b
d = 12 * 6
e = c / d
Problem: a person travels equal distances with speeds of 3 km / hr , 4 km / hr and 5 km / hr and takes a total time of 52 minutes . the total distance is ?
Options: a ) 1 km , b ) 2 km , c ) 3.3 km , d ) 4 km , e ) 5 km
Rationale: "c 3 km let the total distance be 3 x km . then , x / 3 + x / 4 + x / 5 = 52 / 60 47 x / 60 = 52 / 60 = > x = 1.1 total distance = 3 * 1.1 = 3.3 km ."
Answer: c
Python program:
a = 52 / const_60
b = 1 / 3
c = 1 / 4
d = b + c 
e = 1 / 5
f = d + e 
g = a / f
h = g * 3
i = h * 1000
Problem: a batch of cookies was divided among 3 tins : 2 / 3 of all the cookies were placed in either the blue tin or the green tin , and the rest were placed in the red tin . if 1 / 4 of all the cookies were placed in the blue tin , what fraction w of the cookies that were placed in the other tins were placed in the green tin ?
Options: a ) 15 / 2 , b ) 9 / 4 , c ) 5 / 9 , d ) 7 / 5 , e ) 9 / 7
Rationale: blue tin or red tin : 2 / 3 ( n ) red tin : ( 1 / 3 ) n blue tin : ( 1 / 4 ) n what the last statment meant , is it wants this fraction : ( # of cookies in green tin ) / ( # of cookies in red and green tin ) # of cookies in green tin = 2 n / 3 - n / 4 = 8 n - 3 n / 12 = 5 n / 12 # of cookies in red and green tin = n / 3 + 5 n / 12 = 9 n / 12 fraction w = 5 n / 12 * 12 / 9 n = 5 / 9 ( c )
Answer: c
Python program:
a = 2 / 3
b = 1 / 4
c = a - b
d = 2 / 3
e = 1 / 4
f = d - e
g = 1 / 3
h = f + g 
i = c / h
Problem: two trains of equal lengths take 12 sec and 15 sec respectively to cross a telegraph post . if the length of each train be 120 m , in what time will they cross other travelling in opposite direction ?
Options: a ) 22 , b ) 13 , c ) 77 , d ) 99 , e ) 21
Rationale: "speed of the first train = 120 / 12 = 10 m / sec . speed of the second train = 120 / 15 = 8 m / sec . relative speed = 10 + 8 = 18 m / sec . required time = ( 120 + 120 ) / 18 = 13 sec . answer : b"
Answer: b
Python program:
a = 120 * 2
b = speed + ( 
c = a / b
Problem: the difference of two numbers is 11 and one - fifth of their sum is 9 . find the numbers .
Options: a ) 28 and 17 , b ) 27 and 18 , c ) 25 and 15 , d ) 27 and 15 , e ) 25 and 18
Rationale: "let the number be x and y . then , x – y = 11 - - - - ( i ) and 1 / 5 ( x + y ) = 9 = > x + y = 45 - - - - ( ii ) adding ( i ) and ( ii ) , we get : 2 x = 56 or x = 28 . putting x = 28 in ( i ) , we get : y = 17 . hence , the numbers are 28 and 17 . answer is a ."
Answer: a
Python program:
a = 10 / 2
b = a * 9
c = 10 / 2
d = c * 9
e = 11 + d 
f = e / 2
g = b - f
h = 10 / 2
i = g + h
Problem: 40 % of major airline companies equip their planes with wireless internet access . 70 % of major airlines offer passengers free on - board snacks . what is the greatest possible percentage of major airline companies that offer both wireless internet and free on - board snacks ?
Options: a ) 30 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 70 %
Rationale: "to maximize the percentage of companies offering both , let ' s assume that all 40 % of companies which offer wireless internet also offer snacks . the answer is b ."
Answer: b
Python program:
a = 40 * 1
Problem: a boat moves down stream at the rate of 1 km in 6 minutes and upstream at the rate of 1 km in 10 minutes . the speed of current is
Options: a ) 2 kmph , b ) 3 kmph , c ) 4 kmph , d ) 5 kmph , e ) 6 kmph
Rationale: if speed ( in kmph ) of the boat = b and current = c , then in downstream time taken ( in hrs . ) = 1 / ( b + c ) = 6 / 60 = 1 / 10 or b + c = 10 - - - ( i ) & in upstream time taken ( in hrs . ) = 1 / ( b - c ) = 10 / 60 = 1 / 6 or b - c = 6 - - - ( ii ) from ( i ) & ( ii ) , b = 8 , c = 2 answer : a
Answer: a
Python program:
a = 6 / const_60
b = 1 / a
c = 10 / const_60
d = 1 / c
e = b - d
f = e / 2
Problem: a certain car dealership sells economy cars , luxury cars , and sport utility vehicles . the ratio of economy to luxury cars is 5 : 2 . the ratio of economy cars to sport utility vehicles is 4 : 3 . what is the ratio of luxury cars to sport utility vehicles ?
Options: a ) 9 : 8 , b ) 8 : 15 , c ) 3 : 2 , d ) 2 : 3 , e ) 1 : 2
Rationale: "the ratio of economy to luxury cars is 5 : 2 - - > e : l = 5 : 2 = 20 : 8 . the ratio of economy cars to sport utility vehicles is 4 : 3 - - > e : s = 4 : 3 = 20 : 15 . thus , l : s = 8 : 15 . answer : b ."
Answer: b
Python program:
a = 4 * 3
b = 3 * 3
c = a / b
d = 3 * 4
e = 2 * 4
f = d / e
g = c / f
Problem: the sector of a circle has radius of 21 cm and central angle 130 o . find its perimeter ?
Options: a ) 89.7 , b ) 91.4 , c ) 91.7 , d ) 91.3 , e ) 91.1
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 130 / 360 * 2 * 22 / 7 * 21 ) + 2 ( 21 ) = 47.7 + 42 = 89.7 cm answer : a"
Answer: a
Python program:
a = 21 - 3
b = a * 2
c = 4 + 3 
d = b / c
e = 2 * d
f = e * 21
Problem: the population of a city increases by 8 % per year but due to migration it decrease by 1 % per years . what will be the percentage increase in population in 3 years ?
Options: a ) 9 % , b ) 9.27 % , c ) 22.50 % , d ) 12 % , e ) none of these
Rationale: "actual increase in population = 7 % let , earlier population = 100 then the population after 3 years = 100 ( 1 + 7 / 100 ) ^ 3 = 122.5043 ∴ required percentage = 22.50 % answer : c"
Answer: c
Python program:
a = 8 - 1
b = 100 + a 
c = 8 - 1
d = b * c
e = d / 100
f = 8 - 1
g = e + f 
h = 100 + g 
i = 8 - 1
j = h * i
k = j / 100
l = 8 - 1
m = 100 + l 
n = 8 - 1
o = m * n
p = o / 100
q = 8 - 1
r = p + q 
s = k + r
Problem: pipe a can fill a tank in 3 hours . due to a leak at the bottom , it takes 9 hours for the pipe a to fill the tank . in what time can the leak alone empty the full tank ?
Options: a ) 4.5 , b ) 17 , c ) 18 , d ) 19 , e ) 12
Rationale: "let the leak can empty the full tank in x hours 1 / 3 - 1 / x = 1 / 9 = > 1 / x = 1 / 3 - 1 / 9 = ( 3 - 1 ) / 9 = 2 / 9 = > x = 9 / 2 = 4.5 . answer : a"
Answer: a
Python program:
a = 9 * 3
b = 9 - 3
c = a / b
Problem: the radius of a semi circle is 4.8 cm then its perimeter is ?
Options: a ) 32.51 , b ) 32.4 , c ) 32.1 , d ) 32.92 , e ) 24.69
Rationale: "36 / 7 r = 4.8 = 24.69 answer : e"
Answer: e
Python program:
a = circumface / (
b = a + 2
Problem: the number of stamps that p and q had were in the ratio of 9 : 2 respectively . after p gave q 33 stamps , the ratio of the number of p ' s stamps to the number of q ' s stamps was 6 : 5 . as a result of the gift , p had how many more stamps than q ?
Options: a ) 11 , b ) 33 , c ) 45 , d ) 67 , e ) 80
Rationale: "p started with 9 k stamps and q started with 2 k stamps . ( 9 k - 33 ) / ( 2 k + 33 ) = 6 / 5 45 k - 12 k = 178 + 165 33 k = 343 k = 11 p has 9 ( 11 ) - 33 = 66 stamps and q has 2 ( 11 ) + 33 = 55 stamps . the answer is a ."
Answer: a
Python program:
a = 33 * 6
b = 33 * 5
c = a + b 
d = 6 + 5 
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 40 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 ) 1 , d ) 6 , e ) 5
Rationale: explanation : he covered 5 km in 1 hour , so he might cover 40 km in 8 hours . but he took 10 hours . he would have saved 10 â € “ 8 = 2 hours . answer : a
Answer: a
Python program:
a = 40 / 5
b = 10 - a
Problem: how many 3 - digit numerals end with a digit that represents a prime number ?
Options: a ) 16 , b ) 80 , c ) 160 , d ) 180 , e ) 400
Rationale: "prime digits 2 , 3,5 and 7 . three digit numbers _ _ _ 1 st place can be filled in 4 ways 2 nd place can be filled in 10 ways 3 rd place can be filled in 10 ways total = 4 * 10 * 10 = 400 ans : e"
Answer: e
Python program:
a = 100 * 3
b = a + 100
Problem: machine a and machine b process the same work at different rates . machine c processes work as fast as machines a and b combined . machine d processes work 3 times as fast as machine c ; machine d ’ s work rate is also exactly 4 times machine b ’ s rate . assume all 4 machines work at fixed unchanging rates . if machine a works alone on a job , it takes 6 hours and 20 minutes . if all 4 machines work together on the same job simultaneously , how many minutes will it take all of them to complete it ?
Options: a ) 15 , b ) 17 , c ) 19 , d ) 21 , e ) 24
Rationale: c = a + b d = 3 c = 3 ( a + b ) = 4 b then b = 3 a and c = 4 a the combined rate of the four machines is a + 3 a + 4 a + 12 a = 20 a machine a can complete the work in 380 minutes , so its rate is 1 / 380 of the work per minute . the combined rate is 20 / 380 = 1 / 19 so the work will be completed in 19 minutes . the answer is c .
Answer: c
Python program:
a = 6 * const_60
b = a + 20 
c = 1 + 3 
d = 3 + 1 
e = c + d 
f = 3 + 1 
g = f * 3
h = e + g 
i = b / h
Problem: in a fuel station the service costs $ 1.50 per car , every liter of fuel costs 0.65 $ . assuming that a company owns 12 cars and that every fuel tank contains 55 liters and they are all empty , how much money total will it cost to fuel all cars ?
Options: a ) 320 $ , b ) 380 $ , c ) 410 $ , d ) 430 $ , e ) 447 $
Rationale: 12 * 1.50 + 0.65 * 12 * 55 = 447 hence - e
Answer: e
Python program:
a = 0 * 65
b = a * 12
Problem: cole drove from home to work at an average speed of 60 kmh . he then returned home at an average speed of 90 kmh . if the round trip took a total of 2 hours , how many minutes did it take cole to drive to work ?
Options: a ) 66 , b ) 70 , c ) 72 , d ) 75 , e ) 78
Rationale: "let the distance one way be x time from home to work = x / 60 time from work to home = x / 90 total time = 2 hrs ( x / 60 ) + ( x / 90 ) = 2 solving for x , we get x = 72 time from home to work in minutes = ( 72 ) * 60 / 60 = 72 minutes ans = c"
Answer: c
Python program:
a = 90 * 2
b = 60 + 90 
c = a / b
d = c * const_60
Problem: a certain sum of money is divided among a , b and c so that for each rs . a has 80 paisa , b has 65 paisa and c 40 paisa . if c ' s share is rs . 40 , find the sum of money ?
Options: a ) rs . 185 , b ) rs . 410 , c ) rs . 285 , d ) rs . 385 , e ) rs . 475
Rationale: "a : b : c = 80 : 65 : 40 = 16 : 13 : 8 8 - - - - 40 37 - - - - ? = > rs . 185 answer : a"
Answer: a
Python program:
a = 40 / 65
b = 100 + 80 
c = b + 65 
d = a * c
Problem: from a group of 5 boys and 5 girls , 6 children are to be randomly selected . what is the probability that 3 boys and 3 girls will be selected ?
Options: a ) 4 / 15 , b ) 6 / 17 , c ) 8 / 19 , d ) 10 / 21 , e ) 12 / 23
Rationale: "the total number of ways to choose 6 children from 10 is 10 c 6 = 210 the number of ways to choose 3 boys and 3 girls is 5 c 3 * 5 c 3 = 10 * 10 = 100 p ( 3 boys and 3 girls ) = 100 / 210 = 10 / 21 the answer is d ."
Answer: d
Python program:
a = math.comb(5, 2)
b = math.comb(5, 2)
c = a * b
d = 5 + 5 
e = math.comb(d, 6)
f = c / e