euclaise/mathqa_programs huggingface dataset:
Problem: a question paper has 2 parts , a & b , each containing 10 questions . if a student has to choose 5 from part a & 10 from part b , in how many ways can he choose the questions ?
Options: a ) 100 , b ) 120 , c ) 125 , d ) 350 , e ) 252
Rationale: "there 5 questions in part a out of which 10 question can be chosen as = 10 c 5 similarly , 10 questions can be chosen from 10 questions of part b as = 10 c 10 . hence , total number of ways , = 10 c 5 * 10 c 10 = [ 10 ! / ( 5 ! 5 ! ) ] * [ 10 ! / ( 0 ! * 10 ) ] = { 10 * 9 * 8 * 7 * 6 / ( 5 * 4 * 3 * 2 * 1 ) } * 10 ! / 1 * 10 ! = 252 e"
Answer: e
Python program:
a = math.comb(10, 5)
b = math.comb(10, 10)
c = a * b
d = c / 10
Problem: on a certain date , pat invested $ 10,000 at x percent annual interest , compounded annually . if the total value of the investment plus interest at the end of 12 years will be $ 40,000 , in how many years , the total value of the investment plus interest will increase to $ 240,000 ?
Options: a ) 27 , b ) 16 , c ) 18 , d ) 20 , e ) 24
Rationale: "if i were to choose during the test , would go for 18 or 20 . probably 18 cuz it wont take too long to get the value doubled . . . . i found a method : rule of 72 . given an x % return , it takes 10,000 to quadralope 12 years . so according to the rule : 72 / x is the no of years 10 , 000.00 took to double 20 , 000.00 . again , 20 , 000.00 took to double 40 , 000.00 same ( 72 / x ) no of years . 72 / x + 72 / x = 12 x = 12 % ( though rate here is not very much required ) . again , 40 , 000.00 takes the same ( 72 / x ) no of years to double 240 , 000.00 . 72 / x = 6 years . so altogather : 10,000 - 20,000 = 6 years 20,000 - 40,000 = 6 years 40,000 - 80,000 = 6 years 80,000 - 160,000 = 6 years 160,000 - 240,000 = 3 years total 27 years . answer a"
Answer: a
Python program:
a = 3 * 10
b = 4 + 1 
c = a / b
d = math.log(c)
e = 2 * 10
f = 4 + 1 
g = e / f
h = 1 / 12
i = g ** h
j = math.log(i)
k = d / j
Problem: 14.02 ã — 0.001 = ?
Options: a ) 0.1402 , b ) 0.001402 , c ) 1.4021 , d ) 0.01402 , e ) none of these
Rationale: "14.02 ã — 0.001 = 0.01402 the answer is d ."
Answer: d
Python program:
a = 14 / 2
b = a * 100
Problem: mariah has decided to hire three workers . to determine whom she will hire , she has selected a group of 17 candidates . she plans to have one working interview with 3 of the 17 candidates every day to see how well they work together . how many days will it take her to have working interviews with all the different combinations of job candidates ?
Options: a ) 720 , b ) 420 , c ) 300 , d ) 30 , e ) 333
Rationale: "420 . answer b"
Answer: b
Python program:
a = math.factorial(17)
b = 17 - 3
c = math.factorial(b)
d = a / c
e = math.factorial(3)
f = d / e
g = f / 2
h = g - 17
i = h - 17
j = i - 10
Problem: the average ( arithmetic mean ) of 5 numbers is 5 . if 2 is subtracted from each of 4 of the numbers , what is the new average ?
Options: a ) 3.4 , b ) 4.5 , c ) 6.2 , d ) 5.7 , e ) 6.9
Rationale: let the numbers be a , b , c , d , e , f so , total of these 5 numbers must be 25 or , a + b + c + d + e = 25 so , 12 must be subtracted from the total sum i . e a + b + c + d + e - 8 or , 25 - 8 = 17 hence average of the 5 numbers now is 17 / 5 = > 3.4 so , answer will be a
Answer: a
Python program:
a = 5 * 5
b = 2 * 4
c = a - b
d = c / 5
Problem: the weight of a hollow sphere is directly dependent on its surface area . the surface area of a sphere is 4 π · r ^ 2 , where r is the radius of the sphere . if a hollow sphere of radius 0.15 cm made of a certain metal weighs 8 grams , a hollow sphere of radius 0.3 cm made of the same metal would weigh how many q grams ?
Options: a ) q = 16
b ) q = 32
c ) 64
d ) 128
e ) 512
Rationale: weight directly proportional to 4 pi r ^ 2 now , 4 pi is constant , so , weight is directly proportional to r ^ 2 . when radius = 0.15 , weight = 8 , so ( 0.15 ) ^ 2 proportional to 8 ; ( 0.15 ) ^ 2 * 4 proportional to 8 * 4 , solving further ( 0.15 ) ^ 2 * 2 ^ 2 = ( 0.15 * 2 ) ^ 2 = 0.3 ^ 2 ; so answer = 32 ( b )
Answer: b
Python program:
a = 8 * 4
Problem: a man can row upstream at 34 kmph and downstream at 48 kmph , and then find the speed of the man in still water ?
Options: a ) 29 , b ) 92 , c ) 41 , d ) 32 , e ) 23
Rationale: "us = 34 ds = 48 m = ( 48 + 34 ) / 2 = 41 answer : c"
Answer: c
Python program:
a = 34 + 48 
b = a / 2
Problem: a can contains a mixture of liquids a and b is the ratio 7 : 5 . when 6 litres of mixture are drawn off and the can is filled with b , the ratio of a and b becomes 7 : 9 . how many liter of liquid a was contained by the can initially ?
Options: a ) 12 , b ) 18 , c ) 14 , d ) 20 , e ) 22
Rationale: "ci * vi = cf * vf ( 7 / 12 ) * ( v 1 - 6 ) = ( 7 / 16 ) * v 1 ( v 1 - 6 ) / v 1 = 3 / 4 6 accounts for the difference of 1 on ratio scale so initial volume = v 1 = 4 * 6 = 24 litres . 7 / 12 of the initial mixture was liquid a so liquid a was ( 7 / 12 ) * 24 = 14 litres . answer : c"
Answer: c
Python program:
a = 7 + 6 
b = 7 + 5 
c = 5 / b
d = c * 6
e = 6 - d
f = a * e
g = 6 * 7
h = 7 * 5
i = g - h
j = f / i
k = 7 * j
Problem: one ton has 2300 pounds , and one pound has 16 ounces . how many packets containing wheat weighing 16 pounds and 4 ounces each would totally fill a gunny bag of capacity 13 tons ?
Options: a ) 1840 , b ) 1700 , c ) 2350 , d ) 2500 , e ) 8000
Rationale: "16 pounds and 4 ounces = 16 * 16 + 4 = 260 ounces . 13 tons = 13 * 2300 pound = 13 * 2300 * 16 ounces . hence the answer is ( 13 * 2300 * 16 ) / 260 = 1840 . answer : a ."
Answer: a
Python program:
a = 13 * 2300
b = a * 16
c = 16 * 16
d = c + 4 
e = b / d
Problem: a man can row 2 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and black . what is the total distance traveled by the man ?
Options: a ) 1.8 , b ) 1.9 , c ) 1.2 , d ) 1.7 , e ) 1.3
Rationale: "m = 2 s = 1.2 ds = 2.4 us = 0.8 x / 1.2 + x / 0.8 = 1 x = 0.6 d = 0.6 * 2 = 1.2 answer : c"
Answer: c
Python program:
a = 2 + 1 
b = 2 - 1
c = a * b
d = 2 + 1 
e = 2 - 1
f = d + e 
g = c / f
h = g * 2
Problem: total dinning bill for 10 people was $ 211.00 . if they add 15 % tip and divided the bill evenly , approximate . what was each persons find share
Options: a ) $ 30.14 , b ) 45.14 , c ) 34.66 , d ) 32.29 , e ) 24.26
Rationale: 211 * 15 = 3165 / 100 = 31.65 211 + 31.65 = 242.65 242.65 / 10 = 24.26 answer : e
Answer: e
Python program:
a = 15 * 211
b = a / 100
c = 211 + b 
d = c / 10
Problem: a shopkeeper buys two articles for rs . 1000 each and then sells them , making 40 % profit on the first article and 40 % loss on second article . find the net profit or loss percent ?
Options: a ) 200 , b ) 278 , c ) 282 , d ) 400 , e ) 270
Rationale: "profit on first article = 40 % of 1000 = 400 . this is equal to the loss he makes on the second article . that , is he makes neither profit nor loss . answer : d"
Answer: d
Python program:
a = 100 - 40
b = 100 / a
c = b * 1000
d = 100 + 40 
e = 100 / d
f = e * 1000
g = c + f 
h = 1000 + 1000 
i = g - h
j = i * 100
k = 100 - 40
l = 100 / k
m = l * 1000
n = 100 + 40 
o = 100 / n
p = o * 1000
q = m + p 
r = j / q
s = r * 100
Problem: sawyer is mixing up a salad dressing . regardless of the number of servings , the recipe requires that 5 / 8 of the finished dressing mix be peanut oil , 1 / 4 vinegar , and the remainder an even mixture of salt , pepper and sugar . if sawyer accidentally doubles the vinegar and forgets the sugar altogether , what proportion of the botched dressing will be peanut oil ?
Options: a ) 15 / 29 , b ) 5 / 8 , c ) 5 / 16 , d ) 1 / 2 , e ) 13 / 27
Rationale: peanut oil = 5 / 8 = 15 / 24 - - > 15 parts out of 24 ; vinegar = 1 / 4 = 6 / 24 - - > 6 parts out of 24 ; salt + pepper + sugar = 1 - ( 15 / 24 + 6 / 24 ) = 3 / 24 , so each = 1 / 24 - - > 1 part out of 24 each ; if vinegar = 12 ( instead of 6 ) and sugar = 0 ( instead of 1 ) then total = 15 + 12 + 1 + 1 + 0 = 29 parts out of which 15 parts are peanut oil - - > proportion = 15 / 29 . answer : a .
Answer: a
Python program:
a = 5 / 8
b = 1 / 4
c = 1 + b 
d = a / c
Problem: a shopkeeper buys two articles for rs . 1000 each and then sells them , making 30 % profit on the first article and 30 % loss on second article . find the net profit or loss percent ?
Options: a ) 200 , b ) 278 , c ) 282 , d ) 202 , e ) 300
Rationale: "profit on first article = 30 % of 1000 = 300 . this is equal to the loss he makes on the second article . that , is he makes neither profit nor loss . answer : e"
Answer: e
Python program:
a = 100 - 30
b = 100 / a
c = b * 1000
d = 100 + 30 
e = 100 / d
f = e * 1000
g = c + f 
h = 1000 + 1000 
i = g - h
j = i * 100
k = 100 - 30
l = 100 / k
m = l * 1000
n = 100 + 30 
o = 100 / n
p = o * 1000
q = m + p 
r = j / q
s = r * 100
Problem: a number is doubled and 11 is added . if resultant is doubled , it becomes 74 . what is that number
Options: a ) 18 , b ) 10 , c ) 13 , d ) 14 , e ) 16
Rationale: "explanation : = > 2 ( 2 x + 11 ) = 74 = > 4 x + 22 = 74 = > 4 x = 52 = > x = 13 option c"
Answer: c
Python program:
a = 3 * 11
b = 74 - a
c = 3 * 2
d = b / c
Problem: raja and ram can together complete a piece of work in 4 days . if raja alone can complete the same work in 12 days , in how many days can ram alone complete that work ?
Options: a ) 6 days , b ) 5 days , c ) 7 days , d ) 8 days , e ) 10 days
Rationale: ( raja + ram ) ' s 1 days work = 1 / 4 raja 1 day work = 1 / 2 ram 1 day work = ( 1 / 4 - 1 / 12 ) = 1 / 6 = = > 6 days answer a
Answer: a
Python program:
a = 1 / 4
b = 1 / 12
c = a - b
d = 1 / c
Problem: fresh grapes contain 60 % water by weight and raisins obtained by drying fresh grapes contain 25 % water by weight . how many kgs of fresh grapes are needed to get 20 kgs of raisins ?
Options: a ) 75 kgs , b ) 64 kgs , c ) 37.5 kgs , d ) 65 kgs , e ) 70 kgs
Rationale: "the weight of non - water in 20 kg of dried grapes ( which is 100 - 25 = 75 % of whole weight ) will be the same as the weight of non - water in x kg of fresh grapes ( which is 100 - 60 = 40 % of whole weight ) , so 20 * 0.75 = x * 0.4 - - > x = 37.5 . answer : c"
Answer: c
Python program:
a = 100 - 25
b = 20 * a
c = b / 100
d = c + 60
Problem: on the independence day , bananas were be equally distributed among the children in a school so that each child would get two bananas . on the particular day 330 children were absent and as a result each child got two extra bananas . find the actual number of children in the school ?
Options: a ) 237 , b ) 287 , c ) 197 , d ) 660 , e ) 720
Rationale: "explanation : let the number of children in the school be x . since each child gets 2 bananas , total number of bananas = 2 x . 2 x / ( x - 330 ) = 2 + 2 ( extra ) = > 2 x - 660 = x = > x = 660 . answer : d"
Answer: d
Python program:
a = 330 * 2
Problem: what is the remainder when 617 + 1176 is divided by 7 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "617 + 1176 mod 7 = > 617 % 7 + 1176 % 7 = > 1 + 0 = > 1 % 7 = > 1 answer : a"
Answer: a
Python program:
a = 7 / 2
b = 617 * 617
c = a - b
Problem: a and b together can complete a piece of work in 4 days . if a alone can complete the same work in 12 days , in how many days can b alone complete that work ?
Options: a ) 5 , b ) 7 , c ) 6 , d ) 4 , e ) 8
Rationale: "a and b ' s one day work = 1 / 4 a ' s 1 day ' s work = 1 / 12 b ' s 1 day ' s work = ( 1 / 4 ) - ( 1 / 12 ) = 2 / 12 = 1 / 6 hence b alone can complete the work in 6 days . answer is option c"
Answer: c
Python program:
a = 1 / 4
b = 1 / 12
c = a - b
d = 1 / c
Problem: a train 300 m long , running with a speed of 90 km / hr will pass a tree in ?
Options: a ) 17 sec , b ) 16 sec , c ) 18 sec , d ) 14 sec , e ) 12 sec
Rationale: "speed = 90 * 5 / 18 = 25 m / sec time taken = 300 * 1 / 25 = 12 sec answer : e"
Answer: e
Python program:
a = 90 * 1000
b = 300 / a
c = b * 3600
Problem: tourist purchased a total of 30 travelers checks in $ 50 and $ 100 denominations . the total worth of the travelers checks is $ 1800 . how many checks of $ 50 denominations can he spend so that average amount ( arithmetic mean ) of the remaining travelers checks is $ 75 ?
Options: a ) 4 , b ) 18 , c ) 15 , d ) 20 , e ) 24
Rationale: you could set - up a quick table and brute force the answer . a 4 * 50 200 1800 - 200 1600 26 61.54 b 18 * 50 600 1800 - 900 0900 12 75.00 c 15 * 50 750 1800 - 750 1050 15 70.00 d 20 * 50 1000 1800 - 1000 800 10 80.00 e 24 * 50 1200 1800 - 1200 600 6 100.00 answer is b
Answer: b
Python program:
a = 75 * 30
b = a - 1800
c = 75 - 50
d = b / c
Problem: if x is an integer and 2.134 × 10 ^ x is less than 21000 , what is the greatest possible value for x ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "if x = 4 2.134 × 10 ^ 4 = 21340 > 21000 so , x = 3 answer : e"
Answer: e
Python program:
a = 21000 / 2
b = math.log(a)
c = math.log(10)
d = b / c
e = math.floor(d)
Problem: the sum of two consecutive number is 97 . which is the larger number ?
Options: a ) 42 , b ) 49 , c ) 44 , d ) 45 , e ) 46
Rationale: "let consecutive number be x , x + 1 therefore sum of the consecutive number is x + x + 1 = 97 2 x + 1 = 97 2 x = 96 x = 48 therefore larger number is x + 1 = 49 answer : b"
Answer: b
Python program:
a = 97 - 10
b = a - 2
c = b / 4
d = c + 2 
e = d + 2 
f = e ** 2
g = 97 - 10
h = g - 2
i = h / 4
j = i + 2 
k = j + 2 
l = k + 2 
m = l ** 2
n = f + m 
o = 97 - 10
p = o - 2
q = p / 4
r = q ** 2
s = 97 - 10
t = s - 2
u = t / 4
v = u + 2 
w = v ** 2
x = r + w 
y = n + x
Problem: 3,10 , 29,66 , __
Options: a ) 125 , b ) 165 , c ) 145 , d ) 127 , e ) 112
Rationale: "3 = 1 * 1 * 1 + 2 10 = 2 * 2 * 2 + 2 29 = 3 * 3 * 3 + 2 66 = 4 * 4 * 4 + 2 similarly 5 * 5 * 5 + 2 = 127 answer : d"
Answer: d
Python program:
a = 3 / 10
b = a * 100
Problem: the sale price sarees listed for rs . 450 after successive discount is 20 % and 15 % is ?
Options: a ) 321 , b ) 276 , c ) 306 , d ) 265 , e ) 162
Rationale: "explanation : 450 * ( 80 / 100 ) * ( 85 / 100 ) = 306 answer : c"
Answer: c
Python program:
a = 450 * 20
b = a / 100
c = 450 - b
d = 450 * 20
e = d / 100
f = 450 - e
g = f * 15
h = g / 100
i = c - h
Problem: if there are 200 questions in a 3 hr examination . among these questions are 15 type a problems , which requires twice as much as time be spent than the rest of the type b problems . how many minutes should be spent on type a problems ?
Options: a ) 72 min , b ) 25.11628 min , c ) 70 min , d ) 74.11682 min , e ) 76 min
Rationale: "x = time for type b prolems 2 x = time for type a problem total time = 3 hrs = 180 min 185 x + 15 * 2 x = 180 x = 180 / 215 x = 0.837209 time taken for type a problem = 15 * 2 * 0.837209 = 25.11628 min answer : b"
Answer: b
Python program:
a = 3 * const_60
b = 200 - 15
c = 2 * 15
d = b + c 
e = a / d
f = 2 * e
g = f * 15
Problem: express 45 mps in kmph ?
Options: a ) 170 , b ) 160 , c ) 162 , d ) 130 , e ) 122
Rationale: "45 * 18 / 5 = 162 kmph answer : c"
Answer: c
Python program:
a = 45 / 1000
b = a * 3600
Problem: a and b began business with rs . 3000 and rs . 4000 after 8 months , a withdraws rs . 1000 and b advances rs . 1000 more . at the end of the year , their profits amounted to rs . 630 find the share of a
Options: a ) rs . 300 , b ) rs . 56 , c ) rs . 100 , d ) rs . 240 , e ) rs . 90
Rationale: "explanation : ( 3 * 8 + 2 * 4 ) : ( 4 * 8 + 5 * 4 ) 8 : 13 8 / 21 * 630 = rs . 240 answer : d"
Answer: d
Python program:
a = 3000 * 8
b = 3000 - 1000
c = 12 - 8
d = b * c
e = a + d 
f = 4000 * 8
g = 4000 + 1000 
h = 12 - 8
i = g * h
j = f + i 
k = e + j 
l = 630 / k
m = 3000 * 8
n = 3000 - 1000
o = 12 - 8
p = n * o
q = m + p 
r = l * q
Problem: express a speed of 126 kmph in meters per second ?
Options: a ) 10 mps , b ) 35 mps , c ) 26 mps , d ) 97 mps , e ) 16 mps
Rationale: "126 * 5 / 18 = 35 mps answer : b"
Answer: b
Python program:
a = const_0_2778 * 126
Problem: the product of two numbers is 2028 and their h . c . f is 13 . the number of such pairs is ?
Options: a ) 7 , b ) 2 , c ) 3 , d ) 4 , e ) 9
Rationale: "let the numbers be 13 a and 13 b . then , 13 a * 13 b = 2028 = > ab = 12 . now , co - primes with product 12 are ( 1 , 12 ) and ( 3 , 4 ) . so , the required numbers are ( 13 * 1 , 13 * 12 ) and ( 13 * 3 , 13 * 4 ) . clearly , there are 2 such pairs . answer : b"
Answer: b
Python program:
a = 2 * 2028
b = 13 - a
c = math.sqrt(b)
d = c ** 2
e = 4 * 2028
f = d + e 
g = math.sqrt(f)
Problem: a cricket bat is sold for $ 850 , making a profit of $ 245 . the profit percentage would be
Options: a ) 24 % , b ) 25 % , c ) 30 % , d ) 36 % , e ) 40 %
Rationale: "245 / ( 850 - 245 ) = 245 / 605 = 49 / 121 = 40 % . answer : e ."
Answer: e
Python program:
a = 850 - 245
b = 245 / a
c = b * 100
Problem: the speed of a car is 90 km in the first hour and 60 km in the second hour . what is the average speed of the car ?
Options: a ) 12 , b ) 75 , c ) 88 , d ) 54 , e ) 15
Rationale: "s = ( 90 + 60 ) / 2 = 75 kmph answer : b"
Answer: b
Python program:
a = 90 + 60 
b = a / 2
Problem: if shares of two persons in profits are rs . 300 and rs . 600 then ratio of their capitals is
Options: a ) 3 : 4 , b ) 2 : 3 , c ) 4 : 3 , d ) 1 : 3 , e ) 1 : 2
Rationale: "total profit = 1000 ratio = 300 / 600 = 1 : 2 answer : e"
Answer: e
Python program:
a = 300 / 600
Problem: a meeting has to be conducted with 5 managers . find the number of ways in which the managers be selected from among 8 managers , if 2 managers will not attend the meeting together ?
Options: a ) 40 , b ) 36 , c ) 42 , d ) 45 , e ) 47
Rationale: "we can either choose all 5 people from 6 manager who have no problems or choose 4 from the 6 and 1 from the 2 managers who have a problem sitting together so 6 c 5 + ( 6 c 4 * 2 c 1 ) this is 6 + 30 = 36 answer : b"
Answer: b
Python program:
a = math.comb(8, 5)
b = 8 - 2
c = math.comb(b, 2)
d = a - c
Problem: a feed store sells two varieties of birdseed : brand a , which is 40 % millet and 60 % sunflower , and brand b , which is 65 % millet and 35 % sunflower . if a customer purchases a mix of the two types of birdseed that is 50 % sunflower , what percent of the mix is brand a ?
Options: a ) 40 % , b ) 45 % , c ) 50 % , d ) 55 % , e ) 60 %
Rationale: "yes there is a simple method : consider the following method brand a : 40 % millet and 60 % sunflower brand b : 65 % millet and 35 % sunflower mix : 50 % sunflower here the weighted average is 50 % , now brand a has 60 % sunflower , which is 10 % more than the weighted average of mix = + 0.10 a - - - - - - - - - - - - - - - i similarly , brand b has 35 % sunflower , which is 15 % less than the weighted average of mix = - 0.15 b - - - - - - - - - - - - ii now , both brand a and brand b are combined to give a 50 % mix containing millet , so equate i and ii implies , 0.10 a = 0.15 b therefore a / b = 0.15 / 0.10 = 3 / 2 a : b : ( a + b ) = 3 : 2 : ( 3 + 2 ) = 3 : 2 : 5 we have to find , percent of the mix is brand a i . e . a : ( a + b ) = 3 : 5 = ( 3 / 5 ) * 100 = 60 % here is a pictorial representation : brand a = 60 % - - - - - - - - - - - - - - - - - - - - - - - - 10 % or 0.10 above average , a times - - - - - - - - - - - - - - - - - total below = + 0.10 a - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - average = 50 % or 0.50 brand b = 35 % - - - - - - - - - - - - - - - - - - - - - - - - - - 15 % or 0.15 below average , b times - - - - - - - - - - - - - - - - - total above = - 0.15 b since the amount below the average has to equal the average above the average ; therefore , 0.10 a = 0.15 b a / b = 3 / 2 a : b : total = 3 : 2 : 5 therefore a / total = 3 : 5 = 60 % answer : e"
Answer: e
Python program:
a = 3 + 2 
b = 3 / a
c = b * 100
Problem: sakshi can do a piece of work in 20 days . tanya is 25 % more efficient than sakshi . the number of days taken by tanya to do the same piece of work is :
Options: a ) 15 , b ) 16 , c ) 22 , d ) 18 , e ) 25
Rationale: "work done by sakshi in 1 day = 1 / 20 since tanya is 25 % efficient than sakshi , she completes 25 % more work in a day than sakshi . = > tanya ' s 1 day work = 1 / 20 + 1 / 20 * 25 / 100 = 1 / 16 so time taken by tanya to finish the work = 16 days answer : b"
Answer: b
Python program:
a = 25 / 100
b = 1 + a 
c = 20 / b
Problem: in an election a candidate who gets 60 % of the votes is elected by a majority of 1504 votes . what is the total number of votes polled ?
Options: a ) a ) 4500 , b ) b ) 5200 , c ) c ) 6900 , d ) d ) 7520 , e ) e ) 6000
Rationale: let the total number of votes polled be x then , votes polled by other candidate = ( 100 - 60 ) % of x = 40 % of x 60 % of x - 40 % of x = 1504 20 x / 100 = 1504 x = 1504 * 100 / 20 = 7520 answer is d
Answer: d
Python program:
a = 100 - 60
b = 60 - a
c = b / 100
d = 1504 / c
Problem: two boats are heading towards each other at constant speeds of 5 miles / hr and 21 miles / hr respectively . they begin at a distance 20 miles from each other . how far are they ( in miles ) one minute before they collide ?
Options: a ) 1 / 12 , b ) 5 / 12 , c ) 1 / 6 , d ) 13 / 30 , e ) 1 / 5
Rationale: the question asks : how far apart will they be 1 minute = 1 / 60 hours before they collide ? since the combined rate of the boats is 5 + 21 = 26 mph then 1 / 60 hours before they collide they ' ll be rate * time = distance - - > 26 * 1 / 60 = 13 / 30 miles apart . answer : d .
Answer: d
Python program:
a = 21 + 5 
b = a / const_60
Problem: 36 men can complete a piece of work in 18 days . in how many days will 27 men complete the same work ?
Options: a ) 12 , b ) 18 , c ) 22 , d ) 24 , e ) 26
Rationale: "solution let the required number of days be x . then , less men , more days ∴ 27 : 36 : : 18 : x ⇔ 27 × x = 36 × 18 ⇔ x = 36 x 18 / 27 x = 24 . answer d"
Answer: d
Python program:
a = 18 * 36
b = a / 27
Problem: of the 3,600 employees of company x , 1 / 3 are clerical . if the clerical staff were to be reduced by 1 / 2 , what percent of the total number of the remaining employees would then be clerical ?
Options: a ) 25 % , b ) 22.2 % , c ) 20 % , d ) 12.5 % , e ) 11.1 %
Rationale: "let ' s see , the way i did it was 1 / 3 are clerical out of 3600 so 1200 are clerical 1200 reduced by 1 / 2 is 1200 * 1 / 2 so it reduced 600 people , so there is 600 clerical people left but since 600 people left , it also reduced from the total of 3600 so there are 3000 people total since 600 clerical left / 3000 people total you get ( c ) 20 %"
Answer: c
Python program:
a = 1 / 3
b = 1 / 2
c = 1 - b
d = a * c
e = 1 / 3
f = 1 / 2
g = 1 - f
h = e * g
i = 1 / 3
j = 1 - i
k = h + j 
l = d / k
m = l * 100
Problem: toby is 4 years younger than debby . thrice the sum of the ages of toby and debby equals their mother ’ s age . if the age of the mother is 60 , find the ages of toby and debby ?
Options: a ) 8 and 12 , b ) 5 and 9 , c ) 6 and 10 , d ) 5 and 10 , e ) 12 and 16
Rationale: let the age of debby be x and toby be x - 4 3 ( x + x - 4 ) = 60 x = 12 the ages of toby and debby are 8 and 12 . answer : a
Answer: a
Python program:
a = 60 / 3
b = a - 4
c = b / 2
d = c * 100
e = 60 / 3
f = 60 / 3
g = f - 4
h = g / 2
i = e - h
j = d + i
Problem: if a lends rs . 2800 to b at 15 % per annum and b lends the same sum to c at 18.5 % per annum then the gain of b in a period of 3 years is ?
Options: a ) 294 , b ) 289 , c ) 240 , d ) 233 , e ) 200
Rationale: "( 2800 * 3.5 * 3 ) / 100 = > 294 answer : a"
Answer: a
Python program:
a = 2800 * 18
b = a * 3
c = b / 100
d = 2800 * 15
e = d * 3
f = e / 100
g = c - f
Problem: find the average of all prime numbers between 20 and 30
Options: a ) 15 , b ) 20 , c ) 18 , d ) 32 , e ) 26
Rationale: "prime numbers between 20 and 30 are 23,29 required average = ( 23 + 29 ) / 2 = 52 / 2 = 26 answer is e"
Answer: e
Python program:
a = 20 + 1 
b = 20 + 1 
c = b + 2 
d = a + c 
e = 30 - 20
f = 30 - 2
g = e + f 
h = d + g 
i = h / 20