euclaise/mathqa_programs huggingface dataset:
Problem: the sum of three consecutive even numbers is 87 . find the middle number of the three ?
Options: a ) 31 , b ) 21 , c ) 29 , d ) 22 , e ) 12
Rationale: "middle number = 87 / 3 = 29 ans c"
Answer: c
Python program:
a = 87 - 10
b = a - 2
c = b / 4
d = c + 2 
e = d + 2 
f = e ** 2
g = 87 - 10
h = g - 2
i = h / 4
j = i + 2 
k = j + 2 
l = k + 2 
m = l ** 2
n = f + m 
o = 87 - 10
p = o - 2
q = p / 4
r = q ** 2
s = 87 - 10
t = s - 2
u = t / 4
v = u + 2 
w = v ** 2
x = r + w 
y = n + x
Problem: the length of a rectangular plot is 10 mtr more than its width . the cost of fencing the plot along its perimeter at the rate of rs . 6.5 mtr is rs . 1170 . the perimeter of the plot is ?
Options: a ) 126 , b ) 156 , c ) 180 , d ) 321 , e ) 260
Rationale: "sol . let width = x , length = ( 10 + x ) perimeter = 2 ( x + ( 10 + x ) ) = 2 ( 2 x = 10 ) & 2 ( 2 x + 10 ) * 6.5 = 1170 x = 40 required perimeter = 2 ( 40 + 50 ) = 180 c"
Answer: c
Python program:
a = 1170 / 6
b = a / 2
c = b - 10
d = c / 2
e = 1170 / 6
f = e / 2
g = f - 10
h = g / 2
i = h + 10 
j = d + i 
k = j * 2
Problem: there are two circles of different radii . the are of a square is 784 sq cm and its side is twice the radius of the larger circle . the radius of the larger circle is 7 - third that of the smaller circle . find the circumference of the smaller circle .
Options: a ) 165 ∏ cm , b ) 65 ∏ cm , c ) 12 ∏ cm , d ) 14 ∏ cm , e ) 16 ∏ cm
Rationale: let the radii of the larger and the smaller circles be l cm and s cm respectively . let the side of the square be a cm . a 2 = 784 = ( 4 ) ( 196 ) = ( 22 ) . ( 142 ) a = ( 2 ) ( 14 ) = 28 a = 2 l , l = a / 2 = 14 l = ( 7 / 3 ) s therefore s = ( 3 / 7 ) ( l ) = 6 circumference of the smaller circle = 2 ∏ s = 12 ∏ cm . answer : c
Answer: c
Python program:
a = 3 * 100
b = 10 + 4 
c = a + b 
d = c / 100
e = math.sqrt(784)
f = e / 2
g = 7 / 3
h = f / g
i = d * h
j = 2 * i
Problem: the average of first four prime numbers greater than 30 is ?
Options: a ) 38 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: "31 + 37 + 41 + 43 = 152 / 4 = 38 answer : a"
Answer: a
Python program:
a = 30 + 1
Problem: a and b put in rs . 200 and rs . 400 respectively into a business . a reinvests into the business his share of the first year ' s profit of rs . 210 where as b does not . in what ratio should they divide the second year ' s profit ?
Options: a ) 39 : 40 , b ) 39 : 49 , c ) 39 : 42 , d ) 39 : 47 , e ) 17 : 20
Rationale: "explanation : 1 : 2 a = 2 / 3 * 210 = 140 340 : 400 17 : 20 answer : e"
Answer: e
Python program:
a = 400 - 100
b = a + 200 
c = 200 / b
d = 3 + 2 
e = 2 * d
f = 210 + e 
g = c * f
h = 200 + g 
i = 400 - 100
j = h / i
Problem: a train running at the speed of 60 km / hr crosses a pole in 9 seconds . find the length of the train .
Options: a ) 150 , b ) 388 , c ) 266 , d ) 299 , e ) 261
Rationale: "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 9 = 150 meter . answer : a"
Answer: a
Python program:
a = 60 * 1000
b = a / 3600
c = b * 9
Problem: a certain car can travel 40 minutes on a gallon of gasoline at 50 miles per hour . if the car had started with a full tank and had 8 gallons of gasoline left in its tank at the end , then what percent of the tank was used to travel 80 miles at 60 mph ?
Options: a ) 15 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 40 %
Rationale: "let , tank capacity = t gallon used fuel = ( t - 8 ) gallons distance travelled ( @ 50 miles / hr ) = 80 miles distance travelled in 1 gallon = distance travelled in 40 mins ( @ 50 miles / hr ) = ( 50 / 50 ) * 40 = 40 miles fuel used to travel 80 miles = ( 80 / 40 ) = 2 gallon i . e . used fuel = ( t - 8 ) = 2 gallon i . e . t = 10 gallons i . e . used fuel = ( 2 / 10 ) * 100 = 20 % b"
Answer: b
Python program:
a = 40 * 50
b = 80 * 60
c = a / b
d = 40 * 50
e = 80 * 60
f = d / e
g = f + 8 
h = c / g
Problem: the average weight of 8 students decreases by 5 kg when one of them weighing 86 kg is replaced by a new student . the weight of the student is
Options: a ) 46 kg , b ) 48 kg , c ) 70 kg , d ) 72 kg , e ) none of these
Rationale: "explanation : let the weight of student be x kg . given , difference in average weight = 5 kg = > ( 86 - x ) / 8 = 5 = > x = 46 answer : a"
Answer: a
Python program:
a = 8 * 5
b = 86 - a
Problem: a football team lost 5 yards and then gained 8 . what is the team ' s progress ?
Options: a ) 2 , b ) 3 , c ) 5 , d ) 6 , e ) 8
Rationale: "for lost , use negative . for gain , use positive . progress = - 5 + 8 = 3 yards b"
Answer: b
Python program:
a = 8 - 5
Problem: a and b go around a circular track of length 600 m on a cycle at speeds of 36 kmph and 60 kmph . after how much time will they meet for the first time at the starting point ?
Options: a ) 120 sec , b ) 176 sec , c ) 178 sec , d ) 187 sec , e ) 180 sec
Rationale: "time taken to meet for the first time at the starting point = lcm { length of the track / speed of a , length of the track / speed of b } = lcm { 600 / ( 36 * 5 / 18 ) , 600 / ( 60 * 5 / 18 ) } = 180 sec . answer : e"
Answer: e
Python program:
a = 60 * const_0_2778
b = 36 * const_0_2778
c = a - b
d = 600 / c
Problem: divide rs . 1500 among a , b and c so that a receives 1 / 3 as much as b and c together and b receives 2 / 3 as a and c together . a ' s share is ?
Options: a ) 337 , b ) 299 , c ) 375 , d ) 662 , e ) 201
Rationale: "a + b + c = 1500 a = 1 / 3 ( b + c ) ; b = 2 / 3 ( a + c ) a / ( b + c ) = 1 / 3 a = 1 / 4 * 1500 = > 375 answer : c"
Answer: c
Python program:
a = 1500 / 3
Problem: 80 % of the population of a village is 23040 . the total population of the village is ?
Options: a ) 28800 , b ) 24000 , c ) 24936 , d ) 25640 , e ) none
Rationale: "answer ∵ 80 % of p = 23040 ∴ p = ( 23040 x 100 ) / 80 = 28800 correct option : a"
Answer: a
Python program:
a = 100 / 80
b = a * 23040
Problem: a , b and c completed a piece of work , a worked for 6 days , b for 9 days and c for 4 days . their daily wages were in the ratio of 3 : 4 : 5 . find the daily wages of c , if their total earning was rs . 1702 ?
Options: a ) s . 109 , b ) s . 115 , c ) s . 100 , d ) s . 103 , e ) s . 102
Rationale: "3 x 4 x 5 x 6 9 4 18 x + 36 x + 20 x = 1702 74 x = 1702 = > x = 23 5 x = 115 rs . answer : b"
Answer: b
Python program:
a = 6 * 3
b = 9 * 4
c = a + b 
d = 4 * 5
e = c + d 
f = 1702 / e
g = 5 * f
Problem: a hiker walking at a constant rate of 4 kilometers per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 18 kilometers per hour . the cyclist stops and waits for the hiker 5 minutes after passing her while the hiker continues to walk at her constant rate . how many minutes must the cyclist wait until the hiker catches up ?
Options: a ) 7.5 , b ) 12.5 , c ) 17.5 , d ) 22.5 , e ) 27.5
Rationale: in 5 minutes , the cyclist travels a distance of ( 5 / 60 ) * 18 = 1.5 km . the time it takes the hiker to complete this distance is 1.5 / 4 hours = 22.5 minutes the cyclist needs to wait 22.5 - 5 = 17.5 minutes the answer is c .
Answer: c
Python program:
a = 5 / const_60
b = 18 * a
c = 5 / const_60
d = 4 * c
e = b - d
f = e / 4
g = f * const_60
Problem: at 1 : 00 pm , a truck left city p and headed toward city q at a constant speed of 45 km / h . one hour later , a car left city q and headed toward city p along the same road at a constant speed of 40 km / h . if the distance between city p and city q is 300 km , at what time will the truck and the car meet each other ?
Options: a ) 4 : 30 , b ) 5 : 00 , c ) 5 : 30 , d ) 6 : 00 , e ) 6 : 30
Rationale: "at 2 : 00 pm , the truck and the car are 255 km apart . the truck and the car complete a distance of 85 km each hour . the time it takes to meet is 255 / 85 = 3 hours . they will meet at 5 : 00 pm . the answer is b ."
Answer: b
Python program:
a = 300 / 45
b = a - 1
c = 40 / 45
d = 1 + c 
e = b / d
Problem: two cars are driving toward each other . the first car is traveling at a speed of 75 km / h , which is 25 % slower than the second car ' s speed . if the distance between the cars is 1050 km , how many hours will it take until the two cars meet ?
Options: a ) 4 , b ) 4.5 , c ) 5 , d ) 5.5 , e ) 6
Rationale: "the speed of the first car is 75 km / h . the speed of the second car is 75 / 0.75 = 100 km / h . the two cars complete a total of 175 km each hour . the time it takes the cars to meet is 1050 / 175 = 6 hours . the answer is e ."
Answer: e
Python program:
a = 75 * 4
b = 4 * 75
c = 1 + 4 
d = b / c
e = d * 4
f = a + e 
g = 4 * 75
h = 1 + 4 
i = g / h
j = 75 + i 
k = f / j
Problem: an industrial loom weaves 0.128 metres of cloth every second . approximately , how many seconds will it take for the loom to weave 26 metre of cloth ?
Options: a ) 175 seconds , b ) 195 seconds , c ) 155 seconds , d ) 115 seconds , e ) 203 seconds
Rationale: "explanation : let the time required by x seconds . then , more cloth means more time ( direct proportion ) so , 0.128 : 1 : : 26 : x = > x = { \ color { blue } \ frac { 26 \ times 1 } { 0.128 } } = > x = 203.13 so time will be approx 203 seconds answer : e"
Answer: e
Python program:
a = 26 / 0
Problem: in a class of 38 students 26 play football and play 20 long tennis , if 17 play above , many play neither ?
Options: a ) 6 , b ) 8 , c ) 9 , d ) 12 , e ) 14
Rationale: "26 + 20 - 17 = 29 38 - 29 = 9 play neither answer is c"
Answer: c
Python program:
a = 26 + 20 
b = a - 17
c = 38 - b
Problem: if the diameter of circle r is 80 % of the diameter of circle s , the area of circle r is what percent of the area of circle s ?
Options: a ) 74 % , b ) 64 % , c ) 84 % , d ) 94 % , e ) 34 %
Rationale: "let diameter of circle r , dr = 80 and diameter of circle s , ds = 100 radius of circle r , rr = 40 radius of circle s , rs = 50 area of circle r / area of circle s = ( pi * rr ^ 2 ) / ( pi * rs ^ 2 ) = ( 40 / 50 ) ^ 2 = ( 8 / 10 ) ^ 2 = 64 % answer : b"
Answer: b
Python program:
a = circle_area * (
b = a / 100
Problem: the ratio of the volumes of two cubes is 9261 : 12167 . what is the ratio of their total surface areas ?
Options: a ) 1 : 12 , b ) 85 : 31 , c ) 51 : 45 , d ) 58 : 67 , e ) 53 : 58
Rationale: "ratio of the sides = ³ √ 9261 : ³ √ 12167 = 21 : 23 ratio of surface areas = 212 : 232 = 53 : 58 answer : e"
Answer: e
Python program:
a = 9261 / 12167
b = 1 / 3
c = a ** b
Problem: a and b together can do a work in 3 days . if a alone can do it in 12 days . in how many days can b alone do it ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 25
Rationale: "a 4 1 / 3 â € “ 1 / 12 = 1 / 4 = > 4"
Answer: a
Python program:
a = 1 / 3
b = 1 / 12
c = a - b
d = 1/(c)
e = 2 + 3 
f = 2 / e
g = d + f
Problem: solution x is 10 percent alcohol by volume , and solution y is 30 percent alcohol by volume . how many milliliters of solution y must be added to 300 milliliters of solution x to create a solution that is 18 percent alcohol by volume ?
Options: a ) 100 , b ) 150 , c ) 200 , d ) 250 , e ) 300
Rationale: "18 % is 8 % - points higher than 10 % but 12 % - points lower than 30 % . thus there should be 3 parts of solution x for 2 parts of solution y . we should add 200 ml of solution y . the answer is c ."
Answer: c
Python program:
a = 18 - 10
b = 30 - 18
c = a / b
d = c * 300
Problem: if 125 % of j is equal to 25 % of k , 150 % of k is equal to 50 % of l , and 175 % of l is equal to 75 % of m , then 20 % of m is equal to what percent of 100 % of j ?
Options: a ) 0.35 , b ) 3.5 , c ) 35 , d ) 350 , e ) 700
Rationale: "imo answer should be 350 . . . consider j = 10 , then k = 50 , l = 150 and m = 350 . . . . 20 % of 350 , comes out to be 70 . . . . 100 % of 10 is 10 . . . . ( 70 * 100 ) / 10 = 700 . . . . ans : e"
Answer: e
Python program:
a = 125 * 150
b = a * 175
c = 25 * 50
d = c * 75
e = b / d
f = e * 20
g = f / 100
h = g * 100
Problem: a sum of rs . 2200 has been divided among a , b and c such that a gets 1 / 4 of what b gets and b gets 1 / 5 of what c gets . what is b ' s share ?
Options: a ) 342 , b ) 352 , c ) 322 , d ) 332 , e ) 362
Rationale: "let c ' s share = rs . x then b ' s share = x / 5 a ' s share = x / 5 × 1 / 4 = x / 20 hence , x + x / 5 + x / 20 = 2200 ⇒ x ( 1 + 1 / 5 + 1 / 20 ) = 2200 ⇒ x ( 25 / 20 ) = 2200 ⇒ x ( 5 / 4 ) = 2200 ⇒ x = 2200 × 4 / 5 = 440 × 4 = rs . 1760 b ' s share = x / 5 = 1760 / 5 = rs . 352 answer is b ."
Answer: b
Python program:
a = 2200 / 10
b = a * 2
c = b - 12
d = c - 12
Problem: at a certain company , each employee has a salary grade s that is at least 1 and at most 5 . each employee receives an hourly wage p , in dollars , determined by the formula p = 9.50 + 0.25 ( s – 1 ) . an employee with a salary grade of 4 receives how many more dollars per hour than an employee with a salary grade of 1 ?
Options: a ) $ 0.75 , b ) $ 1.00 , c ) $ 1.25 , d ) $ 1.50 , e ) $ 1.75
Rationale: "salary grade of 4 is p ( 4 ) = 9.50 + 0.25 ( 4 – 1 ) = 9.50 + 0.25 * 3 ; salary grade of 1 is p ( 1 ) = 9.50 + 0.25 ( 1 – 1 ) = 9.50 ; p ( 4 ) - p ( 1 ) = 9.50 + 0.25 * 4 - 9.50 = 0.75 . answer : a ."
Answer: a
Python program:
a = 5 - 1
b = 0 * 25
c = b + 0
Problem: the price of a t . v . set worth rs . 8000 is to be paid in 20 installments of rs . 750 each . if the rate of interest be 6 % per annum , and the first installment be paid at the time of purchase , then the value of the last installment covering the interest as well will be ?
Options: a ) 7250 , b ) 7200 , c ) 7820 , d ) 6000 , e ) 2799
Rationale: "money paid in cash = rs . 750 balance payment = ( 8000 - 1000 ) = rs . 7250 answer : a"
Answer: a
Python program:
a = 8000 - 750
Problem: in an examination , 40 % of total students failed in hindi , 40 % failed in english and 15 % in both . the percentage of these who passed in both the subjects is :
Options: a ) 10 % , b ) 20 % , c ) 30 % , d ) 40 % , e ) 50 %
Rationale: "pass percentage = 100 - ( 40 + 45 - 15 ) = 100 - 70 = 30 answer : c"
Answer: c
Python program:
a = 40 + 40 
b = a - 15
c = 100 - b
Problem: some students are standing in a circle in which 6 th and the 16 th student are standing opposite to each other . find how many students were present there .
Options: a ) 10
b ) 15
c ) 20
d ) 25
e ) 30
Rationale: ( n / 2 ) - x = 6 n - x = 16 solving these two = > n = number of students = 20 answer : c
Answer: c
Python program:
a = 16 - 6
b = a * 2
Problem: if the annual increase in the population of a town is 10 % and the present number of people is 13000 , what will the population be in 2 years ?
Options: a ) 15730 , b ) 15240 , c ) 12456 , d ) 11452 , e ) 10002
Rationale: the required population is = 13000 ( 1 + 10 / 100 ) ^ 2 = 13000 * 11 / 10 * 11 / 10 = 15730 answer is a
Answer: a
Python program:
a = 10 + 100 
b = a / 100
c = b * 13000
d = 10 + 100 
e = d / 100
f = c * e
Problem: find the compound interest on $ 46,000 at 20 % per annum for 9 months , compounded quarterly
Options: a ) 2532.05 , b ) 2552.32 , c ) 2524.34 , d ) 7250.75 , e ) 9012.55
Rationale: "principal = $ 46000 ; time = 9 months = 3 quarters ; rate = 20 % per annum = 5 % per quarter . amount = $ [ 46000 x ( 1 + ( 5 / 100 ) ) ^ 3 ] = $ 53250.75 ci . = $ ( 53250.75 - 46000 ) = $ 7250.75 answer d ."
Answer: d
Python program:
a = 9 / 100
b = 1 + a 
c = b ** 20
d = 46 * 0
e = d - 46
Problem: lagaan is levied on the 60 percent of the cultivated land . the revenue department collected total rs . 3 , 44000 through the lagaan from the village of mutter . mutter , a very rich farmer , paid only rs . 480 as lagaan . the percentage of total land of mutter over the total taxable land of the village is :
Options: a ) 0.23255 , b ) 0.14544 , c ) 0.25632 , d ) 0.35466 , e ) 0.63435
Rationale: total land of sukhiya = \ inline \ frac { 480 x } { 0.6 } = 800 x \ therefore cultivated land of village = 344000 x \ therefore required percentage = \ inline \ frac { 800 x } { 344000 } \ times 100 = 0.23255 a
Answer: a
Python program:
a = 60 / 100
b = 480 / a
c = 44000 + 44000 
d = c + 44000 
e = 44000 + 44000 
f = d + e 
g = 44000 + 44000 
h = f + g 
i = h + 44000 
j = i - 3600
k = j - 3600
l = 60 / 100
m = 480 / l
n = k - m
o = b / n
p = o * 100
Problem: how many positive integer solutions does the equation 5 x + 10 y = 100 have ?
Options: a ) 2 , b ) 33 , c ) 38 , d ) 35 , e ) 14
Rationale: formula : ( constant ) / ( lcm of two nos ) = 100 / ( 5 * 10 ) = 2 answer : a
Answer: a
Python program:
a = 10 / 5
Problem: the length of a rectangle is two - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 3025 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 10 units ?
Options: a ) 140 , b ) 150 , c ) 160 , d ) 170 , e ) 220
Rationale: "given that the area of the square = 3025 sq . units = > side of square = √ 3025 = 55 units the radius of the circle = side of the square = 55 units length of the rectangle = 2 / 5 * 55 = 22 units given that breadth = 10 units area of the rectangle = lb = 22 * 10 = 220 sq . units answer : option e"
Answer: e
Python program:
a = math.sqrt(3025)
b = 10 / 2
c = a / b
d = 2 * c
e = 10 * d
Problem: what is the difference between the ci on rs . 5000 for 1 years at 4 % per annum ci yearly and half yearly ?
Options: a ) rs . 2.04 , b ) rs . 2.12 , c ) rs . 2.23 , d ) rs . 3 , e ) rs . 3.04
Rationale: c . i . when interest compounded yearly = rs . 5000 x 1 + 4 x 1 + x 4 100 100 = rs . 5000 x 26 x 51 25 50 = rs . 5304 . c . i . when interest is compounded half - yearly = rs . 5000 x 1 + 2 3 100 = rs . 5000 x 51 x 51 x 51 50 50 50 = rs . 5306.04 difference = rs . ( 5306.04 - 5304 ) = rs . 2.04 a
Answer: a
Python program:
a = 4 / 2
b = a / 100
c = 1 + b 
d = c ** 2
e = 5000 * d
f = e - 5000
g = 5000 * 4
h = g / 100
i = f - h
Problem: 140 is what percent of 40 ?
Options: a ) 5 % , b ) 20 % , c ) 50 % , d ) 350 % , e ) 500 %
Rationale: "40 * x = 140 - - > x = 3.5 - - > 3.5 expressed as percent is 350 % . answer : d ."
Answer: d
Python program:
a = 140 / 40
b = a * 100
Problem: tickets to a certain concert sell for $ 20 each . the first 10 people to show up at the ticket booth received a 40 % discount , and the next 20 received a 15 % discount . if 56 people bought tickets to the concert , what was the total revenue from ticket sales ?
Options: a ) $ 600 , b ) $ 740 , c ) $ 850 , d ) $ 980 , e ) $ 1,140
Rationale: "price of 1 ticket = 20 $ revenue generated from sales of first 10 tickets = 10 * ( 60 / 100 * 20 ) = 10 * 12 = 120 revenue generated from sales of next 20 tickets = 20 * ( 85 / 100 * 20 ) = 20 * 17 = 340 revenue generated from sales of last 26 tickets = 20 * 26 = 520 revenue generated from sales of 56 tickets = 120 + 340 + 520 = 980 $ answer d"
Answer: d
Python program:
a = 56 - 20
b = a - 10
c = 40 / 100
d = 1 - c
e = d * 10
f = b + e 
g = 15 / 100
h = 1 - g
i = h * 20
j = f + i 
k = j * 20
Problem: in the annual cultural programme of indra prastha there was this math quiz going on . yudhisthir faced this last question that will bring the champion ' s trophy . what will be thesolution for the given problem ? the function f is defined is defined asf ( 2 x + 3 ) = ( x - 3 ) ( x + 4 ) what is f ( 29 ) ?
Options: a ) 200 , b ) 230 , c ) 140 , d ) 170 , e ) none of these
Rationale: explanation : f ( 2 x + 3 ) = ( x - 3 ) ( x + 4 ) put x = 13 f ( 2 * 13 + 3 ) = ( 13 - 3 ) * ( 13 + 4 ) = 10 * 17 f ( 29 ) = 170 answer : d
Answer: d
Python program:
a = 29 - 3
b = a / 2
c = b - 3
d = 29 - 3
e = d / 2
f = e + 4 
g = c * f
Problem: a driver goes on a trip of 70 kilometers , the first 35 kilometers at 48 kilometers per hour and the remaining distance at 24 kilometers per hour . what is the average speed of the entire trip in kilometers per hour ?
Options: a ) 30 , b ) 32 , c ) 35 , d ) 36 , e ) 40
Rationale: "the time for the first part of the trip was 35 / 48 hours . the time for the second part of the trip was 35 / 24 hours . the total time fro the trip was 35 / 48 + 35 / 24 = 105 / 48 = 35 / 16 hours . the average speed for the trip was 70 / ( 35 / 16 ) = 32 kph the answer is b ."
Answer: b
Python program:
a = 35 / 48
b = 70 - 35
c = b / 24
d = a + c 
e = 70 / d
Problem: one day a car rental agency rented 2 / 3 of its cars , including 3 / 5 of its cars with cd players . if 3 / 4 of its cars have cd players , what percent of the cars that were not rented had cd players ?
Options: a ) 10 % , b ) 35 % , c ) 45 % , d ) 66.7 % , e ) 90 %
Rationale: let us try to solve this by getting some number for total cars . let there be 3,4 and 5 = 60 cars . . . ( we have taken denominators of 2 / 3,3 / 4 and 3 / 5 least common number ) . 2 / 3 ( 60 ) = 40 cars . . . total rented cars , then 1 / 3 ( 60 ) = 20 cars were not rented . 3 / 4 ( 60 ) = 45 cars with cd players . . . total cdp cars now 3 / 5 ( 3 / 4 ) = 3 / 5 ( 45 ) = 27 cdp cars and these are cars that we rented . non rented cdp = total cdp - rented cdp = 45 - 27 = 18 . 18 / 20 = 90 % . answer : e
Answer: e
Python program:
a = 3 * 5
b = a * 4
c = 3 * b
d = c / 4
e = 3 * 5
f = e * 4
g = 3 * f
h = g / 4
i = h * 3
j = i / 5
k = d - j
l = 3 * 5
m = l * 4
n = 3 * 5
o = n * 4
p = 2 * o
q = p / 3
r = m - q
s = k / r
t = s * 100
Problem: if 183 is divisible by 11 , find the value of the smallest natural no . n ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 10 , e ) 12
Rationale: in aptitude tests , we get questions on divisibility by 11 . a number is divisible by 11 , when the difference between the sum of digits at even places and at odd places is 0 or multiple of 11 the given number is n 183 . ( sum of digits at even places ) – ( sum of digits at odd places ) = 0 ( 8 + n ) - ( 3 + 1 ) = 0 ( 8 + n ) - 4 = 0 here the value of n must be 7 b
Answer: b
Python program:
a = 2 * 4
b = a - 3
c = b - 1
d = 11 - c
Problem: joshua and jose work at an auto repair center with 3 other workers . for a survey on health care insurance , 2 of the 6 workers will be randomly chosen to be interviewed . what is the probability that joshua and jose will both be chosen ?
Options: a ) 1 / 15 , b ) 1 / 10 , c ) 1 / 9 , d ) 1 / 6 , e ) 1 / 3
Rationale: two methods 1 ) probability of chosing josh first = 1 / 5 probability of chosing jose second = 1 / 4 total = 1 / 20 probability of chosing jose first = 1 / 5 probability of chosing josh second = 1 / 4 total = 1 / 20 final = 1 / 20 + 1 / 20 = 1 / 10 b
Answer: b
Python program:
a = math.factorial(6)
b = math.factorial(2)
c = math.factorial(3)
d = b * c
e = a / d
f = math.factorial(6)
g = e / f
Problem: a can do a piece of work in 40 days ; b can do the same in 40 days . a started alone but left the work after 10 days , then b worked at it for 10 days . c finished the remaining work in 10 days . c alone can do the whole work in ?
Options: a ) 20 days , b ) 65 days , c ) 86 days , d ) 45 days , e ) 17 days
Rationale: "10 / 40 + 10 / 40 + 10 / x = 1 x = 20 days answer : a"
Answer: a
Python program:
a = 10 + 10 
b = a / 40
c = 1 - b
d = 10 / c
Problem: in a 280 meters race a beats b by 56 m or 7 seconds . a ' s time over the course is :
Options: a ) 22 seconds , b ) 12 seconds , c ) 10 seconds , d ) 18 seconds , e ) 28 seconds
Rationale: "b runs 56 m in 7 sec . = > b runs 280 m in 7 / 56 * 280 = 35 seconds since a beats b by 7 seconds , a runs 280 m in ( 35 - 7 ) = 28 seconds hence , a ' s time over the course = 28 seconds answer : e"
Answer: e
Python program:
a = 7 / 56
b = a * 280
c = b - 7
Problem: in smithtown , the ratio of right - handed people to left - handed people is 3 to 1 and the ratio of men to women is 3 to 2 . if the number of right - handed men is maximized , then what z percent of all the people in smithtown are left - handed women ?
Options: a ) 50 % , b ) 40 % , c ) 25 % , d ) 20 % , e ) 10 %
Rationale: "looking at the ratio we can take total number of people = 20 . . ans 5 / 20 or 25 % c"
Answer: c
Python program:
a = 3 + 1 
b = 3 + 2 
c = a / b
d = 2 * c
e = 3 + 1 
f = 3 + 2 
g = e / f
h = 3 * g
i = 3 - h
j = d - i
k = 3 + 1 
l = j / k
m = l * 100
Problem: in a kilometer race , a beats b by 80 meters or 10 seconds . what time does a take to complete the race ?
Options: a ) 167 sec , b ) 190 sec , c ) 176 sec , d ) 115 sec , e ) 123 sec
Rationale: "time taken by b run 1000 meters = ( 1000 * 10 ) / 80 = 125 sec . time taken by a = 125 - 10 = 115 sec . answer : d"
Answer: d
Python program:
a = 1 * 1000
b = 80 / 10
c = a / b
d = c - 10