euclaise/mathqa_programs huggingface dataset:
Problem: to be considered for “ movie of the year , ” a film must appear in at least 1 / 4 of the top - 10 - movies lists submitted by the cinematic academy ’ s 795 members . what is the smallest number of top - 10 lists a film can appear on and still be considered for “ movie of the year ” ?
Options: a ) 191 , b ) 199 , c ) 193 , d ) 212 , e ) 213
Rationale: total movies submitted are 795 . as per question we need to take 1 / 4 of 795 to be considered for top 10 movies = 198.75 approximate the value we 199 . imo option b is the correct answer . . .
Answer: b
Python program:
a = 795 / 4
Problem: a man can swim in still water at 9 km / h , but takes twice as long to swim upstream than downstream . the speed of the stream is ?
Options: a ) 1.7 , b ) 1.9 , c ) 3 , d ) 1.5 , e ) 1.2
Rationale: "m = 9 s = x ds = 9 + x us = 9 - x 9 + x = ( 9 - x ) 2 9 + x = 18 - 2 x 3 x = 9 x = 3 answer : c"
Answer: c
Python program:
a = 9 / 3
Problem: the distance from the x - axis to point p is half the distance from the y - axis to point p . if the coordinates of p are ( x , - 6 ) , how many units is p from the y - axis ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 10.5 , e ) 12
Rationale: "the x - axis is 6 units from the point p . thus the y - axis is 12 units from the point p . the answer is e ."
Answer: e
Python program:
a = 6 * 2
Problem: a can do a piece of work in 24 days . when he had worked for 2 days b joins him . if the complete work was finished in 8 days . in how many days b alone can finish the work ?
Options: a ) 9 , b ) 77 , c ) 66 , d ) 55 , e ) 12
Rationale: "8 / 24 + 6 / x = 1 x = 9 days answer : a"
Answer: a
Python program:
a = 1 / 8
b = 1 / 24
c = 2 * b
d = 1 - c
e = a * d
f = 1 / 24
g = e - f
h = 1/(g)
i = 24 + 8 
j = h - i
Problem: milk contains 5 % water . what quantity of pure milk should be added to 10 litres of milk to reduce this to 2 % ?
Options: a ) 5 litres , b ) 7 litres , c ) 15 litres , d ) can not be determined , e ) none of these
Rationale: "here required quantity of pure milk = 10 × ( 5 − 2 ) / 2 = 10 × 3 / 2 = 15 litres . answer c"
Answer: c
Python program:
a = 5 / 100
b = a * 10
c = 2 / 100
d = b / c
e = d - 10
Problem: 40 percent of the members of a study group are women , and 20 percent of those women are lawyers . if one member of the study group is to be selected at random , what is the probability that the member selected is a woman lawyer ?
Options: a ) 0.2 , b ) 0.08 , c ) 0.16 , d ) 0.14 , e ) 0.15
Rationale: "say there are 100 people in that group , then there would be 0.4 * 0.20 * 100 = 8 women lawyers , which means that the probability that the member selected is a woman lawyer is favorable / total = 8 / 100 . answer : b"
Answer: b
Python program:
a = 5 * 5
b = a * 4
c = 40 / b
d = 5 * 5
e = d * 4
f = 20 / e
g = c * f
Problem: two goods trains each 750 m long are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 72 , b ) 45 , c ) 48 , d ) 51 , e ) 44
Rationale: "relative speed = 45 + 30 = 75 km / hr . 75 * 5 / 18 = 125 / 6 m / sec . distance covered = 750 + 750 = 1500 m . required time = 1500 * 6 / 125 = 72 sec . answer : option a"
Answer: a
Python program:
a = 45 + 30
Problem: the banker ' s gain of a certain sum due 2 years hence at 10 % per annum is rs . 24 . the present worth is :
Options: a ) rs . 608 , b ) rs . 6076 , c ) rs . 600 , d ) rs . 602 , e ) rs . 601
Rationale: "t . d . = b . g . x 100 = rs . 24 x 100 = rs . 120 . rate x time 10 x 2 p . w . = 100 x t . d . = rs . 100 x 120 = rs . 600 . rate x time 10 x 2 answer : c"
Answer: c
Python program:
a = 24 * 100
b = 2 * 10
c = a / b
d = 100 * c
e = 2 * 10
f = d / e
Problem: a rectangular plot measuring 90 metres by 60 metres is to be enclosed by wire fencing . if the poles of the fence are kept 5 metres apart , how many poles will be needed ?
Options: a ) 55 , b ) 56 , c ) 60 , d ) 58 , e ) none of these
Rationale: "solution perimeter of the plot = 2 ( 90 + 60 ) = 300 m . ∴ number of poles = [ 300 / 5 ] = 60 m answer c"
Answer: c
Python program:
a = rectangle_perimeter / (
Problem: a 1200 m long train crosses a tree in 80 sec , how much time will i take to pass a platform 1000 m long ?
Options: a ) 288 , b ) 146.66 , c ) 188 , d ) 180 , e ) 12
Rationale: "l = s * t s = 1200 / 80 s = 15 m / sec . total length ( d ) = 2200 m t = d / s t = 2200 / 15 t = 146.66 sec answer : b"
Answer: b
Python program:
a = 1200 + 1000 
b = 1200 / 80
c = a / b
Problem: simplify : ( 7 + 2 ) – ( 5 + 3 + 1 ) - 1 .
Options: a ) - 1 , b ) – 2 , c ) 1 , d ) 2 , e ) 0
Rationale: "solution : ( 7 + 2 ) – ( 5 + 3 + 1 ) - 1 = 9 - 5 - 3 + 1 - 1 = 9 - 8 + 1 - 1 = 2 - 1 = 1 answer : ( c )"
Answer: c
Python program:
a = 7 + 3 
b = 5 - 2
c = b - 1
d = a + c
Problem: how many shots of 1 cm radius can be prepared from a sphere of 7 cm radius ?
Options: a ) 343 , b ) 388 , c ) 327 , d ) 88 , e ) 99
Rationale: "4 / 3 ï € * 7 * 7 * 7 = 4 / 3 ï € * 1 * 1 * 1 * x x = 343 answer : a"
Answer: a
Python program:
a = 7 ** 2
b = a * 7
Problem: on a certain road 10 % of the motorists exceed the posted speed limit and receive speeding tickets , but 10 % of the motorists who exceed the posted speed limit do not receive speeding tickets . what percent of the motorists on the road exceed the posted speed limit ?
Options: a ) 10.5 % , b ) 18 % , c ) 15 % , d ) 22 % , e ) 11.11 %
Rationale: "0.1 m = 0.90 e = > e / m = 1 / 9 * 100 = 11.11 % = e . m - # of motorists e - # of motorists exceeding speed"
Answer: e
Python program:
a = 10 / 100
b = 10 / 100
c = a * b
d = c * 100
e = 100 / d
Problem: a river boat leaves silver town and travels upstream to gold town at an average speed of 6 kilometers per hour . it returns by the same route at an average speed of 3 kilometers per hour . what is the average speed for the round - trip in kilometers per hour ?
Options: a ) 4.0 , b ) 3.8 , c ) 7.2 , d ) 7.5 , e ) 8.0
Rationale: "pick a number which is lcm of 3 and 6 = 12 . upstream time = 12 / 6 = 2 hrs downstream time = 12 / 3 = 4 hrs total time = 6 hrs total distance = 24 average speed = 24 / 6 = 4.0 km / hr"
Answer: a
Python program:
a = 6 * 3
b = a * 2
c = 6 + 3 
d = b / c
Problem: abcd is a square where ab = â ˆ š 4008 . let x be a point on ab and y be a point on cd such that ax = cy . compute the area of trapezoid axyd .
Options: a ) 3008 , b ) 2004 , c ) 1008 , d ) 2016 , e ) 3000
Rationale: "note that trapezoids axy d and bxy c are congruent , so the area of axy d is always 4008 / 2 = 2004 . correct answer b"
Answer: b
Python program:
a = 4008 / 2
Problem: a man swims downstream 72 km and upstream 45 km taking 5 hours each time ; what is the speed of the current ?
Options: a ) 1.7 , b ) 2.8 , c ) 3.6 , d ) 2.7 , e ) 1.1
Rationale: "72 - - - 5 ds = 14.4 ? - - - - 1 45 - - - - 5 us = 9 ? - - - - 1 s = ? s = ( 14.4 - 9 ) / 2 = 2.7 answer : d"
Answer: d
Python program:
a = 45 / 5
b = 72 / 5
c = a + b 
d = c / 2
Problem: two numbers are in the ratio 1 : 2 , if 7 is added to both , their ratio changes to 3 : 5 . the greatest number is
Options: a ) 24 , b ) 26 , c ) 28 , d ) 32 , e ) 44
Rationale: "let the numbers be x and 2 x then , ( x + 7 ) / ( 2 x + 7 ) = 3 / 5 x = 14 there fore answer is 28 answer c 28"
Answer: c
Python program:
a = 1 * 7
b = a * 100
c = 2 * 7
d = b + c
Problem: what is 82 % of 3 / 4 ?
Options: a ) 6.9 , b ) 69.0 , c ) 0.6845 , d ) 0.6859 , e ) 0.615
Rationale: "82 % * ( 3 / 4 ) = 0.82 * 0.75 = 0.615 answer : e"
Answer: e
Python program:
a = 3 + 2 
b = a * 2
c = 3 * 4
d = c * 100
e = b * d
f = 3 + 4 
g = 3 + 2 
h = f * g
i = 3 + 2 
j = i * 2
k = h * j
l = e + k 
m = 3 + 3 
n = l + m 
o = 82 * n
p = o / 100
Problem: points x , y , and z lie , in that order , on a straight railroad track . the distance from point x to point y is twice the distance from point y to point z . a train traveled from point x to point z without stopping . the train ' s average speed when traveling from point x to point y was 300 miles per hour and the train ' s average speed when traveling from point y to point z was 100 miles per hour . what was the train ' s average speed , in miles per hour , when traveling from point x to point z ?
Options: a ) 200 , b ) 220 , c ) 240 , d ) 180 , e ) 260
Rationale: average speed = distance / time because we are looking for average speed we can pick a distance for the variable d . speed x - y = 300 speed y - z = 100 average speed = total distance / total rate rate = distance / time x = = = = = = = = = = = = = = = = = = = = y = = = = = = = = = = z if x - y is twice the length of y - z then let x - y = 2 d and let y - z = d average speed = 3 d / ( 2 d / 300 ) + ( d / 100 ) 3 d / ( 2 d / 300 ) + ( 3 d / 300 ) 3 d / ( 5 d / 300 ) 900 d / 5 d average speed = 180 answer : d
Answer: d
Python program:
a = 300 / 100
b = 2 / a
c = b + 1 
d = 3 / c
e = d * 100
Problem: a 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds . what is the length of the other train ?
Options: a ) 220 meter , b ) 225 meter , c ) 230 meter , d ) 235 meter , e ) none of these
Rationale: "explanation : as trains are running in opposite directions so their relative speed will get added so , relative speed = 120 + 80 = 200 kmph = 200 * ( 5 / 18 ) = 500 / 9 m / sec let the length of other train is x meter then x + 270 / 9 = 500 / 9 = > x + 270 = 500 = > x = 230 so the length of the train is 230 meters option c"
Answer: c
Python program:
a = 120 + 80 
b = a * const_0_2778
c = b * 9
d = c - 270
Problem: if xerox paper costs 5 cents a sheet and a buyer gets 10 % discount on all xerox paper one buys after the first 2000 papers and 20 % discount after first 10000 papers , how much will it cost to buy 20000 sheets of xerox paper ?
Options: a ) $ 1250 , b ) $ 1060 , c ) $ 1350 , d ) $ 900 , e ) $ 1000
Rationale: "30 sec approach - solve it using approximation 20000 sheet at full price , 5 cent = 1000 20000 sheet at max discount price , 4 cent = 800 your ans got to be between these two . ans d it is ."
Answer: d
Python program:
a = 10000 - 2000
b = 1 / 10
c = 1 - b
d = 1 / 10
e = c * d
f = a * e
Problem: there is rain at a rate of 12 centimeters per hour all over new jersey . somewhere downtown in new jersey a group of students are waiting for the rain to stop . if the rain filled a tank the with a base area of 250 square centimeters and a depth of 6 centimeters , how long did the students wait for the rain to stop ?
Options: a ) 8 hours
b ) 4 hours 25 minutes
c ) 3 hours 15 minutes
d ) 6 hours
e ) 2 hours
Rationale: answer is : e , 4 hours and 30 mins the volume of the tank is irrelevant and only height matters since rain fell all over the city . thus , it takes only . 12 / 6 = 2 hours of rain to fill the tank .
Answer: e
Python program:
a = 250 * 6
b = a / 12
c = 6 * 10
d = b / c
Problem: if a and b are positive integers , and a = 3 b + 12 , the greatest common divisor of a and b can not be
Options: a ) 1 , b ) 3 , c ) 2 , d ) 5 , e ) 4
Rationale: "if b is 1 , 2 , 3 , or 4 , then gcd of a and b is 1 , 2 , 3 , and 4 respectively . so , by poe the answer must be d . still : if b is a multiple of 5 , then a is 12 greater than a multiple of 5 , so not a multiple of 5 , so both of them can not be divisive by 5 . answer : d ."
Answer: d
Python program:
a = 12 / 3
b = a + 2
Problem: during a sale , the price of a pair of shoes is marked down 14 % from the regular price . after the sale ends , the price goes back to the original price . what is the percent of increase to the nearest percent from the sale price back to the regular price for the shoes ?
Options: a ) 9 % , b ) 10 % , c ) 11 % , d ) 16 % , e ) 90 %
Rationale: "assume the price = 100 price during sale = 86 price after sale = 100 percent increase = 14 / 86 * 100 = 16 % approx . correct option : d"
Answer: d
Python program:
a = 14 * 100
b = 100 - 14
c = a / b
Problem: two trains of length 60 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively . in what time will they be clear of each other from the moment they meet ?
Options: a ) 10 sec , b ) 32 sec , c ) 17 sec , d ) 20 sec , e ) 89 sec
Rationale: "relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 60 + 280 = 400 m . the time required = d / s = 340 / 20 = 20 sec . answer : c"
Answer: c
Python program:
a = 60 + 280 
b = 42 + 30 
c = b * const_0_2778
d = a / c
Problem: one 100 gallons of fuel are purchased at $ 0.70 per gallon . the fuel is consumed at a rate of $ 0.40 worth of fuel per hour . at this rate , how many hours are required to consume the 100 gallons of fuel ?
Options: a ) 150 , b ) 175 , c ) 200 , d ) 225 , e ) 250
Rationale: the fuel is consumed at this rate : $ 0.40 / $ 0.70 = 4 / 7 gallons per hour . the time it takes to consume 100 gallons is : 100 / ( 4 / 7 ) = 175 hours . the answer is b .
Answer: b
Python program:
a = 0 * 7
b = a / 0
Problem: a chemist mixes one liter of pure water with x liters of a 75 % salt solution , and the resulting mixture is a 15 % salt solution . what is the value of x ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 1 , e ) 3
Rationale: "concentration of salt in pure solution = 0 concentration of salt in salt solution = 75 % concentration of salt in the mixed solution = 15 % the pure solution and the salt solution is mixed in the ratio of - - > ( 75 - 15 ) / ( 15 - 0 ) = 4 / 1 1 / x = 4 / 1 x = 1 / 4 answer : a"
Answer: a
Python program:
a = 75 - 15
b = 15 / a
Problem: if 5 % more is gained by selling an article for rs . 600 than by selling it for rs . 580 , the cost of the article is ?
Options: a ) 127 , b ) 688 , c ) 400 , d ) 121 , e ) 123
Rationale: "let c . p . be rs . x . then , 5 % of x = 600 - 580 = 20 x / 20 = 20 = > x = 400 answer : c"
Answer: c
Python program:
a = 600 - 580
b = 5 / 100
c = a / b
Problem: a boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes . how long will it take to go 5 km in stationary water ?
Options: a ) 40 minutes , b ) 1 hour , c ) 1 hour 15 min , d ) 1 hour 30 min , e ) 1 hour 10 min
Rationale: "speed ( upstream ) = 2 / 1 = 2 kmhr speed ( downstream ) = 1 / ( 10 / 60 ) = 6 kmhr speed in still water = 1 / 2 ( 2 + 6 ) = 4 kmhr time taken in stationary = 5 / 4 = 1 hrs 15 min answer : c"
Answer: c
Python program:
a = 1 / 10
b = a * const_60
c = 2 / 2
d = b + c 
e = d / 2
f = 5 / e
Problem: a , b , c subscribe rs . 50000 for a business . if a subscribes rs . 4000 more than b and b rs . 5000 more than c , out of a total profit of rs . 36000 , what will be the amount a receives ?
Options: a ) 15120 , b ) 14500 , c ) 14900 , d ) 14300 , e ) 14000
Rationale: total amount invested = 50000 assume that investment of c = x . then investment of b = 5000 + x , investment of a = 4000 + 5000 + x = 9000 + x x + 5000 + x + 9000 + x = 50000 ⇒ 3 x + 14000 = 50000 ⇒ 3 x = 50000 – 14000 = 36000 ⇒ x = 36000 / 3 = 12000 investment of c = x = 12000 investment of b = 5000 + x = 17000 investment of a = 9000 + x = 21000 ratio of the investment of a , b and c = 21000 : 17000 : 12000 = 21 : 17 : 12 share of a = total profit × 21 / 50 = 36000 × 21 / 50 = 15,120 answer is a .
Answer: a
Python program:
a = 5000 + 4000 
b = a + 5000 
c = 50000 - b
d = c / 3
e = 5000 + 4000 
f = d + e 
g = f / 50000
h = g * 36000
Problem: steve traveled the first 2 hours of his journey at 30 mph and the last 3 hours of his journey at 80 mph . what is his average speed of travel for the entire journey ?
Options: a ) 68 mph , b ) 56.67 mph , c ) 60 mph , d ) 64 mph , e ) 66.67 mph
Rationale: "answer average speed of travel = total distance travelled / total time taken total distance traveled by steve = distance covered in the first 2 hours + distance covered in the next 3 hours . distance covered in the first 2 hours = speed * time = 30 * 2 = 60 miles . distance covered in the next 3 hours = speed * time = 80 * 3 = 240 miles . therefore , total distance covered = 60 + 240 = 300 miles . total time taken = 2 + 3 = 5 hours . hence , average speed = total distance travelled / total time taken = 300 / 5 = 60 miles per hour . choice c"
Answer: c
Python program:
a = 80 * 3
b = 30 * 2
c = a + b 
d = 3 + 2 
e = c / d
f = 100 / 3
g = f - const_0_33
h = e + g
Problem: a train 600 m long can cross an over brdge of 100 m long in 70 sec and then find the speed of the train ?
Options: a ) 79 , b ) 30 , c ) 36 , d ) 66 , e ) 12
Rationale: length = speed * time speed = l / t s = 700 / 70 s = 10 m / sec speed = 10 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 36 kmph . answer : c
Answer: c
Python program:
a = 600 + 100 
b = a / 70
c = b * const_3_6
Problem: when sold at a 60 % discount , a sweater nets the merchant a 35 % profit on the wholesale cost at which he initially purchased the item . by what % is the sweater marked up from wholesale at its normal retail price ?
Options: a ) 20 % , b ) 40 % , c ) 50 % , d ) 70.38 % , e ) 100 %
Rationale: "we should be careful about what are we measuring % on / what is the base . . let the marked up price = 100 . . selling price = 100 - 60 % of 100 = 40 . . profit = 35 % . . therefore the wholesale purchase cost = x . . . . 1.35 x = 40 or x = 29.62 . . . marked price was 100 so . . . so answer is 70.38 % . . d"
Answer: d
Python program:
a = 100 - 60
b = 35 / 100
c = 1 + b 
d = a / c
e = 100 - d
Problem: from a group of 3 women and 3 girls , 4 are to be randomly selected . what is the probability that equal numbers of women and girls will be selected ?
Options: a ) 3 / 5 , b ) 1 / 5 , c ) 2 / 5 , d ) 4 / 5 , e ) 1
Rationale: using the first example , here is the probability of that exact sequence occurring : wwgg = ( 3 / 6 ) ( 2 / 5 ) ( 3 / 4 ) ( 2 / 3 ) = 36 / 360 = 1 / 10 each of the other 5 options will yield the exact same probability . . . . wgwg = ( 3 / 6 ) ( 3 / 5 ) ( 2 / 4 ) ( 2 / 3 ) = 36 / 360 = 1 / 10 so we have 6 different options that each produce a 1 / 10 chance of occurring . 6 ( 1 / 10 ) = 6 / 10 = 3 / 5 final answer : a
Answer: a
Python program:
a = math.comb(3, 2)
b = math.comb(3, 2)
c = a * b
d = 3 + 3 
e = math.comb(d, 4)
f = c / e
Problem: what is the sum of natural numbers between 50 and 100
Options: a ) 4800 , b ) 4860 , c ) 3825 , d ) 5500 , e ) 5550
Rationale: "a = first number l = last number sn = n / 2 [ a + l ] between 50 and 100 numbers = 51 = > 100 - 50 = 50 + 1 = 51 sn = 51 / 2 ã — 150 = 51 ã — 75 = 3825 answer : c"
Answer: c
Python program:
a = 100 + 1
Problem: an integer n between 1 and 99 , inclusive , is to be chosen at random . what is the probability that n ( n + 1 ) will be divisible by 2 ?
Options: a ) 1 / 9 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6
Rationale: "n ( n + 1 ) to be divisible by 2 either n or n + 1 must be a multiples of 2 . in each following group of numbers : { 1 , 2 , 3 } , { 4 , 5 , 6 } , { 7 , 8 , 9 } , . . . , { 97 , 98 , 99 } there are exactly 2 numbers out of 3 satisfying the above condition . for example in { 1 , 2 , 3 } n can be : 2 , or 3 . thus , the overall probability is 2 / 3 . answer : d ."
Answer: d
Python program:
a = 99 / 3
b = a / 99
c = b * 2
Problem: carl is facing very difficult financial times and can only pay the interest on a $ 30,000 loan he has taken . the bank charges him a quarterly compound rate of 10 % . what is the approximate interest he pays annually ?
Options: a ) $ 1200 , b ) $ 2000 , c ) $ 2150 , d ) $ 2500 , e ) $ 12000
Rationale: "usually , you are given the annual rate of interest and it is mentioned that it is annual rate . the bank charges him a quarterly compounded annual rate of 40 % . here you find per quarter rate as ( 40 / 4 ) % = 10 % i have actually never seen a question with quarter rate given but since this question did not mentionannual rate of interestand since the options did not make sense with 5 % annual rate of interest , it is apparent that the intent was a 10 % quarterly rate . so the bank charges 10 % every quarter and compounds it in the next quarter . had it been a simple quarterly rate , we would have just found 4 * 10 % of 30,000 = $ 12000 as our answer . but since , the interest is compounded , it will be a bit more than $ 12000 . option ( e ) looks correct ."
Answer: e
Python program:
a = 100 * 100
b = 10 / 100
c = 1 + b 
d = c ** 4
e = a * d
f = 100 * 100
g = e - f
Problem: the s . i . on a certain sum of money for 4 years at 12 % per annum is half the c . i . on rs . 6000 for 2 years at 15 % per annum . the sum placed on s . i . is ?
Options: a ) 2019.625 , b ) 2017.625 , c ) 2013.625 , d ) 2015.625 , e ) 2011.625
Rationale: c . i . = [ 6000 * ( 1 + 15 / 100 ) 2 - 6000 ] = ( 6000 * 23 / 20 * 23 / 20 - 6000 ) = rs . 1935 . sum = ( 967.5 * 100 ) / ( 4 * 12 ) = rs . 2015.625 answer : d
Answer: d
Python program:
a = 15 / 100
b = 1 + a 
c = b ** 2
d = 6000 * c
e = d - 6000
f = e / 2
g = 12 / 100
h = 4 * g
i = f / h
Problem: what is the greatest positive integer x such that 2 ^ x is a factor of 8 ^ 10 ?
Options: a ) 5 , b ) 9 , c ) 10 , d ) 20 , e ) 30
Rationale: "8 ^ 10 = ( 2 ^ 3 ) ^ 10 = 2 ^ 30 answer : e"
Answer: e
Python program:
a = 8 - 10
b = a * 10
Problem: of the 80 people in a room , 1 / 4 are women . if 3 / 4 of the people are married , what is the maximum number of women in the room who could be unmarried ?
Options: a ) 20 , b ) 24 , c ) 26 , d ) 28 , e ) 30
Rationale: "women = 1 / 4 * 80 = 20 married = 3 / 4 * 80 = 60 unmarried = 20 max ( un - married women ) = 20 answer a"
Answer: a
Python program:
a = 1 / 4
b = 80 * a
Problem: the ratio of the volumes of two cubes is 125 : 1000 . what is the ratio of their total surface areas ?
Options: a ) 81 : 121 , b ) 9 : 11 , c ) 729 : 1331 , d ) 1 : 4 , e ) none of these
Rationale: "ratio of the sides = â ³ â ˆ š 125 : â ³ â ˆ š 1000 = 5 : 10 ratio of surface areas = 5 ^ 2 : 10 ^ 2 = 25 : 100 = 1 : 4 answer : d"
Answer: d
Python program:
a = 125 / 1000
b = 1 / 3
c = a ** b
Problem: if the mean of numbers 12 , x , 42 , 78 and 104 is 62 , then what is the mean of 128 , 255 , 511 , 1023 and x ?
Options: a ) 395 , b ) 275 , c ) 355 , d ) 415 , e ) 398.2
Rationale: "the mean of numbers 12 , x , 42 , 78 and 104 is 62 : 12 + x + 42 + 78 + 104 = 62 * 5 - - > x = 74 ; so , the mean of 128 , 255 , 511 , 1023 and x is ( 128 + 255 + 511 + 1023 + 74 ) / 5 = 398.2 . answer : e ."
Answer: e
Python program:
a = 4 + 1 
b = 62 * a
c = 12 + 42 
d = c + 78 
e = d + 104 
f = b - e
g = f + 128 
h = g + 255 
i = h + 511 
j = i + 1023 
k = 4 + 1 
l = j / k
Problem: if the perimeter of square region q and the perimeter of rectangular region r are equal and the sides of r are in the ratio 2 : 3 then the ratio of the area of r to the area of q
Options: a ) 25 : 16
b ) 24 : 25
c ) 5 : 6
d ) 4 : 5
e ) 4 : 9
Rationale: we know perimeter of a square ( pq ) = 4 * side perimeter of a rectangle ( pr ) = 2 ( length + breath ) let us assume 40 to be the perimeter of the square ( since we know each side of a square is equal and the perimeter is divisible by 4 , also take in to account the length and breadth of the rectangle is in the ration 2 k : 3 k = 5 k ; we can assume such a number ) therefore , pq = pr = 40 area of the square = 100 sq . units we know 2 ( length + breadth ) = 40 i . e . length + breadth = 20 ( or 5 k = 20 given that l : b ( or b : l ) = 2 : 3 ) therefore length = 8 , breath = 12 area of the rectangle = 8 * 12 = 96 sq . units question asked = area of the rectangle : area of the square = 96 : 100 = = > 24 : 25 = b
Answer: b
Python program:
a = rectangle_area / (
Problem: the ratio of the present ages of ramesh and mahesh is 2 : 5 . 10 years hence , the ratio of their ages will be 10 : 15 . find the difference in their present ages ?
Options: a ) 7.5 , b ) 6 , c ) 5.5 , d ) 6.5 , e ) 5
Rationale: let the present ages of ramesh and mahesh be 2 x and 5 x years respectively . ( 2 x + 10 ) / ( 5 x + 10 ) = 10 / 15 6 x + 30 = 10 x + 20 = > x = 2.5 difference in their ages will be the same at all times . this difference = difference of their present ages = > 5 x - 2 x = 3 x = > 7.5 years answer : a
Answer: a
Python program:
a = 15 / 2