euclaise/mathqa_programs huggingface dataset:
Problem: the average weight of a , b and c is 30 kg . if the average weight of a and b be 25 kg and that of b and c be 28 kg , then the weight of b is :
Options: a ) 14 kg , b ) 15 kg , c ) 18 kg , d ) 19 kg , e ) 16 kg
Rationale: explanation let a , b , c represent their respective weights . then , we have : a + b + c = ( 30 x 3 ) = 90 â € ¦ . ( i ) a + b = ( 25 x 2 ) = 50 â € ¦ . ( ii ) b + c = ( 28 x 2 ) = 56 â € ¦ . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 106 â € ¦ . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 16 . b â € ™ s weight = 16 kg . answer e
Answer: e
Python program:
a = 25 * 2
b = 28 * 2
c = a + b 
d = 30 * 3
e = c - d
Problem: the cost of a one - family home was $ 120000 in 1980 . in 1988 , the price had increased to $ 192000 . what was the percent increase in the cost of the home ?
Options: a ) 60 % , b ) 50 % , c ) 55 % , d ) 40 % , e ) 33.3 %
Rationale: increase = 192000 - 120000 = 72000 % increase = 72000 * 100 / 120000 = 60 % answer : option a
Answer: a
Python program:
a = 192000 / 120000
b = a - 1
c = b * 100
Problem: one fourth of one third of two fifth of a number is 20 . what will be 40 % of that number
Options: a ) a ) 140 , b ) b ) 150 , c ) c ) 180 , d ) d ) 240 , e ) e ) 220
Rationale: explanation : ( 1 / 4 ) * ( 1 / 3 ) * ( 2 / 5 ) * x = 20 then x = 20 * 30 = 600 40 % of 600 = 240 answer : option d
Answer: d
Python program:
a = 1 / 4
b = 1 / 3
c = a * b
d = 2 + 3 
e = 2 / d
f = c * e
g = 20 / f
h = g * 40
i = h / 100
Problem: a card board of 34 * 14 has to be attached to a wooden box and a total of 35 pins are to be used on the each side of the cardbox . find the total number of pins used .
Options: a ) 135 , b ) 136 , c ) 137 , d ) 138 , e ) 139
Rationale: ( 35 * 4 ) - 4 = 136 answer : b
Answer: b
Python program:
a = 35 * 4
Problem: a 200 meter long train crosses a platform in 50 seconds while it crosses a signal pole in 42 seconds . what is the length of the platform ?
Options: a ) 39.9 , b ) 37.88 , c ) 35 , d ) 38.88 , e ) 38.09
Rationale: "speed = [ 200 / 42 ] m / sec = 100 / 21 m / sec . let the length of the platform be x meters . then , x + 200 / 50 = 100 / 21 21 ( x + 200 ) = 5000 è x = 38.09 m . answer : e"
Answer: e
Python program:
a = 200 / 42
b = a * 50
c = b - 200
Problem: how much water should be added to 11 liters of a 20 % - solution of alcohol to reduce the concentration of alcohol in the solution by 75 % ?
Options: a ) 25 liters , b ) 29 liters , c ) 30 liters , d ) 32 liters , e ) 35 liters
Rationale: "let x ltr water to be added 2 ltr alcohol to be represented as ( 20 ( 1 - 3 / 4 ( new soln . = 11 + x ) ) ) 2 = 5 % * ( 11 + x ) - - - - - - - - > x = 29 ans b"
Answer: b
Python program:
a = 2 * 100
b = 75 / 100
c = b * 20
d = 20 - c
e = a / d
f = e - 11
Problem: a van takes 5 hours to cover a distance of 600 km . what speed in kph should the van maintain to cover the same distance in 3 / 2 of the previous time ?
Options: a ) 80 , b ) 84 , c ) 88 , d ) 92 , e ) 96
Rationale: "( 3 / 2 ) * 5 = 7.5 hours 600 / 7.5 = 80 kph the answer is a ."
Answer: a
Python program:
a = 3 / 2
b = a * 5
c = 600 / b
Problem: the ratio of ages of aman , bren , and charlie are in the ratio 5 : 8 : 7 respectively . if 8 years ago , the sum of their ages was 76 , what will be the age of bren 12 years from now ?
Options: a ) 17 , b ) 25 , c ) 27 , d ) 52 , e ) 60
Rationale: "let the present ages of aman , bren , and charlie be 5 x , 8 x and 7 x respectively . 5 x - 8 + 8 x - 8 + 7 x - 8 = 76 x = 5 present age of bren = 8 * 5 = 40 bren ' s age 12 years hence = 40 + 12 = 52 answer = e"
Answer: e
Python program:
a = 8 * 3
b = a + 76 
c = 5 + 8 
d = c + 7 
e = b / d
f = e * 8
g = f + 12
Problem: a and b undertake to do a piece of work for $ 500 . a alone can do it in 5 days while b alone can do it in 10 days . with the help of c , they finish it in 2 days . find the share of c ?
Options: a ) $ 200 , b ) $ 150 , c ) $ 300 , d ) $ 25 , e ) $ 100
Rationale: "c ' s 1 day work = ( 1 / 2 ) - ( 1 / 5 + 1 / 10 ) = 1 / 5 a : b : c = 1 / 5 : 1 / 10 : 1 / 5 = 2 : 1 : 2 b ' s share = 500 * 2 / 5 = $ 200 answer is a"
Answer: a
Python program:
a = 2 * 10
b = 1/(5)
c = a * b
d = 2 * 10
e = 1/(2)
f = 1/(5)
g = 1/(10)
h = f + g 
i = e - h
j = d * i
k = 2 * 10
l = 1/(5)
m = k * l
n = j + m 
o = 2 * 10
p = 1/(10)
q = o * p
r = n + q 
s = c / r
t = s * 500
Problem: a clock store sold a certain clock to a collector for 15 percent more than the store had originally paid for the clock . when the collector tried to resell the clock to the store , the store bought it back at 45 percent of what the collector had paid . the shop then sold the clock again at a profit of 85 percent on its buy - back price . if the difference between the clock ' s original cost to the shop and the clock ' s buy - back price was $ 80 , for how much did the shop sell the clock the second time ?
Options: a ) $ 168.58 , b ) $ 187.54 , c ) $ 158.74 , d ) $ 120.56 , e ) $ 200.84
Rationale: "now , in the question above , lets say the original cost of the clock to store was c $ and then it sold the same to the collector at 15 % profit . this means the clocks ' selling price was c ( 1.15 ) and this becomes cost price for the collector . now , when the collector tries to sell the same clock to the store , the store buys it for 45 % the price at which the collector bought it . thus , you get = 1.15 * 0.45 * c = 0.5175 c furthermore , the store sells the clock for the second time for 85 % profit and thus the selling price of the clock becomes = cost price of the clock for the store at buy - back * 1.85 = 1.85 * 0.5175 c finally given that c - 0.5175 c = 80 - - - - > c = 165.80 $ thus , the cost of the clock the second time around = 1.85 * 0.5175 c = 1.85 * 0.5175 * 165.80 = 158.74 $ . hence c is the correct answer ."
Answer: c
Python program:
a = 80 + 85 
b = 80 + 15 
c = b / 2
d = a * c
e = d / 80
f = 80 * e
g = 80 + 15 
h = g / 2
i = h - 15
j = f / i
Problem: angelina walked 100 meters from her home to the grocery at a constant speed . she then walked 180 meters to the gym at double the speed . she spent 40 seconds less on her way from the grocery to the gym than on her way from home to the grocery . what was angelina ' s speed , in meters per second , from the grocery to the gym ?
Options: a ) 2 , b ) 3 , c ) 0.5 , d ) 6 , e ) 12
Rationale: "let the speed be x . . . so time taken from home to grocery = 100 / x . . the speed to gym = 2 x . . so time taken = 180 / 2 x = 90 / x . . its given 100 / x - 90 / x = 40 . . 10 / x = 40 . . x = 0.25 m / secs . . so grocery to gym = 2 * 0.25 = 0.5 m / s . . . answer : c"
Answer: c
Python program:
a = 180 / 2
b = 100 - a
c = b / 40
d = c * 2
Problem: if 45 % of z is 39 % of y and y is 75 % of x , what percent of x is z ?
Options: a ) 200 , b ) 160 , c ) 100 , d ) 65 , e ) 50
Rationale: "( 45 / 100 ) z = ( 39 / 100 ) y and y = ( 75 / 100 ) x i . e . y = ( 3 / 4 ) x i . e . ( 45 / 100 ) z = ( 39 / 100 ) * ( 3 / 4 ) x i . e . z = ( 39 * 3 ) x / ( 45 * 4 ) i . e . z = ( 0.65 ) x = ( 65 / 100 ) x i . e . z is 65 % of x answer : option d"
Answer: d
Python program:
a = 75 / 100
b = 45 / 100
c = 39 / 100
d = b / c
e = a / d
f = e * 100
Problem: 10 camels cost as much as 24 horses , 16 horses cost as much as 4 oxen and 6 oxen as much as 4 elephants . if the cost of 10 elephants is rs . 130000 , find the cost of a camel ?
Options: a ) s . 9800 , b ) s . 3800 , c ) s . 9800 , d ) s . 5200 , e ) s . 6880
Rationale: "cost of the camel = p 10 camels = 24 horses 16 horses = 4 oxen 6 oxen = 4 elephants 10 elephants = rs . 130000 p = rs . [ ( 24 * 4 * 4 * 130000 ) / ( 10 * 16 * 6 * 10 ) ] p = rs . ( 49920000 / 9600 ) = > p = rs . 5200 answer : d"
Answer: d
Python program:
a = 24 * 4
b = a * 4
c = b * 130000
d = 10 * 16
e = d * 6
f = e * 10
g = c / f
Problem: a worker makes a toy in every 3 h . if he works for 150 h , then how many toys will he make ?
Options: a ) 40 , b ) 54 , c ) 45 , d ) 50 , e ) none
Rationale: no . of toys = 150 / 3 = 50 answer : d
Answer: d
Python program:
a = 150 / 3
Problem: in one hour , a boat goes 11 km along the stream and 5 km against the stream . the speed of the boat in still water in ( km / hr ) is
Options: a ) 3 , b ) 5 , c ) 8 , d ) 9 , e ) 7
Rationale: "solution speed in still water = 1 / 2 ( 11 + 5 ) km / hr = 8 km / hr . answer c"
Answer: c
Python program:
a = 11 + 5 
b = a / 2
Problem: 45 workers work 8 hours to dig a hole 30 meters deep . how many extra workers should be hired to dig another hole 40 meters deep by working for 6 hours ?
Options: a ) 75 , b ) 80 , c ) 50 , d ) 35 , e ) 40
Rationale: 45 workers * 8 hours / 30 meters = x * 6 / 40 x = 80 total workers 80 - 45 = 35 the answer is d .
Answer: d
Python program:
a = 8 / 6
b = 45 * a
c = 40 / 30
d = b * c
e = d - 45
Problem: if an amount of rs 42,900 is distributed equally amongst 22 persons , how much amount would each person get ?
Options: a ) rs 1950 , b ) rs 2000 , c ) rs 745 , d ) rs 765 , e ) none
Rationale: required amount = 42900 / 22 = rs 1950 answer a
Answer: a
Python program:
a = 4 * 10
b = a + 3 
c = b * 1000
d = c - 100
e = d / 22
Problem: what is the value of : - 9 ^ 7 + 9 ^ 9 ?
Options: a ) 9 ^ 2 , b ) - 18 ^ 16 , c ) 63 ( 9 ^ 7 ) , d ) - 80 ( 9 ^ 7 ) , e ) 80 ( 9 ^ 7 )
Rationale: - 9 ^ 7 + 9 ^ 9 = 9 ^ 7 ( - 1 + 9 ^ 2 ) = 9 ^ 7 ( - 1 + 81 ) = 80 ( 9 ^ 7 ) , answer e .
Answer: e
Python program:
a = 100 + const_60 
b = a + 1 
c = b * 9
d = c / 100
Problem: let the sides of a rectangular prism are consecutive multiples of 5 . which among the following could be the base area
Options: a ) 360
b ) 450
c ) 560
d ) 670
e ) 780
Rationale: length = 5 * a breadth = 5 * ( a + 1 ) or 5 * ( a + 2 ) base area - > multiple of 25 450 = 25 * 18 answer : b
Answer: b
Python program:
a = 5 * 3
b = a * 2
c = 5 * 3
d = b * c
Problem: if teena is driving at 55 miles per hour and is currently 7.5 miles behind joe , who is driving at 40 miles per hour in the same direction then in how many minutes will teena be 45 miles ahead of joe ?
Options: a ) 15 , b ) 60 , c ) 75 , d ) 90 , e ) 210
Rationale: "this type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30 - 40 seconds for a difficult one . teena covers 55 miles in 60 mins . joe covers 40 miles in 60 mins so teena gains 15 miles every 60 mins teena need to cover 7.5 + 45 miles . teena can cover 7.5 miles in 30 mins teena will cover 45 miles in 180 mins so answer 30 + 180 = 210 mins . ( answer e )"
Answer: e
Python program:
a = 55 - 40
b = a + 7 
c = 55 - 40
d = b / c
e = d * const_60
Problem: the sum of ages of 4 children born at the intervals of 10 years each is 80 years . what is the age of the youngest child ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 10 ) + ( x + 20 ) + ( x + 30 ) = 80 4 x = 20 x = 5 . age of the youngest child = x = 5 years . answer : b"
Answer: b
Python program:
a = 80 / 4
b = a - 10
c = b - 10
Problem: a bag contains 3 blue and 5 white marbles . one by one , marbles are drawn out randomly until only two are left in the bag . what is the probability x that out of the two , one is white and one is blue ?
Options: a ) 15 / 56 , b ) 41 / 56 , c ) 13 / 28 , d ) 15 / 28 , e ) 5 / 14
Rationale: "the required probability x = probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls . ways to select 6 out of total 8 = 8 c 6 ways to select 4 out of 5 white balls = 5 c 4 ways to select 2 out of 3 blue balls = 3 c 2 thus the required probability = ( 5 c 4 * 3 c 2 ) / 8 c 6 = 15 / 28 . d is thus the correct answer ."
Answer: d
Python program:
a = 3 * 5
b = 3 + 5 
c = 5 + 2 
d = b * c
e = d / 2
f = a / e
Problem: one hour after yolanda started walking from x to y , a distance of 17 miles , bob started walking along the same road from y to x . if yolanda ' s walking rate was 3 miles per hour and bob т ' s was 4 miles per hour , how many miles had bob walked when they met ?
Options: a ) 24 , b ) 23 , c ) 22 , d ) 21 , e ) 8
Rationale: when b started walking y already has covered 3 miles out of 17 , hence the distance at that time between them was 17 - 3 = 14 miles . combined rate of b and y was 3 + 4 = 7 miles per hour , hence they would meet each other in 14 / 7 = 2 hours . in 6 hours b walked 2 * 4 = 8 miles . answer : e .
Answer: e
Python program:
a = 17 - 3
b = 3 + 4 
c = a / b
d = c * 4
Problem: a dozen eggs and 10 pounds of oranges are currently at the same price . if the price of a dozen eggs rises by 9 percent and the price of oranges rises by 6 % . how much more will it cost to buy a dozen eggs and 10 pounds of oranges .
Options: a ) 5 % , b ) 10 % , c ) 15 % , d ) 20 % , e ) 25 %
Rationale: "say currently both a dozen eggs and 10 pounds of oranges cost $ 100 ( they are at the same price ) . so , to buy a dozen eggs and 10 pounds of oranges we need $ 100 . after the increase , the price of a dozen eggs will be $ 109 and the price of 10 pounds of oranges will be $ 106 . so after the increase , to buy a dozen eggs and 10 pounds of oranges we ' ll need $ 215 . increase = 15 % . answer : c ."
Answer: c
Python program:
a = 9 / 100
b = a * 10
c = 10 + b 
d = 6 / 100
e = d * 10
f = 10 + e 
g = c + f 
h = 10 + 10 
i = g - h
j = i * 100
k = 10 + 10 
l = j / k
m = l * 2
Problem: at what price must an article costing rs . 47.50 be marked in order that after deducting 5 % from the list price . it may be sold at a profit of 40 % on the cost price ?
Options: a ) 62.5 , b ) 69.5 , c ) 67.5 , d ) 62.5 , e ) 70
Rationale: "cp = 47.50 sp = 47.50 * ( 140 / 100 ) = 66.5 mp * ( 95 / 100 ) = 66.5 mp = 70 answer : e"
Answer: e
Python program:
a = 47 * 50
b = a / 100
c = 47 + 50 
d = c * 100
e = 100 - 5
f = d / e
Problem: two friends decide to get together ; so they start riding bikes towards each other . they plan to meet halfway . each is riding at 6 mph . they live 36 miles apart . one of them has a pet carrier pigeon and it starts flying the instant the friends start traveling . the pigeon flies back and forth at 19 mph between the 2 friends until the friends meet . how many miles does the pigeon travel ?
Options: a ) 54 , b ) 57 , c ) 60 , d ) 36 , e ) 96
Rationale: "b 57 it takes 3 hours for the friends to meet ; so the pigeon flies for 3 hours at 19 mph = 57 miles"
Answer: b
Python program:
a = 36 / 2
b = a / 6
c = 19 * b
Problem: in a river flowing at 2 km / hr , a boat travels 48 km upstream and then returns downstream to the starting point . if its speed in still water be 6 km / hr , find the total journey time .
Options: a ) 10 hours , b ) 12 hours , c ) 14 hours , d ) 18 hours , e ) none of these
Rationale: "explanation : speed of the boat = 6 km / hr speed downstream = ( 6 + 2 ) = 8 km / hr speed upstream = ( 6 - 2 ) = 4 km / hr distance traveled downstream = distance traveled upstream = 48 km total time taken = time taken downstream + time taken upstream = ( 48 / 8 ) + ( 48 / 4 ) = 18 hr . answer : option d"
Answer: d
Python program:
a = 6 - 2
b = 48 / a
c = 6 + 2 
d = 48 / c
e = b + d
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 x 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: the number of degrees that the hour hand of a clock moves through between noon and 2.30 in the afternoon of the same day is ?
Options: a ) 38 , b ) 27 , c ) 75 , d ) 28 , e ) 21
Rationale: explanation : the hour hand moves from pointing to 12 to pointing to half way between 2 and 3 . the angle covered between each hour marking on the clock is 360 / 12 = 30 . since the hand has covered 2.5 of these divisions the angle moved through is 75 . answer : c
Answer: c
Python program:
a = math.floor(2, 3)
b = math.floor(2, 3)
c = 2 - 3
d = c / const_60
e = d * 100
f = a + e 
g = f * 3
h = g * 10
Problem: a rectangular tiled patio is composed of 30 square tiles . the rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles . after the change in layout , the patio will still have 30 tiles , and it will still be rectangular . how many rows are in the tile patio before the change in layout ?
Options: a ) 5 , b ) 6 , c ) 10 , d ) 13 , e ) 28
Rationale: "suppose there are c columns and there are r rows original situation so , number of tiles = c * r = 30 also . reach column has r tiles and each row has c tiles new situation number of tiles in each column is r - 2 and number of tiles in each row is c + 4 so , number of rows = r - 2 and number of columns is c + 4 so , number of tiles = ( r - 2 ) * ( c + 4 ) = 30 comparing both of them we get c * r = ( r - 2 ) * ( c + 4 ) = > 4 r - 2 c = 8 c = 2 r - 4 putting it in c * r = 30 ( 2 r - 4 ) * r = 30 2 r ^ 2 - 4 r - 30 = 0 r can not be negative so r = 5 and c = 6 so , answer will be a"
Answer: a
Python program:
a = negate + ( 
b = 4 ** 2
c = 30 * 2
d = 4 * c
e = b + d 
f = math.sqrt(e)
g = a / f
h = 30 / g
Problem: a row of ants comprised of 102 ants . a man walked upon it and all except 42 were crushed beneath his foot . how many ants are left alive ?
Options: a ) 41 , b ) 42 , c ) 43 , d ) 44 , e ) 45
Rationale: solution : all except 42 were crushed means that all the ants except 42 were crushed beneath the man ' s foot . hence , 42 ants are alive now answer b
Answer: b
Python program:
a = 42 * 1
Problem: at a certain food stand , the price of each apple is 40 ¢ and the price of each orange is 60 ¢ . mary selects a total of 10 apples and oranges from the food stand , and the average ( arithmetic mean ) price of the 10 pieces of fruit is 54 ¢ . how many oranges must mary put back so that the average price of the pieces of fruit that she keeps is 45 ¢ ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "if the average price is 54 , then mary has 7 oranges and 3 apples ( a ratio of 7 : 3 ) . for the average price to be 45 , the ratio should be 1 : 3 . mary must put back 6 oranges . the answer is e ."
Answer: e
Python program:
a = 60 * 10
b = 54 * 10
c = a - b
d = 60 - 40
e = c / d
f = e * 40
g = 60 * 10
h = 54 * 10
i = g - h
j = 60 - 40
k = i / j
l = 10 - k
m = l * 60
n = f + m 
o = 45 * 10
p = n - o
q = 60 - 45
r = p / q
Problem: what percent is 50 gm of 1 kg ?
Options: a ) 0.5 % , b ) 1 % , c ) 1.5 % , d ) 2 % , e ) 5 %
Rationale: "1 kg = 1000 gm 50 / 1000 × 100 = 5000 / 1000 = 5 % e )"
Answer: e
Python program:
a = 50 / 1
b = a * 100
Problem: the dimensions of a rectangular solid are 6 inches , 5 inches , and 8 inches . if a cube , a side of which is equal to one of the dimensions of the rectangular solid , is placed entirely within thespherejust large enough to hold the cube , what the ratio of the volume of the cube to the volume within thespherethat is not occupied by the cube ?
Options: a ) 10 : 17
b ) 2 : 5
c ) 5 : 16
d ) 10 : 19
e ) 32 : 25
Rationale: answer : d .
Answer: d
Python program:
a = 8 * 2
b = a + 2 
c = b + 1 
d = 10 / c
Problem: john purchased some shirts and trousers for $ 1300 . he paid $ 500 less for the shirts than he did for the trousers . if he bought 5 shirts and the cost of a shirt is $ 20 less than that of a trouser , how many trousers did he buy ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 9
Rationale: "given that the total purchase of two items cost 1300 so the average purchase of one item will cost 1300 / 2 = 650 . its given as total shirt cost 500 $ less . hence total shirt cost = 650 - 250 and total trouser cost = 650 + 250 5 shirts = 400 $ = = > one shirt = 80 $ one trouser = 80 + 20 = 100 $ total trousers = 900 / 100 = 9 . e"
Answer: e
Python program:
a = 20 + 20 
b = 5 * a
c = 1300 - b
d = 20 + 20 
e = d + 20 
f = c / e
Problem: a contractor undertakes to complete the construction of a tunnel 720 meters long in 240 days and employs 50 men for the purpose . after 120 days , he finds that only 240 meters of the tunnel is complete . how many more men should be employ in order to complete the work in time ?
Options: a ) 75 men , b ) 80 men , c ) 70 men , d ) 60 men , e ) 50 men
Rationale: "in 120 days , only 240 m of the tunnel is constructed by 50 men . the remaining 120 days , 480 m of the tunnel can be constructed by 120 men . additional number of men required = 120 - 50 = 70 men . answer : c"
Answer: c
Python program:
a = 120 - 50
Problem: for all integers x > 1 . < x > = 2 x + ( 2 x - 1 ) + ( 2 x - 2 ) + . . . . . . 2 + 1 . what is the value of < 2 > * < 4 > ?
Options: a ) 60 , b ) 116 , c ) 210 , d ) 263 , e ) 360
Rationale: since < x > = 2 x + ( 2 x - 1 ) + ( 2 x - 2 ) + . . . . . . 2 + 1 = 1 + 2 + . . + ( 2 x - 2 ) + ( 2 x - 1 ) + 2 x then < x > is basically the sum of all integers from 1 to 2 x , inclusive . hence < 2 > is the sum of all integers from 1 to 2 * 2 = 4 and < 4 > is the sum of all integers from 1 to 2 * 4 = 8 - > < 4 > = 36 and < 2 > = 10 - - > < 3 > * < 2 > = 21 * 10 = 360 answer : e
Answer: e
Python program:
a = 4 * 2
b = 4 * 2
c = b - 1
d = a + c 
e = 4 * 2
f = e - 2
g = d + f 
h = 4 * 2
i = h - 3
j = g + i 
k = 4 * 2
l = k - 4
m = j + l 
n = 4 * 2
o = 4 * 2
p = o - 3
q = n - p
r = m + q 
s = 4 * 2
t = 4 * 2
u = t - 2
v = s - u
w = r + v 
x = 4 * 2
y = 4 * 2
z = y - 1
A = x - z
B = w + A 
C = 2 * 2
D = 2 * 2
E = D - 1
F = C + E 
G = 2 * 2
H = G - 2
I = F + H 
J = 2 * 2
K = J - 3
L = I + K 
M = B * L
Problem: two identical circles intersect such that their centers and the points at which they intersect form a square of side 4 cm . what is the area of the region where the two circles intersect ?
Options: a ) 16 - 4 pi
b ) 4 - pi
c ) 2 pi - 4
d ) 8 pi - 16
e ) pi ^ 2 - 4
Rationale: drawing a diagram , we see that the radius of the circle equals the side of the square . the area of intersection is : pi * r ^ 2 / 4 - ( r ^ 2 - pi * r ^ 2 / 4 ) = pi * r ^ 2 / 2 - r ^ 2 = 8 pi - 16 the answer is d .
Answer: d
Python program:
a = 3 * math.pi
b = a / 2
c = b + 4
Problem: pradeep has to obtain 35 % of the total marks to pass . he got 150 marks and failed by 25 marks . the maximum marks are
Options: a ) 300 , b ) 600 , c ) 800 , d ) 500 , e ) 900
Rationale: "explanation : let their maximum marks be x . then , 35 % of x = 150 + 25 = > 35 / 100 x = 175 x = ( 17500 / 35 ) x = 500 . answer : d"
Answer: d
Python program:
a = 150 + 25 
b = 35 / 100
c = a / b
Problem: if 4 people are selected from a group of 6 married couples , what is the probability that none of them would be married to each other ?
Options: a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 11 / 12
Rationale: "each couple can send only one ` ` representative ' ' to the committee . we can choose 4 couples ( as there should be 4 members ) to send only one ` ` representatives ' ' to the committee in c 46 c 64 # of ways . but these 4 chosen couples can send two persons ( either husband or wife ) : 2 ∗ 2 ∗ 2 ∗ 2 = 242 ∗ 2 ∗ 2 ∗ 2 = 24 . so # of ways to choose 4 people out 6 married couples so that none of them would be married to each other is : c 46 ∗ 24 c 64 ∗ 24 . total # of ways to choose 4 people out of 12 is c 412 c 124 . p = c 46 ∗ 24 c 412 = 1633 p = c 64 ∗ 24 c 124 = 1633 answer : d ."
Answer: d
Python program:
a = 6 * 2
b = 6 * 2
c = a / b
d = 4 * 4
e = 6 * 2
f = e - 1
g = d / f
h = c * g
i = 4 * 4
j = i - 2
k = 4 * 4
l = j / k
m = h * l
n = 4 * 4
o = n - 2
p = o - 2
q = 4 * 4
r = q - 1
s = p / r
t = m * s
Problem: if the length of a rectangle is increased by 20 % and the breadth is reduced by 20 % , what will be the effect on its area ?
Options: a ) 4 % increase
b ) 6 % increase
c ) 5 % decrease
d ) 4 % decrease
e ) none of these
Rationale: percentage change = x - y - xy ⁄ 100 = 20 – 20 – 20 × 20 / 100 = − 4 % = 4 % decrease answer d
Answer: d
Python program:
a = 20 / 100
b = 1 + a 
c = 20 / 100
d = 1 - c
e = b * d
f = 1 - e
g = f * 100