euclaise/mathqa_programs huggingface dataset:
Problem: a man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 2.5 kmph , find his average speed for the total journey ?
Options: a ) 3.1 kmph , b ) 5 kmph , c ) 6 kmph , d ) 4 kmph , e ) 7 kmph
Rationale: explanation : speed of man = 4.5 kmph speed of stream = 2.5 kmph speed in downstream = 7 kmph speed in upstream = 2 kmph average speed = ( 2 x 7 x 2 ) / 9 = 3.1 kmph . answer : a
Answer: a
Python program:
a = 4 - 5
b = 4 + 5 
c = b / 2
Problem: nails and screws are manufactured at a uniform weight per nail and a uniform weight per screw . if the total weight of one screw and one nail is half that of 6 screws and one nail , then the total weight of 3 screws , and 3 nails is how many times that of 1.5 screws and 4.5 nails ?
Options: a ) a . 4 , b ) b . 5 / 2 , c ) c . 2 , d ) d . 3 / 2 , e ) e . 20 / 11
Rationale: "let the weight of nail be n and that of screw be s . . so s + w = 1 / 2 * ( 6 s + 1 n ) . . . or 1 n = 4 s . . lets see the weight of 3 s and 3 n = 3 s + 3 * 4 s = 15 s . . and weight of 1.5 s and 4.5 n = 1.5 s + 4.5 * 1.5 s = 8.25 s . . ratio = 15 s / 8.25 s = 15 / 8.25 = 20 / 11 e"
Answer: e
Python program:
a = 3 * 4
b = a + 3 
c = b / 10
Problem: a camera lens filter kit containing 5 filters sells for $ 52.50 . if the filters are purchased individually , 2 of them are priced at $ 6.45 each , 2 at $ 11.05 each , 1 at $ 15.50 . the amount saved by purchasing the kit is what percent of the total price of the 5 filters purchased individually ?
Options: a ) 3.76 % , b ) 4.76 % , c ) 5.76 % , d ) 6.76 % , e ) 7.76 %
Rationale: "cost of kit = $ 52.50 if filters are purchased individually - $ 6.45 * 2 + $ 11.05 * 2 + $ 15.50 = $ 50.50 amount saved = $ 52.50 - $ 50.50 = $ 2.50 required % age = ( $ 2.50 / $ 52.50 ) * 100 = 4.76 % so , the correct answer is b ."
Answer: b
Python program:
a = 2 * 6
b = 2 * 11
c = a + b 
d = 15 + 50 
e = 52 - 50
f = e * 100
g = f / 52
Problem: the average age of 35 students in a class is 16 years . the average age of 21 students is 14 . what is the average age of remaining 2 students ?
Options: a ) 133 years , b ) 177 years , c ) 119 years , d ) 212 years , e ) none
Rationale: "solution sum of the ages of 14 students = ( 16 x 35 ) - ( 14 x 21 ) = 560 - 294 . = 266 . ∴ required average = 266 / 2 = 133 years . answer a"
Answer: a
Python program:
a = 35 * 16
b = a + 21 
c = b + 35 
d = 35 * 16
e = c - d
Problem: if the sides of a cube are in the ratio 4 : 3 . what is the ratio of their diagonals ?
Options: a ) 4 : 3 , b ) 4 : 8 , c ) 4 : 1 , d ) 4 : 2 , e ) 4 : 7
Rationale: "a 1 : a 2 = 4 : 3 d 1 : d 2 = 4 : 3 answer : a"
Answer: a
Python program:
a = 4 / 3
Problem: if 638521 is to be divisible by 5 , what is the least whole number that should be added to ?
Options: a ) 8 , b ) 7 , c ) 5 , d ) 4 , e ) 3
Rationale: "a number is divisible by 5 if the last digit is either 0 or 5 . here , 638521 = 1 ( last digit is neither 0 or 5 ) . the next multiple of 5 i . e to make the last digit 0 or 5 add 4 4 must be added to 638521 to make it divisible by 5 d"
Answer: d
Python program:
a = math.floor(5)
b = a + 1
Problem: the manager at a health foods store mixes a unique superfruit juice cocktail that costs $ 1399.45 per litre to make . the cocktail includes mixed fruit juice and a ç ai berry juice , which cost $ 262.85 per litre and $ 3104.35 per litre , respectively . the manager has already opened 37 litres of the mixed fruit juice . how many litres of the a ç ai berry juice does he need to add ?
Options: a ) 17 litres , b ) 24.67 litres , c ) 11 litres , d ) 24.07 litres , e ) 38.67 litres
Rationale: "262.85 ( 37 ) + 3 , 104.35 x = 1 , 399.45 ( 37 + x ) solve the equation . 262.85 ( 37 ) + 3 , 104.35 x = 1 , 399.45 ( 37 + x ) 9725.45 + 3 , 104.35 x = 51779.65 + 1 , 399.45 x 9725.45 + 1 , 704.9 x = 51779.65 1 , 704.9 x = 42054.2 x ≈ 24.67 answer is b ."
Answer: b
Python program:
a = 37 * 1399
b = 37 * 262
c = a - b
d = 3104 - 35
e = c / d
Problem: two equilateral triangle of side 12 cm are placed one on top another , such a 6 pionted star is formed if the six vertices lie on a circle what is the area of the circle not enclosed by the star ?
Options: a ) 21
b ) 88937
c ) 269
d ) 279
e ) 2701
Rationale: answer : a
Answer: a
Python program:
a = math.sqrt(3)
b = a / 2
c = b * 12
d = c * 2
Problem: the average age of a class is 15.8 years . the average age of boys in the class is 16.4 years while that of girls is 15.4 years . what is the ratio of boys to girls in the class ?
Options: a ) 1 : 2 , b ) 3 : 4 , c ) 3 : 5 , d ) 2 : 3 , e ) none of these
Rationale: let x = number of girls y = number of boys sum of girls ages / x = 15.4 sum of boys ages / y = 16.4 the sum of the girls ' ages is 15.4 x , and boys ' sum is 16.4 y ( sum of girls ages + sum of boys ages ) / ( x + y ) = 15.8 ( 15.4 x + 16.4 y ) / ( x + y ) = 15.8 15.4 x + 16.4 y = 15.8 ( x + y ) 15.4 x + 16.4 y = 15.8 x + 15.8 y 0.6 y = 0.4 x 0.6 y / x = 0.4 y / x = 0.4 / 0.6 y / x = 2 / 3 which is the ratio of boys to girls answer : d
Answer: d
Python program:
a = 15 - 8
b = 16 - 4
c = a / b
Problem: subtracting 7 % of a from a is equivalent to multiplying a by how much ?
Options: a ) 0.93 , b ) 9.4 , c ) 0.094 , d ) 94 , e ) none
Rationale: "answer let a - 7 % of a = ab . ⇒ ( 93 x a ) / 100 = ab ∴ b = 0.93 correct option : a"
Answer: a
Python program:
a = 100 - 7
b = a / 100
Problem: a number divided by 84 leaves remainder 57 what is the remainder when same number divided by 12
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "add 84 + 57 = 141 now 141 divided by 12 so we get 9 as reaminder answer : c"
Answer: c
Python program:
a = 57 - 12
b = 57 - 12
c = a / b
Problem: a children ' s gift store sells gift certificates in denominations of $ 3 and $ 5 . the store sold ' m ' $ 3 certificates and ' n ' $ 5 certificates worth $ 93 on a saturday afternoon . if ' m ' and ' n ' are natural numbers , how many different values can ' m ' take ?
Options: a ) 5 , b ) 7 , c ) 6 , d ) 31 , e ) 18
Rationale: explanatory answer step 1 : key data 1 . total value of all certificates sold = $ 93 . 2 . certificates sold were in denominations of $ 3 and $ 5 . 3 . both ' m ' and ' n ' are natural numbers . step 2 : approach the value of all certificates sold , 93 is divisible by 3 . so , a maximum of 31 $ 3 certificates and no $ 5 certificates could have been sold . however , the question states that both ' m ' and ' n ' are natural numbers . hence , at least 1 $ 5 certificate should have been sold . let us reduce the number of $ 3 certificates from theoretical maximum count of 31 by say ' x ' and correspondingly increase $ 5 certificates by ' y ' . evidently , 3 x = 5 y because the value of $ 3 certificates reduced should be the same as the value of $ 5 certificates increased . it means that x has to be a multiple of 5 and y has to be a multiple of 3 . or $ 3 certificates reduce in steps of 5 certificates . step 3 : list down possibilities the following combinations are possible 1 . m = 26 , n = 3 2 . m = 21 , n = 6 3 . m = 16 , n = 9 4 . m = 11 , n = 12 5 . m = 6 , n = 15 6 . m = 1 , n = 18 an alternative way to think of the same concept - replacing five $ 3 certificates with three $ 5 certificates leads to no change in the overall value of certficates sold and gives us a new combination each time . we need to see how many such combinations are possible . answer c
Answer: c
Python program:
a = 93 / 3
b = a / 5
c = math.floor(b)
Problem: how long will a boy take to run round a square field of side 45 meters , if he runs at the rate of 9 km / hr ?
Options: a ) 72 sec , b ) 45 sec , c ) 1 min , d ) 32 sec , e ) 25 sec
Rationale: "speed = 9 km / hr = 9 * 5 / 18 = 5 / 2 m / sec distance = 45 * 4 = 180 m time taken = 180 * 2 / 5 = 72 sec answer is a"
Answer: a
Python program:
a = 45 * 4
b = 1000 / 3600
c = 9 * b
d = a / c
Problem: what is the greatest positive integer w such that 3 ^ w is a factor of 9 ^ 10 ?
Options: a ) 5 , b ) w = 9 , c ) w = 10 , d ) w = 20 , e ) w = 30
Rationale: "what is the greatest positive integer w such that 3 ^ w is a factor of 9 ^ 10 ? 9 ^ 10 = ( 3 ^ 2 ) ^ 10 = 3 ^ 20 d . 20"
Answer: d
Python program:
a = 9 - 10
b = a * 10
Problem: in a group of 100 people , 60 like volleyball , 50 like hockey . how many like both volleyball and hockey ?
Options: a ) 20 , b ) 15 , c ) 10 , d ) 5 , e ) 25
Rationale: "make a venn diagram , and enter your data . let the number of people who like both volleyball and hockey be x 60 - x + x + 50 - x = 100 x = 10 so number who like both volleyball and hockey = 10 answer c"
Answer: c
Python program:
a = 60 - 50
b = 50 + a 
c = b + 50
Problem: triathlete dan runs along a 2 - mile stretch of river and then swims back along the same route . if dan runs at a rate of 10 miles per hour and swims at a rate of 8 miles per hour , what is his average rate for the entire trip in miles per minute ?
Options: a ) 1 / 7 , b ) 2 / 15 , c ) 3 / 15 , d ) 1 / 4 , e ) 3 / 8
Rationale: "dan travels 4 miles round trip . running part : ( 2 / 10 = 1 / 5 * 60 = 12 minutes ) swimming part : ( 2 / 8 = 1 / 4 * 60 = 15 minutes ) 4 miles in ( 12 + 15 ) minutes 4 / 27 = 1 / 7 mile per minute answer : 1 / 7 mile per minute a"
Answer: a
Python program:
a = 2 + 2 
b = 2 / 8
c = b * const_60
d = 2 / 10
e = d * const_60
f = c + e 
g = a / f
Problem: a train 360 m long is running at a speed of 48 km / hr . in what time will it pass a bridge 140 m long ?
Options: a ) 40 sec , b ) 11 sec , c ) 37.5 sec , d ) 19 sec , e ) 10 sec
Rationale: "speed = 48 * 5 / 18 = 40 / 3 m / sec total distance covered = 360 + 140 = 500 m required time = 500 * 3 / 40 = 37.5 sec answer : c"
Answer: c
Python program:
a = 48 - 140
b = a * const_0_2778
c = 360 / b
Problem: a train covers a distance of 100 km in 1 hour . if its speed is decreased by 30 km / hr , the time taken by the car to cover the same distance will be ?
Options: a ) 1 hr , b ) 1 hr 25 min , c ) 50 min , d ) 1 hr 30 min , e ) 1 hr 45 min
Rationale: "speed = 100 / 1 = 100 km / hr new speed = 100 - 30 = 70 km / hr time taken = 100 / 70 = 1 hr 25 min answer is b"
Answer: b
Python program:
a = 100 / 1
b = a - 30
c = 100 / b
Problem: the ratio of the present age of sandy to that of molly is 7 : 2 . sixteen years from now , the ratio of the ages of sandy to molly will be 5 : 2 . what was sandy ' s age 6 years ago ?
Options: a ) 66 , b ) 70 , c ) 74 , d ) 78 , e ) 82
Rationale: let the present age of sandy be 7 x years and that of molly be 2 x years . ( 7 x + 16 ) / ( 2 x + 16 ) = 5 / 2 4 x = 48 x = 12 six years ago , sandy ' s age was 7 ( 12 ) - 6 = 78 the answer is d .
Answer: d
Python program:
a = 10 + 6 
b = 5 * a
c = 10 + 6 
d = 2 * c
e = b - d
f = e * 7
g = 2 + 2 
h = f / g
i = h - 6
Problem: evaluate : 50 - 12 * 3 * 2 = ?
Options: a ) 62 , b ) 52 , c ) 32 , d ) 12 , e ) 42
Rationale: "according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 50 - 12 * 3 * 2 = 50 - 8 = 42 correct answer e"
Answer: e
Python program:
a = 12 * 3
b = a * 2
c = 50 - b
Problem: a grocer has 400 pounds of coffee in stock , 20 percent of which is decaffeinated . if the grocer buys another 100 pounds of coffee of which 60 percent is decaffeinated , what percent , by weight , of the grocer ’ s stock of coffee is decaffeinated ?
Options: a ) 28 % , b ) 30 % , c ) 32 % , d ) 34 % , e ) 40 %
Rationale: "1 . 20 % of 400 = 80 pounds of decaffeinated coffee 2 . 60 % of 100 = 60 pounds of decaffeinated coffee 3 . wt have 140 pounds of decaffeinated out of 500 pounds , that means 140 / 500 * 100 % = 28 % . the correct answer is a ."
Answer: a
Python program:
a = 20 / 100
b = a * 400
c = 60 / 100
d = 100 * c
e = b + d 
f = 400 + 100 
g = e / f
h = g * 100
Problem: the area of a parallelogram is 1764 sq m and its base is nine times size of the corresponding altitude . then the length of the base is ?
Options: a ) 21 , b ) 9 , c ) 11 , d ) 14 , e ) 7
Rationale: "9 x * x = 1764 = > x = 14 answer : d"
Answer: d
Python program:
a = 1764 / 2
b = math.sqrt(a)
Problem: at what rate percent per annum will a sum of money double in 8 years .
Options: a ) 12.5 % , b ) 12.9 % , c ) 18.5 % , d ) 11.5 % , e ) 12.3 %
Rationale: "explanation : let principal = p , then , s . i . = p and time = 8 years rate = [ ( 100 x p ) / ( p x 8 ) ] % = 12.5 % per annum . answer : a ) 12.5 %"
Answer: a
Python program:
a = 100 / 8
Problem: paper charge is rs . 60 per kg . how much expenditure would be there to cover a cube of edge 10 m with a paper , if one kg of paper covers 20 sq . m . area ?
Options: a ) rs . 2250
b ) rs . 3600
c ) rs . 2700
d ) rs . 1800
e ) none of these
Rationale: explanation : total surface area of the cube = 6 x ( 10 ) 2 = 600 sq . m 1 kg covers 20 sq . m area , for 600 we need = 600 / 20 = 30 kg paper . expenditure = rate x quantity = rs . 60 x 30 kg = rs . 1800 answer is d
Answer: d
Python program:
a = 60 / 10
b = 10 * 10
c = a * b
d = c / 20
e = d * 60
Problem: a shopkeeper sells his goods at cost price but uses a weight of 800 gm instead of kilogram weight . what is his profit percentage ?
Options: a ) 25 % , b ) 18 % , c ) 20 % , d ) 40 % , e ) 45 %
Rationale: "100 ( 1000 - 800 ) / 800 = 25 % profit percentage = 25 % answer a"
Answer: a
Python program:
a = 4 + 1 
b = 4 + 1 
c = a + b 
d = c * 100
e = d - 800
f = e / 800
g = f * 100
Problem: how many odd numbers between 10 and 900 are the squares of integers ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: "the square of an odd number is an odd number : 10 < odd < 1,000 10 < odd ^ 2 < 1,000 3 . something < odd < 31 . something ( by taking the square root ) . so , that odd number could be any odd number from 5 to 31 , inclusive : 5 , 7 , 9 , 11 , 13 , 15 , 17 , 19 , 21 , 23 , 25 , 27 , 29 , and 31 . 13 numbers . answer : b ."
Answer: b
Python program:
a = 10 + 4
Problem: what is the value of x ^ 2 yz − xyz ^ 2 , if x = 2 , y = 1 , and z = 2 ?
Options: a ) 20 , b ) 24 , c ) 0 , d ) 32 , e ) 48
Rationale: "4 * 1 * 2 - ( 2 * 1 * 4 ) = 8 + 8 = 0 ans : c"
Answer: c
Python program:
a = negate * (
b = a * 1
c = b * 1
Problem: by selling 18 pencils for a rupee a man loses 10 % . how many for a rupee should he sell in order to gain 35 % ?
Options: a ) 11 , b ) 13 , c ) 15 , d ) 18 , e ) 12
Rationale: 90 % - - - 18 135 % - - - ? 90 / 135 * 18 = 12 answer : e
Answer: e
Python program:
a = 100 + 35 
b = 100 - 10
c = 1 / b
d = a * c
e = 1 / d
f = e * 18
Problem: how many pieces of 0.35 meteres can be cut from a rod 12.5 meteres long
Options: a ) 30 , b ) 40 , c ) 35 , d ) 60 , e ) 70
Rationale: "explanation : we need so simple divide 42.5 / 0.85 , = ( 1250 / 35 ) = 35 option c"
Answer: c
Python program:
a = 12 / 5
Problem: in a class , 7 students like to play basketball and 5 like to play cricket . 3 students like to play on both basketball and cricket . how many students like to play basketball or cricket or both ?
Options: a ) 12 , b ) 15 , c ) 16 , d ) 9 , e ) 22
Rationale: "draw a venn diagram yourself ! b + c - bc = number of students that play either basketball or cricket 7 + 5 - 3 = 9 d )"
Answer: d
Python program:
a = 7 + 5 
b = a - 3
Problem: a jar contains only red , yellow , and orange marbles . if there are 3 red , 6 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ?
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
Rationale: "i started by finding the 2 probabilities , without calculation , like this : p ( yyr ) p ( yry ) p ( ryy ) i calculated the first one and ended in 1 / 22 . i looked at the answer choices at this point and saw answer d : 3 / 22 . this helped me realise that for the 3 possible orderings the probabbility is the same . so , it should be ( 1 / 22 ) * ( 6 ) , which indeed is 6 / 22 . e"
Answer: e
Python program:
a = math.comb(6, 2)
b = math.comb(3, 1)
c = a * b
d = 6 + 4 
e = d + 3 
f = math.comb(e, 3)
g = c / f
Problem: jerry travels 8 miles at an average speed of 40 miles per hour , stops for 12 minutes , and then travels another 20 miles at an average speed of 60 miles per hour . what is jerry ’ s average speed , in miles per hour , for this trip ?
Options: a ) 42 , b ) 42.5 , c ) 44 , d ) 50 , e ) 52.5
Rationale: "total time taken by jerry = ( 8 / 40 ) * 60 minutes + 12 minutes + ( 20 / 60 ) * 60 minutes = 44 minutes average speed = total distance / total time = ( 8 + 20 ) miles / ( 44 / 60 ) hours = 28 * 60 / 44 = 42 miles per hour answer : option a"
Answer: a
Python program:
a = 8 + 20 
b = 8 / 40
c = 12 / 60
d = b + c 
e = 20 / 60
f = d + e 
g = a / f
Problem: 8 men can dig a pit in 20 days . if a men work half as much again as a boy , then 4 men and 9 boys can dig a similar pit . fint the days for 15 boys can dig ?
Options: a ) 17 , b ) 10 , c ) 15 , d ) 20 , e ) 16
Rationale: 1 man = 3 / 2 boys ( 4 men + 9 boys ) = 15 boys 8 men = [ ( 3 / 2 ) + 8 ] = 12 boys now , 12 boys can dig the pit in 20 days . 15 boys can dig = 16 days . answer is option e
Answer: e
Python program:
a = 15 - 9
b = a / 4
c = 8 * b
d = c * 20
e = d / 15
Problem: a man invests in a 16 % stock at 128 . the interest obtained by him is
Options: a ) 22.5 % , b ) 42.5 % , c ) 12.5 % , d ) 62.5 % , e ) 82.5 %
Rationale: by investing rs 128 , income derived = rs . 16 by investing rs . 100 , income derived = = rs . 12.5 interest obtained = 12.5 % answer : c
Answer: c
Python program:
a = 16 / 128
b = a * 100
Problem: in what ratio must tea at rs . 60 per kg be mixed with tea at rs . 70 per kg so that the mixture must be worth rs . 63 per kg ?
Options: a ) 3 : 1 , b ) 3 : 2 , c ) 4 : 3 , d ) 7 : 3 , e ) none
Rationale: "required ratio = 700 : 300 = 7 : 3 answer d"
Answer: d
Python program:
a = 70 - 63
b = 63 - 60
c = a / b
Problem: how many pounds of salt at 80 cents / lb must be mixed with 40 lbs of salt that costs 35 cents / lb so that a merchant will get 20 % profit by selling the mixture at 48 cents / lb ?
Options: a ) 5 , b ) 15 , c ) 40 , d ) 50 , e ) 25
Rationale: "selling price is 48 cents / lb for a 20 % profit , cost price should be 40 cents / lb ( cp * 6 / 5 = 48 ) basically , you need to mix 35 cents / lb ( salt 1 ) with 80 cents / lb ( salt 2 ) to get a mixture costing 40 cents / lb ( salt avg ) weight of salt 1 / weight of salt 2 = ( salt 2 - saltavg ) / ( saltavg - salt 1 ) = ( 80 - 40 ) / ( 40 - 35 ) = 8 / 1 we know that weight of salt 1 is 40 lbs . weight of salt 2 must be 5 lbs . answer ( a )"
Answer: a
Python program:
a = 48 * 40
b = 100 + 20 
c = b / 100
d = 35 * 40
e = c * d
f = a - e
g = 100 + 20 
h = g / 100
i = 80 * h
j = i - 48
k = f / j
Problem: how long does a train 120 meters long running at the rate of 54 kmph take to cross a bridge 660 meters in length ?
Options: a ) 33 , b ) 72 , c ) 52 , d ) 82 , e ) 62
Rationale: explanation : t = ( 660 + 120 ) / 54 * 18 / 5 t = 52 answer : option c
Answer: c
Python program:
a = 120 + 660 
b = 54 * const_0_2778
c = a / b
Problem: if 2 cards are selected at random from the deck of 52 cards then what is the probability of one of the selected cards will be king and other will be 10 ? a deck of cards has a total of 52 cards , consisting of 4 suits ; ( spades ( black ) , hearts ( red ) , diamond ( red ) s , and clubs ( black ) ) ; and 13 cards including 1 king , 1 queen and 1 jack in each suit
Options: a ) 8 / 2652 , b ) 18 / 2652 , c ) 1 / 2652 , d ) 12 / 2652 , e ) 16 / 2652
Rationale: 2 possible cases : king - 10 or 10 - king ( 4 kings and 4 10 ) . either way , the total probability = 2 ( king - 10 ) = 2 ( 4 / 52 * 4 / 51 ) = 18 / 2652 . b is the correct answer .
Answer: b
Python program:
a = 4 - 1
b = 4 - 1
c = a * b
d = c * 2
e = 52 - 1
f = 52 * e
g = d / f
Problem: a and b are two multiples of 14 , and q is the set of consecutive integers between a and b , inclusive . if q contains 10 multiples of 14 , how many multiples of 7 are there in q ?
Options: a ) 20 , b ) 19 , c ) 18 , d ) 17 , e ) 16
Rationale: "halfway between the multiples of 14 , there will be another multiple of 7 . the total number of multiples of 7 is 10 + 9 = 19 . the answer is b ."
Answer: b
Python program:
a = 10 * 2
b = a - 1
Problem: 60 persons like apple . 7 like orange and mango dislike apple . 10 like mango and apple and dislike orange . 4 like all . how many people like apple ?
Options: a ) 47 , b ) 46 , c ) 54 , d ) 58 , e ) 67
Rationale: "orange + mango - apple = 7 mango + apple - orange = 10 apple = 60 orange + mango + apple = 4 60 + 10 + 4 - 7 = 67 like apple answer : e"
Answer: e
Python program:
a = 60 - 4
b = a + 7 
c = 10 - 7
d = b + c
Problem: bhanu spends 30 % of his income on petrol on scooter 20 % of the remaining on house rent and the balance on food . if he spends rs . 300 on petrol then what is the expenditure on house rent ?
Options: a ) 2287 , b ) 140 , c ) 128 , d ) 797 , e ) 123
Rationale: "given 30 % ( income ) = 300 ⇒ ⇒ income = 1000 after having spent rs . 300 on petrol , he left with rs . 700 . his spending on house rent = 20 % ( 700 ) = rs . 140 answer : b"
Answer: b
Python program:
a = 30 / 100
b = 300 / a
c = b - 300
d = 20 / 100
e = c * d
Problem: the average of the first 5 multiples of 9 is :
Options: a ) 20 , b ) 27 , c ) 28 , d ) 30 , e ) none of these
Rationale: solution : required average = ( total sum of multiple of 9 ) / 5 = ( 9 + 18 + 27 + 36 + 45 ) / 5 = 27 note that , average of 9 and 45 is also 27 . and average of 18 and 36 is also 27 . answer : option b
Answer: b
Python program:
a = 9 * 2
b = 9 + a 
c = 9 * 3
d = b + c 
e = 9 * 4
f = d + e 
g = 9 * 5
h = f + g 
i = h / 5
Problem: 13 different biology books and 8 different chemistry books lie on a shelf . in how many ways can a student pick 2 books of each type ?
Options: a ) 80 , b ) 160 , c ) 720 , d ) 1100 , e ) 2184
Rationale: "no . of ways of picking 2 biology books ( from 13 books ) = 13 c 2 = ( 13 * 12 ) / 2 = 78 no . of ways of picking 2 chemistry books ( from 8 books ) = 8 c 2 = ( 8 * 7 ) / 2 = 28 total ways of picking 2 books of each type = 78 * 28 = 2184 ( option e )"
Answer: e
Python program:
a = math.factorial(13)
b = 13 - 2
c = math.factorial(b)
d = a / c
e = d / 2
f = math.factorial(8)
g = 8 - 2
h = math.factorial(g)
i = f / h
j = i / 2
k = e * j
Problem: real - estate salesman z is selling a house at a 20 percent discount from its retail price . real - estate salesman x vows to match this price , and then offers an additional 20 percent discount . real - estate salesman y decides to average the prices of salesmen z and x , then offer an additional 20 percent discount . salesman y ' s final price is what fraction of salesman x ' s final price ?
Options: a ) 29 / 32 , b ) 28 / 31 , c ) 30 / 31 , d ) 40 / 41 , e ) 34 / 15
Rationale: "let the retail price be = x selling price of z = 0.80 x selling price of x = 0.80 * 0.80 x = 0.64 x selling price of y = ( ( 0.80 x + 0.64 x ) / 2 ) * 0.80 = 0.72 x * 0.80 = 0.58 x 0.58 x = k * 0.64 x k = 0.58 / 0.64 = 58 / 64 = 29 / 32 answer : a"
Answer: a
Python program:
a = 100 - 20
b = 100 - 20
c = 100 - 20
d = c / 100
e = b * d
f = a + e 
g = f / 2
h = 100 - 20
i = g * h
j = i / 100
k = 100 - 20
l = 100 - 20
m = l / 100
n = k * m
o = j / n
p = o * 10
Problem: how many integers between 100 and 160 , inclusive , can not be evenly divided by 3 nor 5 ?
Options: a ) 32 , b ) 27 , c ) 25 , d ) 35 , e ) 29
Rationale: "the total numbers between 100 and 160 , inclusive , is 61 . 3 * 34 = 102 and 3 * 53 = 159 so the number of multiples of 3 is 20 . 5 * 20 = 100 and 5 * 32 = 160 so the number of multiples of 5 is 13 . however , the multiples of 15 have been counted twice . 15 * 7 = 105 and 15 * 10 = 150 so the number of multiples of 15 is 4 . thus the total number is 61 - 20 - 13 + 4 = 32 . the answer is a ."
Answer: a
Python program:
a = 2 * 100
b = 3 + 4 
c = b * 10
d = a + c 
e = d + 2 
f = 160 - e
Problem: calculate the share of y , if rs . 690 is divided among x , y and z in the ratio 5 : 7 : 11 ?
Options: a ) 190 , b ) 160 , c ) 120 , d ) 151 , e ) 150
Rationale: "5 + 7 + 11 = 23 690 / 23 = 30 so y ' s share = 5 * 30 = 150 answer : e"
Answer: e
Python program:
a = 5 + 7 
b = a + 11 
c = 690 / b
d = c * 5