euclaise/mathqa_programs huggingface dataset:
Problem: if a randomly selected non - negative single digit integer is added to { 2 , 3 , 4 , 9 } . what is the probability that the median of the set will increase but the range still remains the same ?
Options: a ) 0.2 , b ) 0.3 , c ) 0.4 , d ) 0.5 , e ) 0.6
Rationale: "we are selecting from non - negative single digit integers , so from { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } . these 10 digits represent the total number of outcomes . hence , the total number of outcomes is 10 . we need to find the probability that the median of the set will increase but the range still remains the same . the median of the set is ( 3 + 4 ) / 2 = 3.5 , thus the number selected must be 4 or greater . for the range to remain the same , the number must be between 2 and 9 inclusive . to satisfy both conditions , the number selected must be 4 , 5 , 6 , 7 , 8 , or 9 . the probability is 6 / 10 = 0.6 the answer is e ."
Answer: e
Python program:
a = 4 / 10
Problem: keats library purchases a number of new books , all in the category of biography , and the library does not acquire any other books . with the addition of the new biographies , the biography collection of the library amounts to 32 % of the total number of books in the library . if prior to the purchase , only 20 % of the books in keats library were biographies , by what percent has the number of biographies in the library increased ?
Options: a ) 60 % , b ) 72 % , c ) 88 % , d ) 95 % , e ) 110 %
Rationale: let x be the number of new biographies added to the library . let b be the original number of biographies , so the original number of books was 5 b . 0.32 ( 5 b + x ) = b + x 0.6 b = 0.68 x x = 0.88 b the answer is c .
Answer: c
Python program:
a = 32 * 100
b = 20 * 100
c = a - b
d = 100 - 32
e = c / d
f = e / 20
g = f * 100
Problem: in a class of 20 students in an examination in mathematics 2 students scored 100 marks each , 3 get zero each and the average of the rest was 40 . what is the average of the whole class ?
Options: a ) 46 , b ) 49 , c ) 40 , d ) 38 , e ) 35
Rationale: total marks obtained by a class of 20 students = 2 * 100 + 3 * 0 + 15 * 40 = 200 + 600 = 800 : average marks of whole class = 800 / 20 = 40 answer is c .
Answer: c
Python program:
a = 20 - 2
b = a - 3
c = 40 * b
d = 2 * 100
e = c + d 
f = e / 20
Problem: the cost of an article is decreased by 20 % . if the original cost is $ 40 , find the decrease cost .
Options: a ) 33 , b ) 32 , c ) 68 , d ) 36 , e ) 38
Rationale: "original cost = $ 40 decrease in it = 20 % of $ 40 = 20 / 100 ã — 40 = 800 / 100 = $ 8 therefore , decrease cost = $ 40 - $ 8 = $ 32 answer : b"
Answer: b
Python program:
a = 40 * 20
b = a / 100
Problem: two pipes a and b can separately fill a cistern in 24 minutes and 48 minutes respectively . there is a third pipe in the bottom of the cistern to empty it . if all the three pipes are simultaneously opened , then the cistern is full in 12 minutes . in how much time , the third pipe alone can empty the cistern ?
Options: a ) 90 min , b ) 48 min , c ) 54 min , d ) 120 min , e ) 130 min
Rationale: "1 / 12 - ( 1 / 24 + 1 / 48 ) = - 1 / 48 third pipe can empty in 48 minutes answer : b"
Answer: b
Python program:
a = 1/(24)
b = 1/(48)
c = a + b 
d = 1/(12)
e = c - d
f = 1/(e)
Problem: a can do a piece of work in 20 days , and b can do it in 15 days . how long will they take if both work together ?
Options: a ) 7 days , b ) 8.6 days , c ) 13 days , d ) 5.6 days , e ) 10 days
Rationale: a + b can do the work in 20 * 15 / 20 + 15 = 20 * 15 / 35 = 8.6 days answer is b
Answer: b
Python program:
a = 1/(15)
b = 1/(20)
c = a + b 
d = 1/(c)
Problem: if the sides of a triangle are 28 cm , 26 cm and 12 cm , what is its area ?
Options: a ) 120 cm 2 , b ) 156 cm 2 , c ) 178 cm 2 , d ) 189 cm 2 , e ) 176 cm 2
Rationale: "the triangle with sides 28 cm , 26 cm and 12 cm is right angled , where the hypotenuse is 28 cm . area of the triangle = 1 / 2 * 26 * 12 = 156 cm 2 answer : b"
Answer: b
Python program:
a = 26 * 12
b = a / 2
Problem: the average weight of 29 students is 28 kg . by the admission of a new student , the average weight is reduced to 27.4 kg . the weight of the new student is
Options: a ) 22 kg , b ) 21.6 kg , c ) 22.4 kg , d ) 10 kg , e ) none of these
Rationale: "exp . the total weight of 29 students = 29 * 28 the total weight of 30 students = 30 * 27.4 weight of the new student = ( 30 * 27.4 – 29 * 28 ) = 822 - 812 = 10 answer : d"
Answer: d
Python program:
a = 29 + 1 
b = a * 27
c = 29 * 28
d = b - c
Problem: 22 buckets of water fill a tank when the capacity of each bucket is 13.5 litres . how many buckets will be required to fill the same tank if the capacity of each bucket is 9 litres ?
Options: a ) 33 , b ) 32 , c ) 60 , d ) data inadequate , e ) none of these
Rationale: "capacity of the tank = 22 ã — 13.5 = 297 litres when the capacity of each bucket = 9 litres , then the required no . of buckets = 297 â  „ 9 = 33 answer a"
Answer: a
Python program:
a = 13 * 5
b = a / 9
Problem: find a positive number which when increased by 17 is equal to 60 times the reciprocal of the number ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 9
Rationale: let the number be x . then , x + 17 = 60 x x 2 + 17 x - 60 = 0 ( x + 20 ) ( x - 3 ) = 0 x = 3 option a
Answer: a
Python program:
a = math.gcd(60, 17)
b = 2 + a
Problem: the arithmetic mean and standard deviation of a certain normal distribution are 17.5 and 2.5 , respectively . what value is exactly 2 standard deviations less than the mean ?
Options: a ) 10.5 , b ) 11 , c ) 11.5 , d ) 12 , e ) 12.5
Rationale: "mean = 17.5 two standard deviations is 2.5 + 2.5 = 5.0 there could be two calues for this . mean + two standard deviations = 22.5 mean - two standard deviations = 12.5 answer choice has 12.5 and so e is the answer ."
Answer: e
Python program:
a = 2 * 2
b = 17 - 5
Problem: in a group of 130 people , 90 have an age of more 30 years , and the others have an age of less than 20 years . if a person is selected at random from this group , what is the probability the person ' s age is less than 20 ?
Options: a ) 0.31 , b ) 0.55 , c ) 0.65 , d ) 0.75 , e ) 0.85
Rationale: "number of people whose age is less than 20 is given by 130 - 90 = 40 probability p that a person selected at random from the group is less than 20 is given by 40 / 130 = 0.31 correct answer a"
Answer: a
Python program:
a = 130 - 90
b = a / 130
Problem: a store reported total sales of $ 385 million for february of this year . if the total sales for the same month last year was $ 320 million , approximately what was the percent increase e in sales ?
Options: a ) 2 % , b ) 17 % , c ) 20 % , d ) 65 % , e ) 83 %
Rationale: "last year ' s sales = $ 320 million ; this year ' s sales = $ 385 million ; increase e = $ 65 million . now , 20 % of $ 320 million is $ 64 million , which is very close to actual increase of $ 65 million . answer : c ."
Answer: c
Python program:
a = 385 - 320
b = a / 320
c = b * 100
Problem: a city with a population of 126,160 is to be divided into 7 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district . what is the minimum possible population that the least populated district could have ?
Options: a ) 16,500 , b ) 16,600 , c ) 16,700 , d ) 16,800 , e ) 16,900
Rationale: "the minimum possible population occurs when all the other districts have a population that is 10 % greater than the least populated district . let p be the population of the least populated district . then 126,160 = p + 6 ( 1.1 ) p 7.6 p = 126,160 p = 16,600 the answer is b ."
Answer: b
Python program:
a = 1000 * 100
b = 3600 - 100
c = b - 1000
d = a - c
e = d / 1000
f = 10 / 100
g = 1 + f 
h = 7 - 1
i = g * h
j = i + 1 
k = e / j
Problem: find the largest 3 digit number which is exactly divisible by 88 ?
Options: a ) 765 , b ) 907 , c ) 944 , d ) 954 , e ) 968
Rationale: "largest 3 digit number is 999 after doing 999 ÷ 88 we get remainder 31 hence largest 3 digit number exactly divisible by 88 = 999 - 31 = 968 e"
Answer: e
Python program:
a = 100 * 100
b = 100 * 10
c = a + b 
d = 100 * 3
e = c + d 
f = 3 * 10
g = e + f 
h = g + 3 
i = h * 88
Problem: if a = { 17 , 27 , 31 , 53 , 61 } , what is the sum of mean and median of the numbers in a ?
Options: a ) 69 , b ) 75 , c ) 82 , d ) 91 , e ) 56
Rationale: mean = ( 17 + 27 + 31 + 53 + 62 ) / 5 = 38 median = 31 sum = 38 + 31 = 69 option a
Answer: a
Python program:
a = 17 + 27 
b = a + 31 
c = b + 53 
d = c + 61 
e = 4 + 1 
f = d / e
g = f + 31
Problem: the simple interest on a certain sum of money at the rate of 5 % p . a . for 8 years is rs . 840 . at what rate of intrest the same amount of interest can be received on the same sum after 5 years .
Options: a ) 5 % , b ) 6 % , c ) 7 % , d ) 8 % , e ) 9 %
Rationale: "explanation : here firstly we need to calculate the principal amount , then we can calculate the new rate . p = s . i . ∗ 100 / r ∗ t p = 840 ∗ 100 / 5 ∗ 8 p = 2100 required rate = 840 ∗ 100 / 5 ∗ 2100 r = 8 % option d"
Answer: d
Python program:
a = 840 / 5
b = 840 / 8
c = 5 / 100
d = b / c
e = a / d
f = e * 100
Problem: two cards are drawn together from a pack of 52 cards . the probability that one is a club and other is a diamond , is :
Options: a ) 29 / 34 , b ) 47 / 100 , c ) 3 / 20 , d ) 13 / 102 , e ) none of these
Rationale: explanation : one card drawn . probability of being it club or diamond = ( 13 x 2 ) / 52 . another card drawn . now , probability of being it of other suit ( the suit among the two , not selected in first draw ) = 13 / 51 . hence , probability of event = ( ( 13 x 2 ) / 52 ) x ( 13 / 51 ) = 13 / 102 . answer : d
Answer: d
Python program:
a = 52 / 4
b = 52 / 4
c = a * b
d = 52 * 52
e = c / d
f = e * 2
Problem: a rectangular tiled patio is composed of 160 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 160 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 = 160 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 ) = 160 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 = 160 ( 2 r - 4 ) * r = 160 2 r ^ 2 - 4 r - 160 = 0 r can not be negative so r = 10 and c = 16 so , answer will be c"
Answer: c
Python program:
a = negate + ( 
b = 4 ** 2
c = 160 * 2
d = 4 * c
e = b + d 
f = math.sqrt(e)
g = a / f
h = 160 / g
Problem: 8 machines can do a work in 10 days . how many machines are needed to complete the work in 40 days ?
Options: a ) 2 , b ) 6 , c ) 4 , d ) 7 , e ) 5
Rationale: "required number of machines = 8 * 10 / 40 = 2 answer is a"
Answer: a
Python program:
a = 8 * 10
b = a / 40
Problem: a ' s speed is 15 / 13 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that b beats a by 40 % of the length of the race ?
Options: a ) 44 % , b ) 48 % , c ) 52 % , d ) 42 % , e ) 46 %
Rationale: "first calculate the distance , b has covered with his speed in the time , in which a reached 60 % of the race . then add the remaining distance as head start for b to win the race . its best to apply ratios concept here . since a ' s speed is 15 / 13 of b , therefore , b ' s speed is 13 / 15 of a distance covered by b = speed x time = ( 13 / 15 ) x ( 0.6 ) = 0.52 % ( which means b would have covered 0.52 of the race length during the time in which a has covered 0.6 of the race length . therefore to win , b needs a headstart of ( 1 - 0.52 = ) 0.48 of the race length . so the answer is b"
Answer: b
Python program:
a = 100 - 40
b = a / 100
c = 13 / 15
d = b * c
e = 1 - d
f = e * 100
Problem: what is the radius of the incircle of the triangle whose sides measure 5 , 12 and 13 units ?
Options: a ) 2 units
b ) 12 units
c ) 6.5 units
d ) 6 units
e ) 7.5 units
Rationale: explanatory answer in a right angled triangle , the radius of the incircle = s - h , where ' s ' is the semi perimeter of the triangle and ' r ' is the radius of the inscribed circle . the semi perimeter of the triangle = a + b + c / 2 = 5 + 12 + 13 / 2 = 15 therefore , r = 15 - 13 = 2 units . choice a
Answer: a
Python program:
a = 5 * 12
b = 5 + 12 
c = b + 13 
d = a / c
Problem: along a yard 414 metres long , 24 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between two consecutive trees
Options: a ) 18 , b ) 19 , c ) 10 , d ) 11 , e ) 12
Rationale: explanation : 24 trees have 23 gaps between them , required distance ( 414 / 23 ) = 18 option a
Answer: a
Python program:
a = 24 - 1
b = 414 / a
Problem: at the opening of a trading day at a certain stock exchange , the price per share of stock k was $ 8 . if the price per share of stock k was $ 9 at the closing of the day , what was the percent increase in the price per share of stock k for that day ?
Options: a ) 1.4 % , b ) 5.9 % , c ) 11.1 % , d ) 12.5 % , e ) 23.6 %
Rationale: "opening = 8 closing = 9 rise in price = 1 so , percent increase = 18 ∗ 10018 ∗ 100 = > 12.50 % thus answer will be ( d )"
Answer: d
Python program:
a = 9 / 8
b = a - 1
c = b * 100
Problem: on a certain road 10 % of the motorists exceed the posted speed limit and receive speeding tickets , but 22 % 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 ) 12.8 % , c ) 15 % , d ) 22 % , e ) 30 %
Rationale: "answer is b . this question is in the og and thus well explained by ets . those who exceed : x so x = 10 % + 0,22 x id est x = 12,8 %"
Answer: b
Python program:
a = 10 / 100
b = 22 / 100
c = a * b
d = c * 100
e = 100 / d
Problem: a fruit seller had some oranges . he sells 40 % oranges and still has 480 oranges . how many oranges he had originally ?
Options: a ) 800 , b ) 710 , c ) 720 , d ) 730 , e ) 740
Rationale: "60 % of oranges = 480 100 % of oranges = ( 480 × 100 ) / 6 = 800 total oranges = 700 answer : a"
Answer: a
Python program:
a = 40 / 100
b = 480 * a
c = 480 + b
Problem: fresh grapes contain 70 % by weight while dried grapes contain 10 % water by weight . what is the weight of dry grapes available from 100 kg of fresh grapes ?
Options: a ) 18.33 kg , b ) 21.50 kg , c ) 25.00 kg , d ) 33.33 kg , e ) 40.39 kg
Rationale: "from the question we know : 100 kg * 70 % = 70 kg of water in the fresh grapes 100 kg - 70 kg of water = 30 kg of non - water mass we are looking for the weight of the dry grapes ( x ) . since the question tells us that 10 % of the weight of the dry graps is water and we know that 30 kg is non - water mass we can set up the following equation : x = 1 / 10 ( x ) + 30 kg 9 / 10 ( x ) = 30 kg x = 33.33 kg answer - d"
Answer: d
Python program:
a = 100 - 70
b = a * 100
c = b / 100
d = 100 - 10
e = c / d
f = e * 100
Problem: a hall 20 m long and 15 m broad is surrounded by a verandah of uniform width of 2.5 m . the cost of flooring the verandah at the rate of rs . 3.50 per sq . meter is
Options: a ) 500 , b ) 600 , c ) 650 , d ) 700 , e ) 750
Rationale: area of verandah = [ ( 25 ã ƒ â € ” 20 ) ? ( 20 ã ƒ â € ” 15 ) ] m â ² = 200 m â ² cost of flooring = rs . ( 200 ã ƒ â € ” 3.50 ) = rs . 700 answer : d
Answer: d
Python program:
a = 2 * 5
b = 20 + a 
c = 2 * 5
d = 15 + c 
e = b * d
f = 20 * 15
g = e - f
h = g * 3
Problem: a man rows his boat 90 km downstream and 55 km upstream , taking 3 hours each time . find the speed of the stream ?
Options: a ) 76 kmph , b ) 6 kmph , c ) 14 kmph , d ) 8 kmph , e ) 4 kmph
Rationale: "speed downstream = d / t = 90 / ( 3 ) = 30 kmph speed upstream = d / t = 55 / ( 3 ) = 18 kmph the speed of the stream = ( 30 - 18 ) / 2 = 6 kmph answer : b"
Answer: b
Python program:
a = 90 / 3
b = 55 / 3
c = a - b
d = c / 2
Problem: jim is able to sell a hand - carved statue for $ 540 which was a 35 % profit over his cost . how much did the statue originally cost him ?
Options: a ) $ 400.00 , b ) $ 412.40 , c ) $ 455.40 , d ) $ 474.90 , e ) $ 488.20
Rationale: 540 = 1.35 * x x = 540 / 1.35 = 400 $ 400 , which is ( a ) .
Answer: a
Python program:
a = 35 / 100
b = a + 1 
c = 540 / b
Problem: the speed at which a girl can row a boat in still water is 30 kmph . if she rows downstream , where the speed of current is 6 kmph , what time will he take to cover 240 metres ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 20 , e ) 24
Rationale: speed of the boat downstream = 30 + 6 = 36 kmph = 36 * 5 / 18 = 10 m / s hence time taken to cover 240 m = 240 / 10 = 24 seconds . answer : e
Answer: e
Python program:
a = 240 * const_3_6
b = 30 + 6 
c = a / b
Problem: the standard deviation of a normal distribution of data is 2 , and 3 standard deviations below the mean is greater than 45 . what is a possible value for the mean of the distribution ?
Options: a ) 52 , b ) 47 , c ) 48 , d ) 49 , e ) 50
Rationale: "the standard deviation ( { sd } ) = 2 ; 3 standard deviations below the mean is greater than 45 : { mean } - 3 * { sd } > 45 ; { mean } - 6 > 45 ; { mean } > 51 . answer : a ."
Answer: a
Python program:
a = 3 * 2
b = 45 + a 
c = b + 1
Problem: if 13 = 13 w / ( 1 - w ) , then ( 5 w ) 2 =
Options: a ) 1 / 4 , b ) 5 , c ) 1 , d ) 2 , e ) 3
Rationale: "13 - 13 w = 13 w 26 w = 13 w = 1 / 2 5 w = 5 / 2 5 w * 2 = 5 / 2 * 2 = 5 answer : b"
Answer: b
Python program:
a = 13 + 13 
b = 13 / a
c = b * 5
Problem: two trains of length 100 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 ) 82 sec , d ) 20 sec , e ) 19 sec
Rationale: "relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 100 + 280 = 380 m . the time required = d / s = 380 / 20 = 19 sec . answer : e"
Answer: e
Python program:
a = 100 + 280 
b = 42 + 30 
c = b * const_0_2778
d = a / c
Problem: the ratio of radius of a circle and the side of a square is 2 : 9 . find the ratio of their areas :
Options: a ) 2 : 1 , b ) 4 : 7 , c ) 8 : 77 , d ) 4 : 81 , e ) none
Rationale: "radius / side = 2 / 9 â ‡ ’ area of circle / area of square = 4 / 81 answer : d"
Answer: d
Python program:
a = 2 / 9
b = a ** 2
Problem: if 12 men can reap 120 acres of land in 36 days , how many acres of land can 24 men reap in 62 days ?
Options: a ) 266.5 , b ) 413.3 , c ) 425.8 , d ) 189.3 , e ) 249.6
Rationale: "12 men 120 acres 36 days 24 men ? 62 days 120 * 24 / 12 * 62 / 36 120 * 2 * 31 / 18 240 * 1.72 = 413.3 answer : b"
Answer: b
Python program:
a = 24 / 12
b = 62 / 36
c = a * b
d = 120 * c
Problem: evaluate : 10010 - 12 * 3 * 2 = ?
Options: a ) 30002 , b ) 70002 , c ) 50002 , d ) 90002 , e ) 10002
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 10010 - 12 * 3 * 2 = 10010 - 8 = 10002 correct answer e"
Answer: e
Python program:
a = 12 * 3
b = a * 2
c = 10010 - b
Problem: a car travels at a speed of 10 miles per hour . how far will it travel in 5 hours ?
Options: a ) 50 miles , b ) 62 miles , c ) 325 miles , d ) 70 miles , e ) 20 miles
Rationale: "during each hour , the car travels 65 miles . for 5 hours it will travel 10 + 10 + 10 + 10 + 10 = 5 * 10 = 50 miles correct answer a"
Answer: a
Python program:
a = 10 * 5
Problem: if 42 men do a work in 25 days , in how many days will 50 men do it ?
Options: a ) 23 , b ) 22 , c ) 19 , d ) 20 , e ) 21
Rationale: "42 * 25 = 50 * x x = 21 days answer : e"
Answer: e
Python program:
a = 42 * 25
b = a / 50
Problem: find large number from below question the difference of two numbers is 1345 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder
Options: a ) 1235 , b ) 1345 , c ) 1678 , d ) 1767 , e ) 1611
Rationale: let the smaller number be x . then larger number = ( x + 1345 ) . x + 1345 = 6 x + 15 5 x = 1330 x = 266 large number = 266 + 1345 = 1611 e
Answer: e
Python program:
a = 1345 - 15
b = 6 - 1
c = a / b
d = c * 6
Problem: company s produces two kinds of stereos : basic and deluxe . of the stereos produced by company s last month , 2 / 3 were basic and the rest were deluxe . if it takes 9 / 5 as many hours to produce a deluxe stereo as it does to produce a basic stereo , then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos ?
Options: a ) 7 / 17 , b ) 14 / 31 , c ) 7 / 15 , d ) 17 / 35 , e ) 9 / 19
Rationale: "# of basic stereos was 2 / 3 of total and # of deluxe stereos was 1 / 3 of total , let ' s assume total = 15 , then basic = 10 and deluxe = 5 . now , if time needed to produce one deluxe stereo is 1 unit than time needed to produce one basic stereo would be 9 / 5 units . total time for basic would be 10 * 1 = 10 and total time for deluxe would be 5 * 9 / 5 = 9 - - > total time for both of them would be 10 + 9 = 19 - - > deluxe / total = 9 / 19 . answer : e ."
Answer: e
Python program:
a = 3 + 2 
b = a / 10
Problem: a train 250 meters long completely crosses a 300 meters long bridge in 45 seconds . what is the speed of the train is ?
Options: a ) 32 , b ) 28 , c ) 29 , d ) 44 , e ) 21
Rationale: "s = ( 250 + 300 ) / 45 = 550 / 45 * 18 / 5 = 44 answer : d"
Answer: d
Python program:
a = 250 + 300 
b = a / 1000
c = 45 / 3600
d = b / c
Problem: the salaries of a and b together amount to $ 500 . a spends 90 % of his salary and b , 80 % of his . if now , their savings are the same , what is a ' s salary ?
Options: a ) $ 50 , b ) $ 150 , c ) $ 69 , d ) $ 34 , e ) $ 52
Rationale: "let a ' s salary is x b ' s salary = 500 - x ( 100 - 90 ) % of x = ( 100 - 80 ) % of ( 500 - x ) x = $ 34 ( approximately ) answer is d"
Answer: d
Python program:
a = 100 - 80
b = 100 - 90
c = a / b
d = c + 1 
e = 500 / d
f = 500 - e
Problem: if there are 10 peanuts in a box and mary puts 8 more peanuts inside , how many peanuts are in the box ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 18
Rationale: "10 + 8 = 18 correct answer is e ) 18"
Answer: e
Python program:
a = 10 + 8
Problem: how many positive integers less than 1960 are such that the product of their digits is 10 .
Options: a ) 220 , b ) 230 , c ) 280 , d ) 220 , e ) 240
Rationale: "1960 is divisible by 10 ( or 2 * 5 ) = 196 196 is divisible by 4 = > 49 49 = 7 * 7 hence 1960 is divisible by 2 , 4,5 , 7 , 7 if there were only one 7 , i . e if the problem were 280 c"
Answer: c
Python program:
a = 4 + 10 
b = a - 1
c = math.factorial(b)
d = math.factorial(10)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: the average runs of a cricket player of 10 innings was 32 . how many runs must he makes ih his next innings so as to increase his average of runs by 4 ?
Options: a ) 2 , b ) 4 , c ) 70 , d ) 76 , e ) none
Rationale: "sol . average after 11 innings = 36 . therefore required numbert of runs = ( 36 × 11 ) – ( 32 × 10 ) = 396 - 320 = 76 . answer d"
Answer: d
Python program:
a = 10 + 1 
b = 32 + 4 
c = a * b
d = 32 * 10
e = c - d
Problem: an outlet pipe can empty 2 / 3 of a cistern in 16 minutes . in 4 minutes , what part of the cistern will be emptied ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 6 , e ) 1 / 8
Rationale: "4 / 16 * 2 / 3 = 1 / 6 the answer is d ."
Answer: d
Python program:
a = 2 / 3
b = 4 * a
c = b / 16