euclaise/mathqa_programs huggingface dataset:
Problem: a , b , c subscribe rs . 50,000 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 . 39,000 , what will be the amount a receives ?
Options: a ) 14700 , b ) 14500 , c ) 14900 , d ) 16380 , 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 = 39000 × 21 / 50 = 16380 answer is d"
Answer: d
Python program:
a = 5000 * 10
b = 4000 + 5000 
c = b + 5000 
d = a - c
e = d / 3
f = 4000 + 5000 
g = e + f 
h = 3 * 12
i = h * 1000
j = 5000 * 10
k = i / j
l = g * k
Problem: if the operation € is defined for all x and y by the equation x € y = 3 * x * y , then 3 € ( 4 € 5 ) =
Options: a ) 80 , b ) 120 , c ) 160 , d ) 540 , e ) 660
Rationale: "working inside out , ( 4 € 5 ) = 3 * 4 * 5 = 60 3 € 60 = 3 * 3 * 60 = 540 hence , answer is d"
Answer: d
Python program:
a = 3 * 3
b = 3 * 4
c = b * 5
d = a * c
Problem: a person can swim in still water at 8 km / h . if the speed of water 4 km / h , how many hours will the man take to swim back against the current for 8 km ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "m = 8 s = 4 us = 8 - 4 = 4 d = 4 t = 8 / 4 = 2 answer : a"
Answer: a
Python program:
a = 8 - 4
b = 8 / a
Problem: thomas and matt has some money with them in the ratio of 3 : 4 . if their father gives rs . 30 to each of them then the ratio becomes 4 : 5 . what would be the ratio if thomas spend rs . 40 and matt spend rs . 20 from what they have now ?
Options: a ) 1 : 2 , b ) 2 : 3 , c ) 3 : 4 , d ) 4 : 5 , e ) 5 : 6
Rationale: let money of thomas and matt be x and y respectively . x / y = 3 / 4 = > x = 3 / 4 y ( x + 30 ) / ( y + 30 ) = 4 / 5 = > 5 x + 150 = 4 y + 120 = > 5 x = 4 y - 30 but x = 3 / 4 y 5 * 3 / 4 y = 4 y - 30 15 y = 16 y - 120 = > y = 120 = > x = 3 * 120 / 4 = > x = 90 ratio of their money , if thomas spend rs . 40 and matt spend rs . 20 = > ( 90 - 40 ) / ( 120 - 20 ) = 50 / 100 . = > 1 : 2 answer : a
Answer: a
Python program:
a = 30 * 4
b = 3 / 4
c = a * b
d = c - 40
e = 30 * 4
f = e - 20
g = d / f
Problem: if the integer n has exactly 5 positive divisors , including 1 and n , how many positive divisors does √ n have ?
Options: a ) 6 , b ) 5 , c ) 2 , d ) 3 , e ) 4
Rationale: take the example of 16 . . . it has 3 positive divisors ( 1 , 2,4 , 8,16 ) now , take the example of 4 . . . it has only 3 divisors . . so d is the ans
Answer: d
Python program:
a = 1 + 1 
b = 5 - a
Problem: a straight line in the xy - plane has a slope of 2 and a y - intercept of 2 . on this line , what is the x - coordinate of the point whose y - coordinate is 480 ?
Options: a ) 249 , b ) 498 , c ) 239 , d ) 823 , e ) 1,002
Rationale: "slope of 2 and a y - intercept of 2 y - coordinate is 480 y = 2 x + 2 478 = 2 x x = 239 answer : c . 239"
Answer: c
Python program:
a = 480 - 2
b = a / 2
Problem: bruce purchased 7 kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) a ) 985 , b ) b ) 1050 , c ) c ) 1055 , d ) d ) 1065 , e ) e ) 1075
Rationale: cost of 7 kg grapes = 70 × 7 = 490 . cost of 9 kg of mangoes = 55 × 9 = 495 . total cost he has to pay = 490 + 495 = 985 a
Answer: a
Python program:
a = 7 * 70
b = 9 * 55
c = a + b
Problem: if the sum of two positive integers is 26 and the difference of their squares is 52 , what is the product of the two integers ?
Options: a ) 108 , b ) 119 , c ) 128 , d ) 135 , e ) 168
Rationale: let the 2 positive numbers x and y x + y = 26 - - 1 x ^ 2 - y ^ 2 = 52 = > ( x + y ) ( x - y ) = 52 - - 2 using equation 1 in 2 , we get = > x - y = 2 - - 3 solving equation 1 and 3 , we get x = 14 y = 12 product = 14 * 12 = 168 answer e
Answer: e
Python program:
a = 52 / 26
b = 26 - a
c = 52 / 26
d = b / c
e = 52 / 26
f = 26 - e
g = 52 / 26
h = f / g
i = 52 / 26
j = h + i 
k = d * j
Problem: fonzie , aunt bee and lapis paid $ 7000 , $ 8000 and $ 9000 respectively to buy a map to capt . plaidstache ' s treasure . when they found it , the treasure turned out to be worth a cool $ 900000 . how much of it should lapis get ?
Options: a ) $ 300000 , b ) $ 320000 , c ) $ 335000 , d ) $ 336500 , e ) $ 337500
Rationale: a = 7000 b = 8000 c = 9000 a share 7 parts , b share 8 parts & c share 9 parts total 24 parts - - - - - > 900000 - - - - > 1 part - - - - - - - > 37500 c share = 9 parts - - - - - > 337500 e
Answer: e
Python program:
a = 7000 + 8000 
b = 9000 + a 
c = 900000 / b
d = 9000 * c
Problem: for all positive integers m , [ m ] = 3 m when m is odd and [ m ] = ( 1 / 2 ) * m when m is even . what is [ 9 ] * [ 4 ] equivalent to ?
Options: a ) [ 108 ] , b ) [ 54 ] , c ) [ 36 ] , d ) [ 27 ] , e ) [ 18 ]
Rationale: "[ 9 ] * [ 4 ] = 27 * 2 = 54 = ( 1 / 2 ) ( 108 ) = [ 108 ] the answer is a ."
Answer: a
Python program:
a = 4 / 2
b = 3 * 9
c = a * b
d = c / 3
Problem: two pipes p and q can fill a cistern in 10 and 15 minutes respectively . both are opened together , but at the end of 4 minutes the first is turned off . how many more minutes will it take for the cistern to fill after the first pipe is turned off ?
Options: a ) 3.5 , b ) 4 , c ) 4.5 , d ) 5 , e ) 5.5
Rationale: "let x be the total time it takes for the cistern to fill . 4 / 10 + x / 15 = 1 x / 15 = 3 / 5 x = 9 after the first pipe is turned off , it takes 5 more minutes to fill the cistern . the answer is d ."
Answer: d
Python program:
a = 1 / 10
b = 1 / 15
c = a + b 
d = c * 4
e = 1 - d
f = e * 15
Problem: express 20 mps in kmph ?
Options: a ) 23 , b ) 88 , c ) 90 , d ) 72 , e ) 21
Rationale: 20 * 18 / 5 = 72 kmph answer : d
Answer: d
Python program:
a = 20 / 1000
b = a * 3600
Problem: you hold some gold in a vault as an investment . over the past year the price of gold increases by 40 % . in order to keep your gold in the vault , you must pay 5 % of the total value of the gold per year . what percentage has the value of your holdings changed by over the past year .
Options: a ) 35 % , b ) 33 % , c ) 36 % , d ) 38 % , e ) 40 %
Rationale: "( 100 % + 40 % ) * ( 100 % - 5 % ) = 140 * 0.95 = 133 % an increase of 33 % your gold holdings have increased in value by 33 % . the answer is b"
Answer: b
Python program:
a = 40 / 5
b = 40 - a
Problem: a large tanker can be filled by two pipes a and b in 60 and 40 minutes respectively . how many minutes will it take to fill the tanker from empty state if b is used for half the time and a and b fill it together for the other half ?
Options: a ) 30 , b ) 15 , c ) 20 , d ) 25 , e ) 50
Rationale: suppose the tank is filled in x minutes . then , x / 2 ( 1 / 24 + 1 / 40 ) = 1 x / 2 * 1 / 15 = 1 = > x = 30 min answer a
Answer: a
Python program:
a = 1/(40)
b = 1/(60)
c = 1/(40)
d = b + c 
e = a + d 
f = 1 / e
g = f * 2
Problem: the captain of a cricket team of 11 members is 27 years old and the wicket keeper is 1 year older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average age of the team ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: "let the average age of the whole team be x years . 11 x - ( 27 + 28 ) = 9 ( x - 1 ) 11 x - 9 x = 46 2 x = 46 x = 23 . the average age of the team is 23 years . the answer is d ."
Answer: d
Python program:
a = 27 + 1 
b = 27 + a 
c = 3 * 0
d = b - c
e = d / 2
Problem: if log 1087.5 = 6.9421 , then the number of digits in ( 875 ) 10 is ?
Options: a ) 30 , b ) 28 , c ) 80 , d ) 26 , e ) 25
Rationale: "x = ( 875 ) 10 = ( 87.5 x 10 ) 10 therefore , log 10 x = 10 ( log 1087.5 + 1 ) = 10 ( 6.9421 + 1 ) = 10 ( 7.9421 ) = 79.421 x = antilog ( 79.421 ) therefore , number of digits in x = 80 . answer : c"
Answer: c
Python program:
a = 4 * 6
b = math.log(100)
c = math.log(10)
d = b / c
e = a + d
Problem: two heavily loaded sixteen - wheeler transport trucks are 787 kilometers apart , sitting at two rest stops on opposite sides of the same highway . driver a begins heading down the highway driving at an average speed of 90 kilometers per hour . exactly one hour later , driver b starts down the highway toward driver a , maintaining an average speed of 80 kilometers per hour . how many kilometers farther than driver b , will driver a have driven when they meet and pass each other on the highway ?
Options: a ) 90 , b ) 131 , c ) 150 , d ) 320 , e ) 450
Rationale: i ' ve been reading the website for a while and i ' m always keen to see different approaches so i would like to share one that works for me : short version : truck a travels for an hour . distance remaining = 787 - 90 = 697 k ratio of speeds 9 : 8 - > 697 / 17 = 41 truck a = 90 + 41 * 9 = 459 truck b = 41 * 8 = 328 delta = 131 km answer b
Answer: b
Python program:
a = 787 - 90
b = 90 + 80 
c = a / b
d = 90 - 80
e = c * d
f = 90 + e
Problem: in a group of 800 people , 1 / 5 play at least one instrument , 64 play two or more . what is the probability that one student play exactly one instrument ?
Options: a ) 3 / 25 , b ) 3 / 125 , c ) c ) 2 / 25 , d ) 3 / 25 , e ) 1 / 5
Rationale: "p ( playing 2 or more instruments ) = 64 / 800 = 2 / 25 . then , the probability of playing exactly one instrument is given by : p ( playing 1 or more instruments ) - p ( playing 2 or more instruments ) = 1 / 5 - 2 / 25 = 3 / 25 . answer a ."
Answer: a
Python program:
a = 800 * 1
b = a / 5
c = b - 64
d = c / 800
Problem: what is the angle between the hands of a clock when time is 8 : 30 ?
Options: a ) 65 deg , b ) 75 deg , c ) 45 deg , d ) 15 deg , e ) 30 deg
Rationale: "angle between two hands = 30 h - 11 / 2 m = 30 * 8 - 30 * 11 / 2 = 240 - 165 = 75 deg answer : b"
Answer: b
Python program:
a = 3 * 2
b = 30 * a
c = b - 8
Problem: if the difference between compound interest ( interest compounded yearly ) and simple interest on a certain sum at the rate 20 % p . a . after 3 years is rs . 1280 then what is the principal ?
Options: a ) 7900 , b ) 8,000 , c ) 10,000 , d ) 8,300 , e ) 9,300
Rationale: "let p is the principal , so p ( [ 120 / 100 ] ^ 3 - 1 ) - p * 20 / 100 * 3 = 1280 p [ 728 / 1000 - 3 / 5 ] = 1280 p = 1280 * 5 * 1000 / 728 * 5 - 3000 = 10000 answer : c"
Answer: c
Python program:
a = 1280 * 3
b = a * 3
Problem: in the xy - coordinate system , if ( m , n ) and ( m + 4 , n + k ) are two points on the line with the equation x = 2 y + 5 , then k =
Options: a ) 1 / 2 , b ) 1 , c ) 2 , d ) 5 / 2 , e ) 4
Rationale: "since ( m , n ) and ( m + 2 , n + k ) are two points on the line with the equation x = 2 y + 5 they should satisfy m = 2 n + 5 and m + 4 = 2 * ( n + k ) + 5 . by 1 st equation we have m - 2 n = 5 and by 2 nd equation m - 2 n = 2 k + 1 - - - > 5 = 2 k + 1 - - - > k = 2 . the answer is , therefore , ( c ) ."
Answer: c
Python program:
a = 5 + 4 
b = a - 5
c = b / 2
Problem: during the first week of performances of a certain play , 5400 tickets were sold , all at reduced price . during the remaining weeks of performances , 5 times as many tickets were sold at full price as were sold at reduced price . if the total number of tickets r sold was 25200 , how many of them were sold at full price ?
Options: a ) 21000 , b ) 19800 , c ) 16500 , d ) 15800 , e ) 8700
Rationale: given : the question tells us about the number of tickets sold in the first week at reduced price = 5400 . it also tells us that during the remaining weeks , the number of tickets sold at full price was 5 times the no . of tickets sold at reduced price . the total tickets sold was 25200 , and we are asked to find the number of tickets that where sold at full price . approach : the question asks us to find the number of ticket sold at full price . we know that the number of tickets sold at full price was 5 times the no . of tickets sold at reduced price in remaining weeks . hence , assuming tickets sold at reduced price in remaining weeks to be x would give us the no . of tickets sold at full price to be 5 x . tickets sold in first week + tickets sold in remaining weeks = total no . of tickets soldi . e . tickets sold in first week + tickets sold at full price in remaining weeks + tickets sold at reduced price in remaining weeks = total no . of tickets sold we know the no . of tickets sold during first week and the total no . of tickets sold . we will use this relation to get to our answer . working out : tickets sold in first week + tickets sold at full price in remaining weeks + tickets sold at reduced price in remaining weeks = total no . of tickets sold substituting values in the equation , we get 5400 + 5 x + x = 25200 x = 3300 tickets sold at full price = 5 x = 16500 answer : option c
Answer: c
Python program:
a = 25200 - 5400
b = 5 + 1 
c = a / b
d = c * 5
Problem: income and expenditure of a person are in the ratio 10 : 4 . if the income of the person is rs . 19000 , then find his savings ?
Options: a ) 79754 , b ) 87689 , c ) 59875 , d ) 11400 , e ) 87648
Rationale: "let the income and the expenditure of the person be rs . 10 x and rs . 4 x respectively . income , 10 x = 19000 = > x = 1900 savings = income - expenditure = 10 x - 4 x = 6 x = 6 ( 1900 ) so , savings = rs . 11400 . answer : d"
Answer: d
Python program:
a = 4 / 10
b = a * 19000
c = 19000 - b
Problem: a , b and c started a business with capitals of rs . 8000 , rs . 10000 and rs . 12000 respectively . at the end of the year , the profit share of b is rs . 2000 . the difference between the profit shares of a and c is ?
Options: a ) 621 , b ) 276 , c ) 236 , d ) 800 , e ) 211
Rationale: "explanation : ratio of investments of a , b and c is 8000 : 10000 : 12000 = 4 : 5 : 6 and also given that , profit share of b is rs . 2000 = > 5 parts out of 15 parts is rs . 2000 now , required difference is 6 - 4 = 2 parts required difference = 2 / 5 ( 2000 ) = rs . 800 answer : d"
Answer: d
Python program:
a = 12000 / 10000
b = 8000 / 10000
c = a - b
d = c * 2000
Problem: if a card is drawn from a well shuffled deck of cards , what is the probability of drawing a black card or a face card ?
Options: a ) 7 / 13 , b ) 15 / 26 , c ) 9 / 12 , d ) 8 / 13 , e ) 29 / 52
Rationale: "p ( b á ´ œ f ) = p ( b ) + p ( f ) - p ( b â ˆ © f ) , where b denotes black cards and f denotes face cards . p ( b á ´ œ f ) = 26 / 52 + 12 / 52 - 6 / 52 = 8 / 13 answer : d"
Answer: d
Python program:
a = 3 / const_52
b = const_52 / 4
c = b / const_52
d = a + c
Problem: a cistern 4 m long and 2 m wide contains water up to a depth of 1 m 25 cm . the total area of the wet surface is :
Options: a ) 23 m 2 , b ) 20 m 2 , c ) 52 m 2 , d ) 24 m 2 , e ) 55 m 2
Rationale: "area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 2 x 1.25 + 4 x 1.25 ) + 4 x 2 ] m 2 = 23 m 2 . answer : a"
Answer: a
Python program:
a = 25 / 100
b = a + 1 
c = b * 2
d = 25 / 100
e = d + 1 
f = e * 4
g = c + f 
h = 2 * g
i = 2 * 4
j = h + i
Problem: jane makes toy bears . when she works with an assistant , she makes 62 percent more bears per week and works 10 percent fewer hours each week . having an assistant increases jane ’ s output of toy bears per hour by what percent ?
Options: a ) 20 % , b ) 80 % , c ) 100 % , d ) 180 % , e ) 200 %
Rationale: "let ' s assume just jane 40 bears per 40 / hrs a week , so that is 1 bear / hr . with an assistant she makes 64.8 bears per 36 hours a week or 1.8 bears / hr ( [ 40 bears * 1.62 ] / [ 40 hrs * . 90 ] ) . [ ( 1.8 - 1 ) / 1 ] * 100 % = 80 % answer : b"
Answer: b
Python program:
a = 100 - 62
b = a - 10
c = 10 / b
d = c * 100
Problem: find the average of all numbers between 5 and 37 which are divisible by 4
Options: a ) 25 , b ) 20 , c ) 45 , d ) 30 , e ) 35
Rationale: "explanation : average = ( 4 + 8 + 12 + 16 + 20 + 24 + 28 + 32 + 36 ) / 4 ) = 180 / 4 = 45 option c"
Answer: c
Python program:
a = 4 * 3
b = 4 * 2
c = 4 + b 
d = a + c 
e = 4 * 4
f = d + e 
g = 4 + 1 
h = g * 4
i = f + h 
j = i / 4
Problem: uncle bruce is baking chocolate chip cookies . he has 36 ounces of dough ( with no chocolate ) and 18 ounces of chocolate . how many ounces of chocolate are left over if he uses all the dough but only wants the cookies to consist of 20 % chocolate ?
Options: a ) 3 , b ) 6 , c ) 7.2 , d ) 7.8 , e ) 9
Rationale: "answer is e . x / x + 36 = 1 / 5 x = 9 18 - 9 = 9"
Answer: e
Python program:
a = 20 / 100
b = a * 20
Problem: a broker invested her own money in the stock market . during the first year , she increased her stock market wealth by 50 percent . in the second year , largely as a result of a slump in the stock market , she suffered a 30 percent decrease in the value of her stock investments . what was the net increase or decrease on her overall stock investment wealth by the end of the second year ?
Options: a ) − 5 % , b ) 5 % , c ) 15 % , d ) 20 % , e ) 80 %
Rationale: "assume the broker invested $ 100 . after year 1 ( 50 % increase in wealth ) : $ 100 * 0.5 = $ 50 increase + $ 100 = $ 150 after year 2 ( 30 % decrease in wealth ) : $ 150 * 0.3 = $ 45 ; $ 150 - $ 45 decrease = $ 105 net increase = $ 105 / $ 100 - 1 = 5 % answer is b ."
Answer: b
Python program:
a = 50 / 100
b = 1 + a 
c = 30 / 100
d = 1 - c
e = b * d
f = e - 1
g = f * 100
Problem: the sum of the squares of three numbers is 225 , while the sum of their products taken two at a time is 200 . their sum is :
Options: a ) 10 , b ) 30 , c ) 40 , d ) 25 , e ) none of these
Rationale: "x ^ + y ^ 2 + z ^ 2 = 225 xy + yz + zx = 200 as we know . . ( x + y + z ) ^ 2 = x ^ 2 + y ^ 2 + z ^ 2 + 2 ( xy + yz + zx ) so ( x + y + z ) ^ 2 = 225 + ( 2 * 200 ) ( x + y + z ) ^ 2 = 625 so x + y + z = 25 answer : d"
Answer: d
Python program:
a = 225 - 200
b = a / 2
c = math.sqrt(b)
d = c * 100
e = 225 - 200
f = e / 2
g = 225 - f
h = math.sqrt(g)
i = d + h
Problem: a train travels from new york to chicago , a distance of approximately 480 miles , at an average rate of 40 miles per hour and arrives in chicago at 6 : 00 in evening , chicago time . at what hour in the morning , new york time , did the train depart for chicago ? ( note : chicago time is one hour earlier than new york time )
Options: a ) 3 : 00 , b ) 4 : 00 , c ) 5 : 00 , d ) 6 : 00 , e ) 7 : 00
Rationale: "6 : 00 in evening in chicago = 7 : 00 in evening in new york . so , the train was in chicago 7 : 00 in the evening , new york time . the trip took t = d / r = 480 / 40 = 12 hours . therefore , the train depart from new york at 7 : 00 - 12 hours = 7 : 00 in the morning , new york time . answer : e ."
Answer: e
Python program:
a = 6 + 1 
b = a * 3
c = 480 / 40
d = b - c
Problem: if m is the set of all consecutive multiples of 9 between 100 and 500 , what is the median of m ?
Options: a ) 300 , b ) 301 , c ) 301.5 , d ) 302.5 , e ) 306
Rationale: since 100 / 9 = 11.11 , 500 / 9 = 55.55 , m can be written as { 9 * 12 , 9 * 13 , . . . . , 9 * 54 , 9 * 55 } . the number of elements of m is , therefore , 44 ( = 55 - 12 + 1 ) . since the number of elements is even number the median is the average of the 22 nd element ( = 9 * 33 ) and 23 rd element ( = 9 * 34 ) . so the median is ( 9 * 33 + 9 * 34 ) / 2 = 301.5 . the answer is c .
Answer: c
Python program:
a = 100 / 9
b = math.floor(a)
c = 9 * b
d = 500 - 100
e = d / 9
f = math.floor(e)
g = f / 2
h = g * 9
i = c + h 
j = 100 / 9
k = math.floor(j)
l = 9 * k
m = 500 - 100
n = m / 9
o = math.floor(n)
p = o / 2
q = p * 9
r = l + q 
s = r + 9 
t = i + s 
u = t / 2
Problem: a 300 meter long train crosses a platform in 42 seconds while it crosses a signal pole in 18 seconds . what is the length of the platform ?
Options: a ) 99 , b ) 289 , c ) 350 , d ) 882 , e ) 400
Rationale: "speed = [ 300 / 18 ] m / sec = 50 / 3 m / sec . let the length of the platform be x meters . then , x + 300 / 42 = 50 / 3 3 ( x + 300 ) = 2100 è x = 400 m . answer : e"
Answer: e
Python program:
a = 300 / 18
b = a * 42
c = b - 300
Problem: shop offered 20 % offer for every shirt , smith bought a shirt at rs . 780 . and what was the shop ' s original selling price ?
Options: a ) 500 , b ) 550 , c ) 600 , d ) 700 , e ) 975
Rationale: "sp * ( 80 / 100 ) = 780 sp = 9.75 * 100 = > cp = 975 answer : e"
Answer: e
Python program:
a = 20 / 100
b = 1 - a
c = 780 / b
Problem: two positive integers differ by 4 , and sum of their reciprocals is 1 . then one of the numbers is
Options: a ) 2 , b ) b ) 1 , c ) c ) 5 , d ) d ) 21 , e ) e ) 28
Rationale: algebraic approach : let n be the smaller integer = > 1 / n + 1 / ( n + 4 ) = 1 or ( ( n + 4 ) + n ) / n ( n + 4 ) = 1 or n ^ 2 + 4 n = 2 n + 4 or n = 2 as n can not be - negative solve for n = > n = 2 . hence , a
Answer: a
Python program:
a = 1 + 1
Problem: john has rs 360 for his expenses . if he exceeds his days by 4 days he must cut down daily expenses by rs 3 . the number of days of john ' s tour program is
Options: a ) 10 , b ) 15 , c ) 20 , d ) 24 , e ) 27
Rationale: let john under takes a tour of x days . then , expenses for each day = 360 x 360 x + 4 = 360 x − 3 x = 20 and − 24 hence , x = 20 days . c
Answer: c
Python program:
a = 360 * 4
b = a * 4
c = b * 3
d = 3 * 4
e = d ** 2
f = c + e 
g = math.sqrt(f)
h = 3 * 4
i = g - h
j = 2 * 3
k = i / j
Problem: three numbers are in the ratio 3 : 4 : 5 and their l . c . m . is 1200 . their h . c . f is ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60
Rationale: "let the numbers be 3 x , 4 x and 5 x their l . c . m . = 60 x 60 x = 1200 x = 20 the numbers are 3 * 20 , 4 * 20 , 5 * 20 hence required h . c . f . = 20 answer is a"
Answer: a
Python program:
a = 3 * 5
b = a * 100
c = 4 * 5
d = b + c
Problem: the price of food in the area where the sims family lives is scheduled to increase by 50 % next year . since the sims family can not afford an increase in their food bill , how much will they have to reduce consumption to keep their cost the same ?
Options: a ) 17 % , b ) 25.6 % , c ) none % , d ) 33.3 % , e ) 50 %
Rationale: solution : let the current food expense be represented by rs . 100 . the cost of food rises 50 % . so , to buy same amount of food , they need to increase their expense , = ( 100 + 50 % of 100 ) = rs . 150 . but , they want to keep food expense the same , so they have to cut rs . by 50 to keep it to rs . = 100 . the % decrease in consumption is , ( 50 / 150 ) * 100 = 33.3 % . mental calculation method ; 100 - - - - - 50 % ↑ - - - → 150 - - - - - - x % ↓ - - - → 100 . here , x = ( 50 / 125 ) * 100 = 33.3 % . answer : option d
Answer: d
Python program:
a = 100 + 50 
b = a / 100
c = 1 / b
d = 1 - c
e = d * 100
Problem: find the simple interest on $ 10000 at 5 % per annum for 12 months ?
Options: a ) $ 410 , b ) $ 500 , c ) $ 650 , d ) $ 710 , e ) $ 1000
Rationale: "p = $ 10000 r = 5 % t = 12 / 12 years = 1 year s . i . = p * r * t / 100 = 10000 * 5 * 1 / 100 = $ 500 answer is b"
Answer: b
Python program:
a = 5 / 100
b = 10000 * a
Problem: if the given two numbers are respectively 8 % and 16 % of a third number , then what percentage is the first of the second ?
Options: a ) 20 % , b ) 25 % , c ) 18 % , d ) 50 % , e ) none of these
Rationale: "here , l = 8 and m = 16 therefore , first number = l / m x 100 % of second number = 8 / 16 x 100 % of second number = 50 % of second number answer : d"
Answer: d
Python program:
a = 8 / 100
b = 16 / 100
c = a / b
d = c * 100
Problem: if you keep rolling a pair of dice together till a sum of 5 or 7 is obtained , then what is the probability that a sum of 5 comes before a sum of 7 ?
Options: a ) 5 / 5 , b ) 4 / 5 , c ) 3 / 5 , d ) 2 / 5 , e ) 1 / 5
Rationale: this can be solved in a generic and complex way but let us not go into all that . there can be four ways through which the pair of dice results in a sum of 5 . there can be six ways through which the pair of dice can result in a sum of 7 . now , we want the probability of the pair of dice resulting in a sum of 5 before a sum of 7 . thus probability = 4 / ( 4 + 6 ) = 4 / 10 or 2 / 5 . correct answer is d ) 2 / 5
Answer: d
Python program:
a = 4 + 6 
b = 4 / a