euclaise/mathqa_programs huggingface dataset:
Problem: a , b and c enter into partnership . a invests some money at the beginning , b invests double the amount after 6 months , and c invests thrice the amount after 8 months . if the annual gain be rs . 18900 . a ' s share is ?
Options: a ) 6300 , b ) 2765 , c ) 6000 , d ) 1298 , e ) 1261
Rationale: "x * 12 : 2 x * 6 : 3 x * 4 1 : 1 : 1 1 / 3 * 18900 = 6300 answer : a"
Answer: a
Python program:
a = 1 * 12
b = 1 * 12
c = 12 - 6
d = c * 2
e = b + d 
f = 12 - 8
g = f * 3
h = e + g 
i = 18900 / h
j = a * i
Problem: bottle r contains 250 capsules and costs $ 8.25 . bottle t contains 130 capsules and costs $ 2.99 . what is the difference between the cost per capsule for bottle r and the cost per capsule for bottle t ?
Options: a ) $ 0.25 , b ) $ 0.01 , c ) $ 0.05 , d ) $ 0.03 , e ) $ 0.002
Rationale: "cost per capsule in r is 8.25 / 250 = 0.825 / 25 = 0.033 cost per capsule in t is 2.99 / 130 = 0.023 the difference is 0.01 the answer is b"
Answer: b
Python program:
a = 2 / 99
b = 8 / 25
c = a - b
Problem: if albert ’ s monthly earnings rise by 30 % , he would earn $ 598 . if , instead , his earnings rise by only 35 % , how much ( in $ ) would he earn this month ?
Options: a ) 621 , b ) 652 , c ) 660 , d ) 690 , e ) 693
Rationale: "= 598 / 1.3 ∗ 1.35 = 621 = 621 answer is a"
Answer: a
Python program:
a = 30 / 100
b = 1 + a 
c = 598 / b
d = 35 / 100
e = 1 + d 
f = c * e
Problem: the unit digit in the product 3421 * 6721 * 4584 * 6784 is ?
Options: a ) 0 , b ) 1 , c ) 6 , d ) 3 , e ) 4
Rationale: "unit digit in the given product = unit digit in 1 * 1 * 4 * 4 = 6 answer is c"
Answer: c
Python program:
a = 3421 * 6721
b = a * 4584
c = b * 6784
d = 3421 * 6721
e = d * 4584
f = e * 6784
g = 4 + 4 
h = f - g
i = c - h
Problem: the sum of the present ages of two persons a and b is 60 . if the age of a is twice that of b , find the sum of their ages 4 years hence ?
Options: a ) 22 , b ) 77 , c ) 70 , d ) 68 , e ) 71
Rationale: "a + b = 60 , a = 2 b 2 b + b = 60 = > b = 20 then a = 40 . 4 years , their ages will be 44 and 24 . sum of their ages = 44 + 24 = 68 . answer : d"
Answer: d
Python program:
a = 60 / 4
b = a * 2
c = b + 4 
d = 60 / 4
e = d + 4 
f = c + e
Problem: robert is travelling on his cycle andhas calculated to reach point a at 2 pm . if he travels at 10 kmph , he will reach there at 12 pm if he travels at 15 kmph . at what speed must he travel to reach a at 1 pm ?
Options: a ) 8 kmph , b ) 9 kmph , c ) 12 kmph , d ) 14 kmph , e ) 16 kmph
Rationale: let the distance travelled by x km . then , x - x = 2 10 15 3 x - 2 x = 60 x = 60 km . time taken to travel 60 km at 10 km / hr = 60 hrs = 6 hrs . 10 so , robert started 6 hours before 2 p . m . i . e . , at 8 a . m . required speed = 60 kmph . = 12 kmph . 5 c
Answer: c
Python program:
a = 1 / 10
b = 1 / 15
c = a - b
d = 2 / c
e = 1 / 10
f = 1 / 15
g = e - f
h = 2 / g
i = h / 10
j = i - 1
k = d / j
Problem: let f ( x , y ) be defined as the remainder when ( x – y ) ! is divided by x . if x = 36 , what is the maximum value of y for which f ( x , y ) = 0 ?
Options: a ) 9 , b ) 12 , c ) 18 , d ) 20 , e ) 30
Rationale: "the question is finding y such that ( 36 - y ) ! is a multiple of 36 . that means we need to have 2 ^ 2 * 3 ^ 2 in ( 36 - y ) ! 6 ! is the smallest factorial number with 2 ^ 2 * 3 ^ 2 as a factor . 36 - y = 6 y = 30 the answer is e ."
Answer: e
Python program:
a = 36 / 2
b = 1 + 4 
c = a / b
d = 2 * c
e = 36 - d
Problem: a computer factory produces 4032 computers per month at a constant rate , how many computers are built every 30 minutes assuming that there are 28 days in one month ?
Options: a ) 2.25 . , b ) 3.00 . , c ) 4.5 . , d ) 5.225 . , e ) 6.25 .
Rationale: number of hours in 28 days = 28 * 24 number of 30 mins in 28 days = 28 * 24 * 2 number of computers built every 30 mins = 4032 / ( 28 * 24 * 2 ) = 3 answer b
Answer: b
Python program:
a = 4032 / 28
b = 28 - 4
c = b * 2
d = a / c
Problem: the ratio of the radius of two circles is 1 : 4 , and then the ratio of their areas is ?
Options: a ) 1 : 16 , b ) 1 : 6 , c ) 1 : 9 , d ) 1 : 3 , e ) 1 : 2
Rationale: "r 1 : r 2 = 1 : 4 π r 12 : π r 22 r 12 : r 22 = 1 : 16 answer : a"
Answer: a
Python program:
a = circle_area / (
Problem: the average age of a class of 39 students is 15 years . if the age of the teacher be included , then the average increased by 3 months . find the age of the teacher ?
Options: a ) 25 , b ) 28 , c ) 30 , d ) 35 , e ) 39
Rationale: "total age of 39 persons = 39 * 15 = 585 years average age of 40 persons = 15 yrs 3 months = 61 / 4 years total age of 40 persons = 61 / 4 * 40 = 610 years age of the teacher = 610 - 585 = 25 years answer is a"
Answer: a
Python program:
a = 39 + 3 
b = 15 + 3 
c = a * b
d = 39 * 15
e = c - d
Problem: country x imported approximately $ 1.44 billion of goods in 1996 . if country x imported $ 488 million of goods in the first two months of 1997 and continued to import goods at the same rate for the rest of the year , by how much would country xs 1997 imports exceed those of 1996 ?
Options: a ) $ 1124 million , b ) $ 1120 million , c ) $ 1144 million , d ) $ 1240 million , e ) $ 1488 million
Rationale: convert units to millions as answer is in millions 1996 imports = $ 1.44 bill = $ 1440 mill i . e . 1440 / 12 = $ 120 mill / month 1997 imports = $ 488 mill / 2 month i . e . $ 244 mill / month difference / month = 244 - 120 = 124 difference / year = $ 124 mill * 12 = $ 1488 mill answer : e
Answer: e
Python program:
a = 12 / 2
b = 488 * a
c = 1 * 44
d = b - c
Problem: the ratio of 2 numbers is 2 : 7 and their h . c . f . is 18 . their l . c . m . is ?
Options: a ) 252 , b ) 243 , c ) 521 , d ) 361 , e ) 600
Rationale: "let the numbers be 2 x and 7 x their h . c . f . = 18 so the numbers are 2 * 18 , 7 * 18 = 36,126 l . c . m . = 252 answer is a"
Answer: a
Python program:
a = 7 ** 2
b = 2 ** 2
c = 2 ** 2
d = b + c 
e = a + d 
f = 18 / e
g = math.sqrt(f)
Problem: 110 people are attending a newspaper conference . 45 of them are writers and more than 38 are editors . of the people at the conference , x are both writers and editors and 2 x are neither . what is the largest possible number of people who are both writers and editors ?
Options: a ) 34 , b ) 32 , c ) 30 , d ) 26 , e ) 28
Rationale: "{ total } = { writers } + { editors } - { both } + { neither } . { total } = 110 ; { writers } = 45 ; { editors } > 38 ; { both } = x ; { neither } = 2 x ; 110 = 45 + { editors } - x + 2 x - - > x = 65 - { editors } . we want to maximize x , thus we should minimize { editors } , minimum possible value of { editors } is 39 , thus x = { both } = 65 - 39 = 26 . answer : d ."
Answer: d
Python program:
a = 38 + 1 
b = a + 45 
c = 110 - b
Problem: in may mrs lee ' s earnings were 70 percent of the lee family ' s total income . in june mrs lee earned 20 percent more than in may . if the rest of the family ' s income was the same both months , then , in june , mrs lee ' s earnings were approximately what percent of the lee family ' s total income ?
Options: a ) 64 % , b ) 68 % , c ) 72 % , d ) 74 % , e ) 83 %
Rationale: "let in may lee family ' s total income = 100 in may mrs lee ' s income = 70 in may rest of the family ' s income = 30 in june mrs lees income = 70 * 120 / 100 = 84 in june total income = 84 + 30 = 114 % of mrs lee ' s income = 84 / 114 = 73.68 ( d )"
Answer: d
Python program:
a = 100 + 20 
b = 100 + 20 
c = b + 100 
d = a / c
e = d * 100
Problem: one year ago , the ratio of roonie ’ s and ronaldo ’ s age was 6 : 7 respectively . 4 years hence , this ratio would become 7 : 8 . how old is ronaldo ?
Options: a ) 32 , b ) 33 , c ) 34 , d ) 35 , e ) 36
Rationale: 7 ( x - 1 ) = 6 ( y - 1 ) = > 7 x - 6 y - 1 = 0 - - - - eq 1 8 ( x + 4 ) = 7 ( y + 4 ) = > 8 x - 7 y + 4 = 0 - - - - eq 2 on solving eq 1 n eq 2 y = 36 answer : e
Answer: e
Python program:
a = 4 + 1 
b = 8 * a
c = 4 + 1 
d = 7 * c
e = b - d
f = 7 * e
g = 7 * 7
h = 6 * 8
i = g - h
j = f / i
k = j + 1
Problem: a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets rs . 900 more than d , what is b ' s share ?
Options: a ) rs . 500 , b ) rs . 1800 , c ) rs . 2000 , d ) rs . 2500 , e ) none of the above
Rationale: "let the shares of a , b , c and d be rs . 5 x , rs . 2 x , rs . 4 x and rs . 3 x respectively . then , 4 x - 3 x = 900 x = 900 . b ' s share = rs . 2 x = rs . ( 2 x 900 ) = rs . 1800 . answer = b"
Answer: b
Python program:
a = 4 - 3
b = a * 900
c = b * 3
Problem: the speed at which a man can row a boat in still water is 14 kmph . if he rows downstream , where the speed of current is 2 kmph , what time will he take to cover 40 metres ?
Options: a ) 16 seconds , b ) 34 seconds , c ) 9 seconds , d ) 12 seconds , e ) 15 seconds
Rationale: "speed of the boat downstream = 14 + 2 = 16 kmph = 16 * 5 / 18 = 40 / 9 m / s hence time taken to cover 40 m = 40 * 9 / 40 = 9 seconds . answer : c"
Answer: c
Python program:
a = 14 + 2 
b = a * const_0_2778
c = 40 / b
Problem: a , b and c started a business with a total investment of rs . 90000 . a invests rs . 6000 more than b and b invests rs . 3000 less than c . if the total profit at the end of a year is rs . 8640 , find c ' s share .
Options: a ) rs . 3240 , b ) rs . 2520 , c ) rs . 2880 , d ) rs . 3360 , e ) none of these
Rationale: "explanation : let c ' s investment = rs . x b ' s investment = rs . ( x - 3000 ) a ' s investment = rs . ( x - 3000 + 6000 ) = rs . ( x + 3000 ) now , ( a + b + c ) ' s investment = rs . 90000 = > x + ( x - 3000 ) + ( x + 3000 ) = 90000 = > 3 x = 90000 = > x = 30000 hence , a ' s investment = rs . 33000 b ' s investment = rs . 27000 c ' s investment = rs . 30000 ratio of the capitals of a , b and c = 33000 : 27000 : 30000 = 11 : 9 : 10 a ' s share = rs . [ ( 10 / 30 ) ã — 8640 ] = rs . 2880 answer : option c"
Answer: c
Python program:
a = 6000 + 3000 
b = 90000 - a
c = b / 3
d = c + 6000 
e = d / 90000
f = 8640 * e
Problem: the ratio of the present age of sandy to that of molly is 9 : 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 ) 30 , b ) 36 , c ) 42 , d ) 48 , e ) 54
Rationale: "let the present age of sandy be 9 x years and that of molly be 2 x years . ( 9 x + 16 ) / ( 2 x + 16 ) = 5 / 2 8 x = 48 x = 6 six years ago , sandy ' s age was 9 ( 6 ) - 6 = 48 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 * 9
g = 2 + 2 
h = f / g
i = h - 6
Problem: how many 3 - digits number are palindromic numbers ? a palindromic number reads the same forward and backward , example 121 .
Options: a ) 90 , b ) 610 , c ) 729 , d ) 900 , e ) 1000
Rationale: "take the task of building palindromes and break it intostages . stage 1 : select the hundreds digit we can choose 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , or 9 so , we can complete stage 1 in 9 ways stage 2 : select the tens digit we can choose 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , or 9 so , we can complete stage 2 in 10 ways important : at this point , the remaining digits are alreadylocked in . stage 3 : select the units digit this digit must be the same as the thousands digit ( which we already chose in stage 2 ) so , we can complete this stage in 1 way . by thefundamental counting principle ( fcp ) , we can complete all 5 stages ( and thus build a 3 - digit palindrome ) in ( 9 ) ( 10 ) ( 1 ) ways ( = 900 ways ) answer : a"
Answer: a
Python program:
a = 3 * 10
b = a * 10
c = b * 10
d = c * 10
Problem: the average of the 5 numbers is 6.8 . if one of the numbers is multiplied by 3 , the average of the numbers increases to 9.2 . which of the 5 numbers is multiplied by 3 ?
Options: a ) 1.5 , b ) 3.0 , c ) 3.9 , d ) 4.0 , e ) 6.0
Rationale: initial avg is 6.8 so the summation of the nos is 6.8 * 5 = 34 now the new avg is 9.2 so summation will be 9.2 * 5 = 46 . so change in summation is 12 . this comes when a number is multiplied by 3 . in the original sum we already have that number added once . to bring additional 12 increment by multiplying by 3 , we get a total increase of 18 . thus , 6 is multiplied by 3 . answer : e
Answer: e
Python program:
a = 9 * 2
b = 6 * 8
c = a - b
d = c / 2
Problem: ( 3192 + 6160 ) / 28
Options: a ) 380 , b ) 350 , c ) 334 , d ) 310 , e ) none of these
Rationale: "explanation : as per bodmas rule , first we will solve the equation in bracket then we will go for division = ( 9352 ) / 28 = 334 option c"
Answer: c
Python program:
a = 4 + 1 
b = a ** 4
c = 3192 * b
Problem: a ferry can transport 100 tons of vehicles . automobiles range in weight from 1,800 to 3,200 pounds . what is the greatest number of automobiles that can be loaded onto the ferry ?
Options: a ) 115 , b ) 120 , c ) 110 , d ) 100 , e ) 90
Rationale: "to get maximum vehicles we must take into consideration the minimum weight i . e 1800 pounds here since , 1 ton = 2000 pounds 78 tons will be 200,000 pounds from the answer choices : let max number of vehicles be 110 total weight will be = 110 * 1800 = 198000 pounds , which is lesser than the maximum weight allowed . ans : c"
Answer: c
Python program:
a = 100 * 2
b = a * 1000
c = 1000 + 100 
d = c + 100 
e = d + 100 
f = e + 100 
g = f + 100 
h = g + 100 
i = b / h
Problem: when positive integer n is divided by positive integer j , the remainder is 25 . if n / j = 204.05 , what is value of j ?
Options: a ) 600 , b ) 500 , c ) 800 , d ) 200 , e ) 900
Rationale: "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 204.05 here 204 is the quotient . given that remainder = 25 so , 204.05 = 204 + 25 / j so , j = 500 answer : b"
Answer: b
Python program:
a = 4 * 10
b = a + 2 
c = 100 + b 
d = 204 - 5
e = 25 / d
Problem: a , b , c subscribe rs . 50000 for a business . a subscribes rs . 4000 more than b and b rs . 5000 more than c . out of a total profit of rs . 30000 , b receives :
Options: a ) s . 10,000 , b ) s . 10,200 , c ) s . 10,400 , d ) s . 10,700 , e ) s . 10,800
Rationale: let c = x . then , b = x + 5000 and a = x + 5000 + 4000 = x + 9000 . so , x + x + 5000 + x + 9000 = 50000 3 x = 36000 x = 12000 a : b : c = 21000 : 17000 : 12000 = 21 : 17 : 12 . b ' s share = rs . ( 30000 x 17 / 50 ) = rs . 10,200 . b
Answer: b
Python program:
a = 5000 - 4000
b = 50000 + a 
c = b / 3
d = c / 50000
e = 30000 * d
Problem: a man swims downstream 48 km and upstream 18 km taking 3 hours each time , what is the speed of the man in still water ?
Options: a ) 2 , b ) 8 , c ) 9 , d ) 11 , e ) 14
Rationale: "48 - - - 3 ds = 16 ? - - - - 1 18 - - - - 3 us = 6 ? - - - - 1 m = ? m = ( 16 + 6 ) / 2 = 11 answer : d"
Answer: d
Python program:
a = 18 / 3
b = 48 / 3
c = a + b 
d = c / 2
Problem: if the population of a certain country increases at the rate of one person every 30 seconds , by how many persons does the population increase in 10 minutes ?
Options: a ) 20 , b ) 30 , c ) 15 , d ) 10 , e ) 80
Rationale: "answer = 2 * 10 = 20 answer = a"
Answer: a
Python program:
a = const_60 / 30
b = a * 10
Problem: a can complete a project in 20 days and b can complete the same project in 30 days . if a and b start working on the project together and b quits 15 days before the project is completed , in how many days total will the project be completed ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "a ' s rate is 1 / 20 of the project per day . b ' s rate is 1 / 30 of the project per day . the combined rate is 1 / 12 of the project per day . in the last 15 days , a can do 3 / 4 of the project . thus a and b must complete 1 / 4 of the project , which takes 3 days . the total number of days is 3 + 15 = 18 . the answer is d ."
Answer: d
Python program:
a = 1 / 30
b = a * 15
c = 1 - b
d = 1 / 20
e = 1 / 30
f = d + e 
g = c / f
h = g + 15
Problem: a meeting has to be conducted with 4 managers . find the number of ways in which the managers be selected from among 7 managers , if 2 managers will not attend the meeting together ?
Options: a ) 25 , b ) 20 , c ) 35 , d ) 36 , e ) 38
Rationale: "we can either choose all 4 people from 5 manager who have no problems or choose 3 from the 5 and 1 from the 2 managers who have a problem sitting together so 5 c 4 + ( 5 c 3 * 2 c 1 ) this is 5 + 20 = 25 answer : a"
Answer: a
Python program:
a = math.comb(7, 4)
b = 7 - 2
c = math.comb(b, 2)
d = a - c
Problem: two trains each 150 m in length each , are running on two parallel lines in opposite directions . if one goes at the speed of 95 km / h while the other travels at 85 km / h . how long will it take for them to pass each other completely .
Options: a ) 25 sec , b ) 23 sec , c ) 34 sec , d ) 22 sec , e ) 6 sec
Rationale: "explanation : d = 150 m + 150 m = 300 m rs = 95 + 85 = 180 * 5 / 18 = 50 t = 300 * 1 / 50 = 6 sec answer : option e"
Answer: e
Python program:
a = 150 + 150 
b = a / 1000
c = 95 + 85 
d = b / c
e = 3600 * d
Problem: p is 10 % more efficient than q . p can complete a work in 21 days . if p and q work together , how many days will it take to complete the same work ?
Options: a ) 7 , b ) 9 , c ) 11 , d ) 13 , e ) 15
Rationale: "the work done by p in 1 day = 1 / 21 let work done by q in 1 day = q q × ( 110 / 100 ) = 1 / 21 q = 100 / ( 21 × 110 ) = 10 / ( 21 × 11 ) the work done by p and q in 1 day = 1 / 21 + 10 / ( 21 × 11 ) = 21 / ( 21 × 11 ) = 1 / 11 p and q together can do the work in 11 days . the answer is c ."
Answer: c
Python program:
a = 10 / 100
b = a + 1 
c = b * 21
d = 10 / 100
e = d + 1 
f = e + 1 
g = c / f
Problem: the average weight of a , b and c is 44 kg . if the average weight of a and b be 40 kg and that of b and c be 43 kg , then the weight of b is :
Options: a ) 17 kg , b ) 28 kg , c ) 26 kg , d ) 31 kg , e ) 35 kg
Rationale: "let d sum of a , b , c is 3 * 44 = 132 and sum of a and b s 2 * 40 = 80 sum of b and c is 2 * 43 = 86 hence 80 + 86 - 132 = 28 ans = 28 answer : b"
Answer: b
Python program:
a = 40 * 2
b = 43 * 2
c = a + b 
d = 44 * 3
e = c - d
Problem: a , b , k start from the same place and travel in the same direction at speeds of 30 km / hr , 40 km / hr , 100 km / hr respectively . b starts two hours after a . if b and k overtake a at the same instant , how many hours after a did k start ?
Options: a ) 4.2 , b ) 4.8 , c ) 5.6 , d ) 6.4 , e ) 7.2
Rationale: "in 2 hours , a travels 60 km . b can catch a at a rate of 10 km / hr , so b catches a 6 hours after b starts . so a and b both travel a distance of 240 km . c needs 2.4 hours to travel 240 km , so c leaves 5.6 hours after a . the answer is c ."
Answer: c
Python program:
a = 40 - 30
Problem: a shopkeeper bought 600 oranges and 400 bananas . he found 15 % of oranges and 4 % of bananas were rotten . find the percentage of fruits in good condition ?
Options: a ) 92.5 % , b ) 89.4 % , c ) 85.2 % , d ) 96.8 % , e ) 78.9 %
Rationale: "total number of fruits shopkeeper bought = 600 + 400 = 1000 number of rotten oranges = 15 % of 600 = 15 / 100 × 600 = 9000 / 100 = 90 number of rotten bananas = 4 % of 400 = 16 therefore , total number of rotten fruits = 90 + 16 = 106 therefore number of fruits in good condition = 1000 - 106 = 894 therefore percentage of fruits in good condition = ( 894 / 1000 × 100 ) % = ( 89400 / 1000 ) % = 89.4 % answer : b"
Answer: b
Python program:
a = 600 + 400 
b = 15 / 100
c = 600 * b
d = 4 / 100
e = 400 * d
f = c + e 
g = a - f
h = 600 + 400 
i = g / h
j = i * 100
Problem: james took a 3 - hour bike ride . in the second hour he travlled 18 miles , which was 20 percent farther than he traveled the first hour . if he traveled 25 percent farther in the third hour than he did in the second hour , how many miles did jose travel during the entire ride ?
Options: a ) 54.0 , b ) 54.9 , c ) 55.5 , d ) 57.0 , e ) 63.0
Rationale: let the distance travelled in the first hour be x . thus , 1.2 x = 18 , x = 15 . now , the distance travelled in the 3 rd hour = 18 + 1 / 4 ∗ 18 = the only option ending with a 0.5 in the decimal place is c . answer : c
Answer: c
Python program:
a = 1 * 100
b = a * 18
c = 1 * 100
d = c + 20 
e = b / d
f = 25 * 18
g = f / 20
h = e + g 
i = h + 18
Problem: by weight , liquid x makes up 2 percent of solution p and 7.5 percent of solution q . if 400 grams of solution p are mixed with 600 grams of solution q , then liquid x accounts for what percent of the weight of the resulting solution ?
Options: a ) 4.5 % , b ) 4.7 % , c ) 4.9 % , d ) 5.1 % , e ) 5.3 %
Rationale: "the number of grams of liquid x is 2 ( 400 ) / 100 + 7.5 ( 600 ) / 100 = 8 + 45 = 53 grams . 53 / 1000 = 5.3 % the answer is e ."
Answer: e
Python program:
a = 7 * 5
b = a / 100
c = 1 + b 
d = c / 1000
e = d * 100
Problem: a train traveling at 216 kmph crosses a platform in 30 seconds and a man standing on the platform in 12 seconds . what is the length of the platform in meters ?
Options: a ) 240 meters , b ) 360 meters , c ) 420 meters , d ) 720 meters , e ) can not be determined
Rationale: "answer distance covered by the train when crossing a man and when crossing a platform when a train crosses a man standing on a platform , the distance covered by the train is equal to the length of the train . however , when the same train crosses a platform , the distance covered by the train is equal to the length of the train plus the length of the platform . the extra time that the train takes when crossing the platform is on account of the extra distance that it has to cover . i . e . , length of the platform . compute length of platform length of the platform = speed of train * extra time taken to cross the platform . length of platform = 216 kmph * 12 seconds convert 216 kmph into m / sec 1 kmph = 5 / 18 m / s ( this can be easily derived . but if you can remember this conversion , it saves a good 30 seconds ) . ∴ 216 kmph = 5 / 18 ∗ 216 = 60 m / sec therefore , length of the platform = 60 m / s * 12 sec = 720 meters . choice d"
Answer: d
Python program:
a = 216 * 1000
b = a / 3600
c = b * 30
d = 216 * 1000
e = d / 3600
f = e * 12
g = c - f
Problem: for my anniversary , i decided to surprise my wife . since she is a voracious reader , i decided to collect a lot of books for her . on the first day of the month , i bought one book , on the second , i bought two and on the third , i bought three . this process went on till the anniversary and on the day , i had 190 books with me to gift her . can you calculate , on which day is our anniversary ?
Options: a ) 31 , b ) 28 , c ) 19 , d ) 33 , e ) 25
Rationale: c 19 rd day 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 = 190 thus our anniversary falls on the 19 rd day of the month . you can apply other formulas to shorten the process but that is the simplest way to do it .
Answer: c
Python program:
a = 190 / 10
Problem: at a tanning salon , customers are charged $ 10 for their first visit in a calendar month and $ 3 for each visit after that in the same calendar month . in the last calendar month , 100 customers visited the salon , of which 30 made a second visit , and 10 made a third visit . all other customers made only one visit . if those visits were the only source of revenue for the salon , what was the revenue for the last calendar month at the salon ?
Options: a ) $ 1220 , b ) $ 1120 , c ) $ 1300 , d ) $ 1340 , e ) $ 1880
Rationale: "i get b . this question seems too straightforward for 600 + . am i missing something ? 100 first - time visits - - > 100 ( 10 ) = $ 1000 30 + 10 = 40 subsequent visits - - > 40 ( 3 ) = $ 120 total revenue : 1000 + 120 = $ 1120 the answer is b ."
Answer: b
Python program:
a = 10 + 3 
b = a * 30
c = 100 - 30
d = c * 10
e = b + d
Problem: there are 7 players in a bowling team with an average weight of 94 kg . if two new players join the team , one weighs 110 kg and the second weighs 60 kg , what will be the new average weight ?
Options: a ) 75 kg . , b ) 80 kg . , c ) 86 kg . , d ) 90 kg . , e ) 92 kg .
Rationale: "the new average will be = ( 94 * 7 + 110 + 60 ) / 9 = 92 kgs e is the answer"
Answer: e
Python program:
a = 7 * 94
b = 110 + 60 
c = a + b 
d = 7 + 2 
e = c / d