euclaise/mathqa_programs huggingface dataset:
Problem: when a number is divided by 13 , the remainder is 11 . when the same number is divided by 17 , then remainder is 9 . what is the number ?
Options: a ) 349 , b ) 300 , c ) 500 , d ) 450 , e ) 250
Rationale: x = 13 p + 11 and x = 17 q + 9 13 p + 11 = 17 q + 9 17 q - 13 p = 2 q = 2 + 13 p / 17 least value of p which q = 2 + 13 p / 17 = > 26 x = ( 13 * 26 + 11 ) = 349 answer a
Answer: a
Python program:
a = 10 + 12 
b = a + 4 
c = 13 * b
d = c + 11
Problem: a football player scores 3 goals in his fifth match thus increasing his average goals score by 0.2 . the total number of goals in his 5 matches would be
Options: a ) 4 , b ) 6 , c ) 8 , d ) 11 , e ) 12
Rationale: while this question can be solved with a rather straight - forward algebra approach ( as the other posters have noted ) , it can also be solved by testing the answers . one of those numbers must be the total number of goals . . . from a tactical standpoint , it ' s best to test either answer b or answer d , so if the answer is not correct , then you would have a gauge for whether you should go higher or lower with your next test . here , i ' ll start with answer d = 11 goals if . . . . total goals = 11 goals 5 th game = 3 goals 1 st 4 games = 8 goals avg . for 4 games = 8 / 4 = 2 goals / game avg . for all 5 games = 6 / 5 = 2.2 goals / game 2.2 * 5 = 11 so answer d
Answer: d
Python program:
a = 4 * 3
b = 4 * 5
c = b * 0
d = a - c
e = d + 3
Problem: 350 metres long yard , 26 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between 2 consecutive trees
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 17
Rationale: "26 trees have 25 gaps between them , required distance ( 350 / 25 ) = 14 c"
Answer: c
Python program:
a = 26 - 2
b = a + 1 
c = 350 / b
Problem: the population of a town is 8000 . it decreases annually at the rate of 20 % p . a . what will be its population after 2 years ?
Options: a ) 4300 , b ) 4500 , c ) 5120 , d ) 5230 , e ) 5366
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 8000 × 80 / 100 × 80 / 100 = 5120 c"
Answer: c
Python program:
a = 20 / 100
b = 8000 * a
c = 8000 - b
d = 20 / 100
e = 8000 * d
f = 8000 - e
g = 20 / 100
h = f * g
i = c - h
Problem: a pair of articles was bought for $ 900 at a discount of 10 % . what must be the marked price of each of the article ?
Options: a ) $ 300 , b ) $ 500 , c ) $ 350 , d ) $ 400 , e ) $ 600
Rationale: "s . p . of each of the article = 900 / 2 = $ 450 let m . p = $ x 90 % of x = 450 x = 450 * 100 / 90 = $ 500 answer is b"
Answer: b
Python program:
a = 100 - 10
b = 900 / 2
c = a * b
d = c / 100
Problem: what will be the fraction of 10 %
Options: a ) 1 / 10 , b ) 1 / 50 , c ) 1 / 75 , d ) 1 / 25 , e ) none of these
Rationale: "explanation : 10 * 1 / 100 = 1 / 10 option a"
Answer: a
Python program:
a = 10 / 2
b = circle_area / (
Problem: a man buys an item at rs . 600 and sells it at the loss of 20 percent . then what is the selling price of that item
Options: a ) rs . 480 , b ) rs . 760 , c ) rs . 860 , d ) rs . 960 , e ) none of these
Rationale: "explanation : here always remember , when ever x % loss , it means s . p . = ( 100 - x ) % of c . p when ever x % profit , it means s . p . = ( 100 + x ) % of c . p so here will be ( 100 - x ) % of c . p . = 80 % of 600 = 80 / 100 * 600 = 480 option a"
Answer: a
Python program:
a = 20 / 100
b = 1 - a
c = 600 * b
Problem: last month , john rejected 0.5 % of the products that he inspected and jane rejected 0.8 percent of the products that she inspected . if total of 0.75 percent of the products produced last month were rejected , what fraction of the products did jane inspect ?
Options: a ) 1 / 6 , b ) 1 / 2 , c ) 5 / 8 , d ) 5 / 6 , e ) 15 / 16
Rationale: "x - fraction of products jane inspected ( 1 - x ) - fraction of products john inspected 0.8 ( x ) + 0.5 ( 1 - x ) = 0.75 0.3 x = 0.75 - 0.5 x = 0.25 / 0.3 x = 5 / 6 therefore the answer is d : 5 / 6 ."
Answer: d
Python program:
a = 0 - 75
b = 0 - 8
c = a / b
Problem: if k is an integer and 0.00010101 x 10 ^ k is greater than 10 , what is the least possible value of k ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "0.00010101 * 10 ^ k > 10 we need to move the decimal point to the right 5 places to get 10.101 this is equivalent to multiplying by 10 ^ 5 . the answer is c ."
Answer: c
Python program:
a = 10 / 0
b = math.log(a)
c = math.log(10)
d = b / c
Problem: what least number must be subtracted from 42398 so that remaining no . is divisible by 15
Options: a ) 3 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: "explanation : on dividing 42398 by 15 we get the remainder 8 , so 8 should be subtracted option d"
Answer: d
Python program:
a = 42398 / 15
b = math.floor(a)
c = b * 15
d = 42398 - c
Problem: what is 35 % of 4 / 13 of 650 ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "this problem can be solved easily if we just use approximation : 35 % is a little over 1 / 3 , while 4 / 13 is a little less than 4 / 12 , which is 1 / 3 . thus , the answer is about 1 / 3 of 1 / 3 of 650 , or 1 / 9 of 650 . since the first 1 / 3 is a slight underestimate and the second 1 / 3 is a slight overestimate , the errors will partially cancel each other out . our estimate will be relatively accurate . the number 650 is a bit more than 630 , so ( 1 / 9 ) * 630 will be about 70 . keeping track not only of your current estimate , but also of the degree to which you have overestimated or underestimated , can help you pinpoint the correct answer more confidently . the answer is c ."
Answer: c
Python program:
a = 3 + 2 
b = a * 2
c = 3 * 4
d = c * 100
e = b * d
f = 3 + 4 
g = 3 + 2 
h = f * g
i = 3 + 2 
j = i * 2
k = h * j
l = e + k 
m = 3 + 3 
n = l + m 
o = 35 * n
p = o / 100
Problem: a man is 24 years older than his son . in two years , his age will be twice the age of his son . the present age of his son is :
Options: a ) 14 years , b ) 18 years , c ) 20 years , d ) 22 years , e ) 17 years
Rationale: "let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . ( x + 24 ) + 2 = 2 ( x + 2 ) x + 26 = 2 x + 4 x = 22 . answer d"
Answer: d
Python program:
a = 2 * 2
b = a - 2
c = 24 - b
d = 2 - 1
e = c / d
Problem: 79 laboratories raise the bacterium , the laboratory have 48 culture dishes on average , which has about 25073 bacteria each . how many bacteria are there approximately ?
Options: a ) 10 ^ 7 , b ) 10 ^ 9 , c ) 10 ^ 8 , d ) 10 ^ 10 , e ) 10 ^ 11
Rationale: 79 laboratories raise the bacterium , the laboratory have 48 culture dishes on average , which has about 25,073 bacteria each . how many bacteria are there approximately ? a . 10 ^ 7 b . 10 ^ 8 c . 10 ^ 9 d . 10 ^ 10 e . 10 ^ 11 - > due to approximately , 79 = 80 , 48 = 50 , 25,073 = 25,000 are derived , which makes ( 79 ) ( 48 ) ( 25,075 ) = ( 80 ) ( 50 ) ( 25,000 ) = 10 ^ 8 . the answer is c .
Answer: c
Python program:
a = 79 * 48
b = a * 25073
Problem: the simple form of the ratio 5 / 3 : 2 / 5 is ?
Options: a ) 10 : 6 , b ) 10 : 3 , c ) 25 : 6 , d ) 25 : 3 , e ) 30 : 3
Rationale: "5 / 3 : 2 / 5 = 25 : 6 answer : c"
Answer: c
Python program:
a = 2 / 5
Problem: pat , kate and mark charged a total of 180 hours to a certain project . if pat charged twice as much time to the project as kate and 1 / 3 as much times as mark , how many more hours did mark charge to the project than kate .
Options: a ) 18 , b ) 36 , c ) 72 , d ) 90 , e ) 100
Rationale: let kate charge for x hours , then pat charged for 2 x and mat - for 6 x . so , 2 x + 6 x + x = 180 - total hours charged for , x = 20 . mat charged 6 x - x or 5 x for more hours than kate , or for 100 hours . e is correct
Answer: e
Python program:
a = 1 + 2 
b = 2 * 3
c = a + b 
d = 180 / c
e = 2 * 3
f = e - 1
g = d * f
Problem: one tap , working alone at its maximum constant rate , can fill a certain sink in 287 seconds . a second tap , working alone at its maximum constant rate , can fill the same sink in 283 seconds . if both taps work together at their respective maximum constant rates , the time it will take to fill the sink is closest to
Options: a ) 142 seconds , b ) 150 seconds , c ) 177 seconds , d ) 200 seconds , e ) 270 seconds
Rationale: tap 1 : 283 secs tap 2 : 287 secs considering the average of these 2 taps : 285 secs . so 1 tap can fill the tank in 285 secs , so 2 taps can fill the tank in 285 / 2 = 142.5 secs . closest answer is a .
Answer: a
Python program:
a = 1 / 287
b = 1 / 283
c = a + b 
d = 1 / c
Problem: of the 85 house in a development , 50 have a two - car garage , 40 have an in - the - ground swimming pool , and 35 have both a two - car garage and an in - the - ground swimming pool . how many houses in the development have neither a two - car garage nor an in - the - ground swimming pool ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: "neither car nor garage = total - garage - ( swim - common ) = 85 - 50 - ( 40 - 35 ) = 85 - 55 = 30 answer e"
Answer: e
Python program:
a = 50 - 35
b = 40 - 35
c = a + b 
d = c + 35 
e = 85 - d
Problem: a train running at the speed of 240 km / hr crosses a pole in 21 seconds . what is the length of the train ?
Options: a ) 1300 m , b ) 1350 m , c ) 1400 m , d ) 1450 m , e ) 1500 m
Rationale: "speed = ( 240 * 5 / 18 ) m / sec = ( 200 / 3 ) m / sec length of the train = ( speed x time ) = ( 200 / 3 * 21 ) m = 1400 m . answer : c"
Answer: c
Python program:
a = 240 * 1000
b = a / 3600
c = b * 21
Problem: the difference between the squares of two consecutive odd integers is a square < 1000 whose root equals the combined sum of the digits of the two integers . what is the sum of the digits m of the larger integer ?
Options: a ) m = 2 , b ) m = 5 , c ) m = 8 , d ) 10 , e ) 11
Rationale: really hard . but let ' s start with few concepts : 1 . square of an odd integer will be odd . 2 . difference of odd and odd will be even . 3 . any odd integer can be expressed as difference of two squares . 4 . an even integer can be expressed as difference of two squares only if that even integer is a multiple of 4 . assume two odd integers to be ( 2 x - 1 ) and ( 2 x + 1 ) . difference of their squares = ( 2 x + 1 ) ^ 2 - ( 2 x - 1 ) ^ 2 = 4 x ^ 2 + 1 + 4 x - ( 4 x ^ 2 + 1 - 4 x ) = 4 x ^ 2 + 1 + 4 x - 4 x ^ 2 - 1 + 4 x = 8 x now root of 8 x needs to be an integer such that it is equal to the sum of the digits of the two odd integers . 8 = 2 ^ 3 , so x needs to be such that itcompletesa perfect square . if we find x , we can find the value of 2 x + 1 ( larger integer ) and then sum of its digits . let ' s check the options , starting with c . for sum to be 8 , few possibilities are : 17 , 35 , 53 , 71 if we take 17 , the pair is 15 and 17 , meaning x = 8 . 8 x = 64 root of 64 = 4 but 4 is not equal to 1 + 5 + 1 + 7 . reject . if we take 35 , the pair is 33 and 35 , meaning x = 17 . 8 x = 8 * 17 reject since perfect square is not possible . if we take 53 , the pair is 51 and 53 , meaning x = 26 . 8 x = 8 * 26 reject since perfect square is not possible . if we take 71 , the pair is 69 and 71 , meaning x = 35 . 8 x = 8 * 35 reject since perfect square is not possible . i tried each option and the possibilities and then got lost . then , it occurred to me that i was only checking 2 - digit integers . what about 3 - digits ? starting with option a , only 2 - digit odd integer whose sum is 2 is 101 . if we take 101 , the pair is 99 and 101 , meaning x = 50 . 8 x = 8 * 50 = 400 root of 400 = 20 which is indeed equal to 9 + 9 + 1 + 1 . answer ( a ) .
Answer: a
Python program:
a = 1000 / 10
b = a + 1 
c = b ** 2
d = 1000 / 10
e = d + 1 
f = e - 2
g = f ** 2
h = c - g
i = math.sqrt(h)
j = i / 10
Problem: if f ( x ) = 2 x + 3 , & g ( x ) = ( x - 3 ) / 2 , then what is the value of , fo ( fo ( go ( go ( fo ( fo ( go ( go . . . . . . . . . . . . . . . . ( fo ( fo ( go ( gof ( x ) ) ) ) ) . . . . . ) ) ) ) ) ) ?
Options: a ) 3 , b ) 2 , c ) 9 , d ) 7 , e ) 1
Rationale: f ( x ) = 2 x + 3 g ( x ) = ( x - 3 ) / 2 gof ( x ) = 2 x + 3 − 32 = x 2 x + 3 − 32 = x gogof ( x ) = x − 32 x − 32 fogogof ( x ) = 2 ( x − 32 ) + 32 ( x − 32 ) + 3 = 2 x − 6 + 622 x − 6 + 62 = x fofogogof ( x ) = 2 x + 3 this means , when we apply two times g ( x ) and two time f ( x ) on f ( x ) we get f ( x ) . this pattern continues , hence the answer is option ( d ) .
Answer: d
Python program:
a = 4 * 3
b = a + 2 
c = b / 2
Problem: find the number which is nearest to 3105 and is exactly divisible by 21
Options: a ) 1208 , b ) 3108 , c ) 241 , d ) 217 , e ) 3147
Rationale: "on dividing 3105 by 21 , we get 18 as remainder .  number to be added to 3105 = ( 21 - 18 ) - 3 . hence , required number = 3105 + 3 = 3108 . answer b 3108"
Answer: b
Python program:
a = 21 - reminder
b = 3105 + a
Problem: the ratio of pens to pencils is 5 to 6 . there are 5 more pencils than pens . how many pencils are there ?
Options: a ) 24 , b ) 30 , c ) 36 , d ) 42 , e ) 48
Rationale: "let the number of pens be 5 x and the number of pencils be 6 x . 6 x - 5 x = 5 x = 5 the number of pencils is 30 . the answer is b ."
Answer: b
Python program:
a = 5 * 5
b = a + 5
Problem: p is 3 times as old as q . in 11 years , p will be twice as old as q . how old was p 3 years ago ?
Options: a ) 21 , b ) 24 , c ) 27 , d ) 30 , e ) 33
Rationale: p = 3 q so q = p / 3 p + 11 = 2 ( q + 11 ) = 2 ( p / 3 + 11 ) p / 3 = 11 p = 33 three years ago , p was 30 . the answer is d .
Answer: d
Python program:
a = 3 * 11
b = a - 3
Problem: a person can row at 9 kmph and still water . he takes 8 1 / 2 hours to row from a to b and back . what is the distance between a and b if the speed of the stream is 1 kmph ?
Options: a ) 32 , b ) 38 , c ) 29 , d ) 54 , e ) 20
Rationale: "let the distance between a and b be x km . total time = x / ( 9 + 1 ) + x / ( 9 - 1 ) = 8.5 = > x / 10 + x / 8 = 17 / 2 = > ( 4 x + 5 x ) / 40 = 17 / 2 = > x = 38 km . answer : b"
Answer: b
Python program:
a = 9 - 1
b = 9 + 1 
c = a * b
d = c * 8
e = 9 + 1 
f = 9 - 1
g = e + f 
h = d / g
Problem: a walks at 30 kmph and 30 hours after his start , b cycles after him at 50 kmph . how far from the start does b catch up with a ?
Options: a ) 1200 km , b ) 1500 km , c ) 2000 km , d ) 2250 km , e ) 3600 km
Rationale: "suppose after x km from the start b catches up with a . then , the difference in the time taken by a to cover x km and that taken by b to cover x km is 30 hours . x / 30 - x / 50 = 30 x = 2250 km answer is d"
Answer: d
Python program:
a = 30 * 50
Problem: a box contains 1 red balls and 5 black balls . one by one , every ball is selected at random without replacement . what is the probability that the fourth ball selected is black ?
Options: a ) 1 / 4 , b ) 1 / 2 , c ) 1 / 2 , d ) 5 / 8 , e ) 2 / 3
Rationale: "my complicated version of your simple approach let the 5 black balls be bbbbb and 1 red balls be r they can be arranged in 6 slots _ _ _ _ _ _ _ _ in ( 6 ! ) / ( 5 ! x 1 ! ) if the fourth slot is black ball then the arrangement will be to fill _ _ _ b _ _ _ _ we have 5 slots and 4 black ( bbbb ) and 1 red ( r ) they can be arranged in ( 5 ! ) / ( 4 ! x 1 ! ) hence required probability = [ ( 6 ! ) / ( 5 ! x 1 ! ) ] / [ ( 5 ! ) / ( 4 ! x 1 ! ) ] = 6 / 5 c"
Answer: c
Python program:
a = 1 + 5 
b = a / 5
Problem: in a class of 40 students , 2 students did not borrow any books from the library , 12 students each borrowed 1 book , 13 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "the class borrowed a total of 40 * 2 = 80 books . the 27 students who borrowed 0 , 1 , or 2 books borrowed a total of 12 + 13 * 2 = 38 . to maximize the number of books borrowed by 1 student , let ' s assume that 12 students borrowed 3 books and 1 student borrowed the rest . 80 - 38 - 3 * 12 = 6 the maximum number of books borrowed by any student is 6 . the answer is d ."
Answer: d
Python program:
a = 40 * 2
b = 12 * 1
c = b + 13 
d = c + 2 
e = 40 - d
f = e - 1
g = f * 3
h = 12 * 1
i = 13 * 2
j = h + i 
k = g + j 
l = a - k
Problem: if 5400 mn = k ^ 4 , where m , n , and k are positive integers , what is the least possible value of 4 m + n ?
Options: a ) 11 , b ) 18 , c ) 55 , d ) 25 , e ) 33
Rationale: "k ^ 4 = 5400 ∗ mn k ^ 4 = 3 ^ 3.2 ^ 3.5 ^ 2 . mn in order to make rhs a perfect power of 4 , we require it to be multiplied by 3 , 2 & 5 ^ 2 mn = 3 . 2.5 ^ 2 mn = 150 = 10 * 15 ( least possible ) answer = 4 * 10 + 15 = 55 answer : c"
Answer: c
Python program:
a = 3 ** 4
b = 4 * a
Problem: on rainy mornings , mo drinks exactly n cups of hot chocolate ( assume that n is an integer ) . on mornings that are not rainy , mo drinks exactly 3 cups of tea . last week mo drank a total of 26 cups of tea and hot chocolate together . if during that week mo drank 10 more tea cups than hot chocolate cups , then how many rainy days were there last week ?
Options: a ) 0 , b ) 1 , c ) 4 , d ) 5 , e ) 6
Rationale: "t = the number of cups of tea c = the number of cups of hot chocolate t + c = 26 t - c = 10 - > t = 18 . c = 8 . mo drinks 3 cups of tea a day then number of days that are not rainy = 18 / 3 = 6 so number of rainy days = 7 - 6 = 1 b is the answer ."
Answer: b
Python program:
a = 4 + 3 
b = 26 + 10 
c = b / 2
d = c / 3
e = a - d
Problem: the mean of 50 observations was 36 . it was found later that an observation 45 was wrongly taken as 23 . the corrected new mean is ?
Options: a ) 36.7 , b ) 36.4 , c ) 36.5 , d ) 36.9 , e ) 36.3
Rationale: "correct sum = ( 36 * 50 + 45 - 23 ) = 1822 . correct mean = 1822 / 50 = 36.4 answer : b"
Answer: b
Python program:
a = 36 * 50
b = 50 - 2
c = b - 23
d = a + c 
e = d / 50
Problem: a and b are two partially filled buckets of water . if 4 liters are transferred from a to b , then a would contain one - third of the amount of water in b . alternatively , if 4 liters are transferred from b to a , b would contain one - half of the amount of water in a . bucket a contains how many liters of water ?
Options: a ) 44 / 5 , b ) 13 , c ) 17 , d ) 21 , e ) 23
Rationale: "let bucket a be a and bucket b be b scenario 1 a - 4 = 1 / 3 ( b + 4 ) - - - - > 3 a - 12 = b + 4 scenario 2 b - 4 = 1 / 2 ( a + 4 ) - - - - - > 2 b - 8 = a + 4 from scenario 1 , b = 3 a - 16 substitute b with this information in stmt 2 2 ( 3 a - 16 ) - 8 = a + 4 - - - - - - > 6 a - 32 - 8 = a + 4 - - - - - - > 6 a - a = 40 + 4 - - - > 5 a = 44 a = 44 / 5 , answer choice a"
Answer: a
Python program:
a = 4 + 3 
b = a + 2 
c = 4 / 2
d = b * c
e = 1 / 2
f = 2 + e 
g = d / f
Problem: pipe a can fill a tank in 4 hours . due to a leak at the bottom , it takes 6 hours for the pipe a to fill the tank . in what time can the leak alone empty the full tank ?
Options: a ) 12 , b ) 67 , c ) 95 , d ) 36 , e ) 66
Rationale: "let the leak can empty the full tank in x hours 1 / 4 - 1 / x = 1 / 6 = > 1 / x = 1 / 4 - 1 / 6 = ( 3 - 2 ) / 12 = 1 / 12 = > x = 12 . answer : a"
Answer: a
Python program:
a = 6 * 4
b = 6 - 4
c = a / b
Problem: an individual deposited 20 % of 25 % of 30 % of what he had into his account with a bank . if he deposited rs . 750 , how much was he having initially with him before depositing ?
Options: a ) rs . 500000 , b ) rs . 50000 , c ) rs . 5000 , d ) rs . 15000 , e ) rs . 6000
Rationale: let x amount he has then 20 % of 25 % of 30 % of x = 750 so x = 50000 answer : b
Answer: b
Python program:
a = 30 / 100
b = 20 / 100
c = 25 / 100
d = b * c
e = a * d
f = 750 / e
Problem: in a market , a dozen eggs cost as much as a pound of rice , and a half - liter of kerosene costs as much as 8 eggs . if the cost of each pound of rice is $ 0.33 , then how many r cents does a liter of kerosene cost ? [ one dollar has 100 cents . ]
Options: a ) 0.33 , b ) 0.44 , c ) 0.55 , d ) 44 , e ) 55
Rationale: "main thing to remember is answer is asked in cents , however when we calculate , it comes up as 0.44 $ just multiply by 100 , answer r = 44 . d"
Answer: d
Python program:
a = 1 / 2
b = 8 / a
c = b / 12
d = 0 * 33
e = c * d
Problem: dacid obtained 96 , 98 , 99 , 100 and 98 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 79 , b ) 99 , c ) 88 , d ) 88 , e ) 98
Rationale: "average = ( 96 + 98 + 99 + 100 + 98 ) / 5 = 491 / 5 = 98 . answer : e"
Answer: e
Python program:
a = 96 + 98 
b = a + 99 
c = b + 100 
d = c + 98 
e = 10 / 2
f = d / e
Problem: if 4 x + 3 y = 8 and y − 3 x = 2 , then what is the value of x + 4 y ?
Options: a ) 10 , b ) 3 , c ) 15 , d ) 52 / 7 , e ) 60 / 7
Rationale: "4 x + 3 y = 8 − 3 x + y = 2 adding both the equations - - > x + 4 y = 10 answer : a"
Answer: a
Python program:
a = 8 + 4 
b = 3 + 4 
c = a / b
d = 8 + 4 
e = 3 + 4 
f = d / e
g = 3 * f
h = g - 4
i = h / 3
j = c * i
Problem: a lemonade stand sold only small and large cups of lemonade on tuesday . 3 / 5 of the cups sold were small and the rest were large . if the large cups were sold for 1 / 6 as much as the small cups , what fraction of tuesday ' s total revenue was from the sale of large cups ?
Options: a ) 7 / 16 , b ) 7 / 15 , c ) 10 / 21 , d ) 17 / 35 , e ) 1 / 10
Rationale: "let the total # of cups be 10 . # of small cups sold 3 / 5 * 10 = 6 ; # of large cups sold 10 - 6 = 4 ; let the price of small cup be $ 6 , then the price of larges cup would be 1 / 6 * 6 = $ 1 ; revenue from small cups : 6 * $ 6 = $ 36 ; revenue from large cups cups : 4 * $ 1 = $ 4 ; fraction of total revenue from large cups : 4 / ( 36 + 4 ) = 1 / 10 . answer : e ."
Answer: e
Python program:
a = 3 / 5
b = a * 10
c = 10 - b
d = 1 / 6
e = 3 / 5
f = e * 10
g = d * f
h = c * g
i = 3 / 5
j = i * 10
k = 3 / 5
l = k * 10
m = j * l
n = 3 / 5
o = n * 10
p = 10 - o
q = 1 / 6
r = 3 / 5
s = r * 10
t = q * s
u = p * t
v = m + u 
w = h / v
Problem: there are 10 baskets numbered from 1 to 10 and filled with apples . 10 children are asked to pick apples one by one from each basket such that the number of apples picked by each child from each basket is equal to the number marked on the basket . if there were 1000 apples in total and the baskets were filled in such a way that none of the basket became empty in the process , how many apples were left in the end ?
Options: a ) 330 , b ) 390 , c ) 450 , d ) 510 , e ) 570
Rationale: "each child takes a total of 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 10 * 11 / 2 = 55 apples . the total number of apples taken by 10 children is 10 * 55 = 550 the number of apples left in the end is 1000 - 550 = 450 apples . the answer is c ."
Answer: c
Python program:
a = 1 + 10 
b = 10 / 2
c = a * b
d = 10 / 2
e = c + d 
f = e + 1 
g = f * 10
h = 1000 - g
Problem: the positive numbers w , x , y , and z are such that x is 30 percent greater than y , y is 20 percent greater than z , and w is 20 percent less than x . what percent greater than z is w ?
Options: a ) 15.2 % , b ) 16.0 % , c ) 20.0 % , d ) 23.2 % , e ) 24.8 %
Rationale: "my strategy is same as thedobermanbut instead take z = 100 , which makes life a bit easy . as : z = 100 y = 120 ( 20 % greater than z ) z = 144 ( 20 % greater than y ) now calculate w 20 % less than z = 144 * 80 / 100 = 115.2 now by just looking , relation between w and z : w - z / z * 100 = 20 - answer c"
Answer: c
Python program:
a = 30 + 100 
b = a / 100
c = 30 + 100 
d = c / 100
e = b * d
f = 100 - 30
g = f / 100
h = e * g
i = h - 1
j = 100 * i