euclaise/mathqa_programs huggingface dataset:
Problem: an investor can sell her microtron stock for 36 $ per share and her dynaco stock for 44 $ per share , if she sells 300 shares altogether , some of each stock , at an average price per share of 40 $ , how many shares of dynaco stock has she sold ?
Options: a ) 52 , b ) 75 , c ) 92 , d ) 136 , e ) 150
Rationale: w 1 / w 2 = ( a 2 - aavg ) / ( aavg - a 1 ) = ( 44 - 40 ) / ( 40 - 36 ) = 4 / 4 = 1 / 1 = number of microtron stocks / number of dynaco stocks so for every 1 microtron stock , she sold 1 dynaco stock . so out of 300 total stocks , ( 1 / 1 ) th i . e . 300 / 2 = 150 must be dynaco stock . answer ( e )
Answer: e
Python program:
a = 44 - 36
b = 40 / a
c = 300 * b
d = 36 + 44 
e = 44 - 36
f = d / e
g = c / f
Problem: a man is 35 years older than his son . in two years , his age will be twice the age of his son . the present age of this son is
Options: a ) 78 years , b ) 22 years , c ) 33 years , d ) 66 years , e ) 65 years
Rationale: "let ' s son age is x , then father age is x + 35 . = > 2 ( x + 2 ) = ( x + 35 + 2 ) = > 2 x + 4 = x + 37 = > x = 33 years answer : c"
Answer: c
Python program:
a = 2 * 2
b = a - 2
c = 35 - b
d = 2 - 1
e = c / d
Problem: a jogger running at 9 km / hr along side a railway track is 120 m ahead of the engine of a 120 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?
Options: a ) 89 , b ) 20 , c ) 36 , d ) 24 , e ) 34
Rationale: "speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 120 + 120 = 360 m . time taken = 240 / 10 = 24 sec . answer : option d"
Answer: d
Python program:
a = 120 + 120 
b = 45 - 9
c = 10 / 2
d = 45 - 9
e = d / 2
f = c / e
g = b * f
h = a / g
Problem: the width of a rectangular hall is ½ of its length . if the area of the hall is 200 sq . m , what is the difference between its length and breadth ?
Options: a ) 8 m
b ) 10 m
c ) 12 m
d ) 15 m
e ) 17 m
Rationale: let the length of the hall be x m breadth of the hall = 1 x / 2 m area of the hall = length * breadth 200 = x * 1 x / 2 x ² = 400 x = 20 difference between the length and breadth of the hall = x - 1 x / 2 = x / 2 = 20 / 2 = 10 m answer : b
Answer: b
Python program:
a = 1 / 2
b = 200 / a
c = math.sqrt(b)
d = c / 2
Problem: a work which could be finished in 10 days was finished 3 days earlier after 10 more men joined . the number of men employed was ?
Options: a ) 15 , b ) 20 , c ) 88 , d ) 71 , e ) 11
Rationale: "x - - - - - - - 10 ( x + 10 ) - - - - 6 x * 10 = ( x + 10 ) 6 x = 15 \ answer : a"
Answer: a
Python program:
a = 3 * 2
b = a * 10
c = 3 * 2
d = 10 - c
e = b / d
Problem: in a dairy farm , 30 cows eat 30 bags of husk in 30 days . in how many days one cow will eat one bag of husk ?
Options: a ) 1 , b ) 40 , c ) 20 , d ) 26 , e ) 30
Rationale: "explanation : one bag of husk = 30 cows per day ⇒ 30 × 1 × 30 = 1 × 30 × x for one cow = 30 days answer : e"
Answer: e
Python program:
a = 30 / 30
b = a * 30
Problem: each week , harry is paid x dollars per hour for the first 30 hours and 1.5 x dollars for each additional hour worked that week . each week , annie is paid x dollars per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week annie worked a total of 56 hours . if harry and annie were paid the same amount last week , how many hours did harry work last week ?
Options: a ) 52 , b ) 54 , c ) 56 , d ) 58 , e ) 60
Rationale: "annie earned 40 x + 16 ( 2 x ) = 72 x let h be the number of hours that harry worked . harry earned 30 x + 1.5 x ( h - 30 ) = 72 x ( 1.5 x ) ( h ) = 87 x h = 58 hours the answer is d ."
Answer: d
Python program:
a = 40 + 2 
b = a - 30
c = b / 1
d = c + 30
Problem: car dealership x , the total profit from sales increased by 9 percent over the previous years , while the number of cars sold decreased by 9 percent over the previous years . approximately what was the average percent increase in profit per car over the previous year .
Options: a ) 18 % , b ) 19.78 % , c ) 22 % , d ) 23 % , e ) 25 %
Rationale: "let profit be x and cars sold be y originally profit / car = x / y now it is 1.09 x / 0.91 y = 109 / 91 ( x / y ) increase in profit per car = ( ( 18 / 91 ) ( x / y ) ) / ( x / y ) * 100 = 19.78 % answer = b"
Answer: b
Python program:
a = 100 + 9 
b = 10 - 3
c = a / b
d = 100 / 10
e = c - d
f = 100 / 10
g = e / f
h = g * 100
Problem: when positive integer n is divided by 2 , the remainder is 2 . when n is divided by 7 , the remainder is 5 . how many values less than 100 can n take ?
Options: a ) 0 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "a quick approac to this q is . . the equation we can form is . . 3 x + 2 = 7 y + 5 . . 3 x - 3 = 7 y . . . 3 ( x - 1 ) = 7 y . . . so ( x - 1 ) has to be a multiple of 7 as y then will take values of multiple of 3 . . here we can see x can be 1 , 8,15 , 22,29 so 5 values till 100 is reached as ( 29 - 1 ) * 3 = 84 and next multiple of 7 will be 84 + 21 > 100 . . ans 5 . . c"
Answer: c
Python program:
a = 100 - reminder
Problem: two goods trains each 250 m long are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 24 , b ) 45 , c ) 48 , d ) 51 , e ) 44
Rationale: "relative speed = 45 + 30 = 75 km / hr . 75 * 5 / 18 = 125 / 6 m / sec . distance covered = 250 + 250 = 500 m . required time = 500 * 6 / 125 = 24 sec . answer : option a"
Answer: a
Python program:
a = 45 + 30
Problem: if x / y = 2 / 7 , then ( x + y ) / ( x - y ) = ?
Options: a ) 5 , b ) 1 / 5 , c ) - 1 / 6 , d ) - 9 / 5 , e ) - 5
Rationale: "any x and y satisfying x / y = 2 / 7 should give the same value for ( x + y ) / ( x - y ) . say x = 2 and y = 7 , then ( x + y ) / ( x - y ) = ( 2 + 7 ) / ( 2 - 7 ) = - 9 / 5 . answer : d ."
Answer: d
Python program:
a = 2 + 7 
b = 2 - 7
c = a / b
Problem: two goods trains each 500 m long are running in opposite directions on parallel tracks . their speeds are 70 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 22 , b ) 36 , c ) 48 , d ) 99 , e ) 23
Rationale: "relative speed = 70 + 30 = 100 km / hr . 100 * 5 / 18 = 250 / 9 m / sec . distance covered = 500 + 500 = 1000 m . required time = 1000 * 9 / 250 = 36 sec answer : b"
Answer: b
Python program:
a = 70 + 30
Problem: p works 25 % more efficiently than q and q works 50 % more efficiently than r . to complete a certain project , p alone takes 50 days less than q alone . if , in this project p alone works for 60 days and then q alone works for 140 days , in how many days can r alone complete the remaining work ?
Options: a ) 50 days , b ) 102.7 days , c ) 100 days , d ) 150 days , e ) 80 days
Rationale: "p works 25 % more efficiently than q : something that takes q 5 days , takes p 4 days q works 50 % more efficiently than r : something that takes r 7.5 days , takes q 5 days p alone takes 50 days less than q : for every 4 days p works , q has to work an extra day . hence p alone can do it in 200 days and q alone in 250 days and hence r alone in 390 days p works for 60 days - - > 60 / 200 work done = > 30 % q works for 140 days - - > 140 / 250 work done = > 56 % 260 % work left . . . r alone will take 26 % * 395 = 102.7 days answer is ( b )"
Answer: b
Python program:
a = 4 * 50
b = 140 / 100
c = b * 60
d = a - c
Problem: a train 560 m in length crosses a telegraph post in 16 seconds . the speed of the train is ?
Options: a ) 126 kmph , b ) 77 kmph , c ) 54 kmph , d ) 71 kmph , e ) 88 kmph
Rationale: "s = 560 / 16 * 18 / 5 = 126 kmph answer : a"
Answer: a
Python program:
a = 560 / 16
b = const_3_6 * a
Problem: a man invests rs . 3,000 at the rate of 5 % per annum . how much more should he invest at the rate of 8 % , so that he can earn a total of 6 % per annum ?
Options: a ) rs . 1200 , b ) rs . 1300 , c ) rs . 1500 , d ) rs . 2000 , e ) none of these
Rationale: "explanation : interest on rs . 3000 at 5 % per annum = ( 3000 × 5 × 1 ) / 100 = rs . 150 let his additional investment at 8 % = x interest on rs . x at 8 % per annum = ( x × 8 × 1 ) / 100 = 2 x / 25 . to earn 6 % per annum for the total , interest = ( 3000 + x ) × 6 × 1 / 100 . = > 150 + 2 x / 25 = ( 3000 + x ) × 6 × 1 / 100 . = > 15000 + 8 x = ( 3000 + x ) × 6 . = > 15000 + 8 x = 18000 + 6 x . = > 2 x = 3000 . = > x = 1500 . answer : c"
Answer: c
Python program:
a = 8 * 1000
b = 6 - 5
c = 8 - 6
d = b / c
e = a * d
Problem: k is 50 % faster than l . if l starts at 9 a . m . and k starts at 10 a . m . l travels at a speed of 50 km / hr . if l and k are 300 kms apart , the time when they meet when they travel in opposite direction is ?
Options: a ) 12 pm , b ) 22 pm , c ) 72 pm , d ) 92 pm , e ) 23 pm
Rationale: explanation : let ' t ' be the time after which they met since l starts . given k is 50 % faster than l 50 t + 1.5 * 50 ( t - 1 ) = 300 50 t + 75 t = 300 + 75 t = 375 / 125 = 3 hrs past the time that l starts so they meet at ( 9 + 3 ) hrs = 12 : 00 noon . answer : a
Answer: a
Python program:
a = 300 - 50
b = 50 / 100
c = 1 + b 
d = c * 50
e = d + 50 
f = a / e
g = f + 10
Problem: how many prime numbers between 1 and 100 are factors of 10010 ?
Options: a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1
Rationale: "factor of 10010 = 2 * 5 * 7 * 11 * 13 - - - 5 prime numbers a"
Answer: a
Python program:
a = 4 * 1
Problem: one lady has 2 children , one of her child is boy , what is the probability of having both are boys
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) 3 / 4
Rationale: n ( s ) = one of her child is boy out of 2 children = bb , bg = 2 n ( e ) = both are boys = bb = 1 so p = n ( e ) / n ( s ) = 1 / 2 answer : a
Answer: a
Python program:
a = 1 / 2
Problem: 7 / 10 of the population of the country of venezia lives in montague province , while the rest lives in capulet province . in the upcoming election , 80 % of montague residents support romeo , while 70 % of capulet residents support juliet ; each resident of venezia supports exactly one of these two candidates . rounded if necessary to the nearest percent , the probability that a juliet supporter chosen at random resides in capulet is
Options: a ) 28 % , b ) 41 % , c ) 60 % , d ) 72 % , e ) 78 %
Rationale: "total population = 100 ( assume ) . 7 / 10 * 100 = 70 people from montague . 3 / 10 * 100 = 30 people from capulet . 0.2 * 70 = 14 people from montague support juliet . 0.7 * 30 = 21 people from capulet support juliet . the probability that a juliet supporter chosen at random resides in capulet is 21 / ( 14 + 21 ) = ~ 60 . answer : c"
Answer: c
Python program:
a = 70 / 100
b = 10 - 7
c = b / 10
d = a * c
e = 100 - 80
f = e / 100
g = 7 / 10
h = f * g
i = 70 / 100
j = 10 - 7
k = j / 10
l = i * k
m = h + l 
n = d / m
o = n * 100
Problem: car a runs at the speed of 58 km / hr & reaches its destination in 8 hr . car b runs at the speed of 70 km / h & reaches its destination in 4 h . what is the respective ratio of distances covered by car a & car b ?
Options: a ) 11 : 6 , b ) 12 : 7 , c ) 29 : 18 , d ) 15 : 6 , e ) 13 : 6
Rationale: "sol . distance travelled by car a = 58 ã — 8 = 464 km distance travelled by car b = 70 ã — 4 = 280 km ratio = 464 / 280 = 29 : 18 c"
Answer: c
Python program:
a = 58 * 8
b = 70 * 4
c = a / b
Problem: for any positive integer n , the sum of the first n positive integers equals n ( n + 1 ) / 2 . what is the sum y of all the even integers between 99 and 301 ?
Options: a ) 10,100 , b ) 20,200 , c ) 22,650 , d ) 40,200 , e ) 45,150
Rationale: "i would solve it in a different way . first of all , total number of even integers between 99 and 301 are , ( 301 - 99 ) / 2 = 202 / 2 = 101 average = ( 301 + 99 ) / 2 = 400 / 2 = 200 sum y = average * total count = 200 * 101 = 20,200 answer is b"
Answer: b
Python program:
a = 301 - 1
b = 99 + 1 
c = a - b
d = c / 2
e = d + 1
Problem: in what ratio p : q should the mixture p of milk and water in the ratio of 4 : 1 be mixed with another mixture q of milk and water in the ratio 2 : 3 so that the resultant mixture contains equal quantities of milk and water ?
Options: a ) 1 : 3 , b ) 2 : 3 , c ) 1 : 4 , d ) 3 : 4 , e ) 3 : 5
Rationale: "( 4 / 5 ) * p + ( 2 / 5 ) * q = ( 1 / 5 ) * p + ( 3 / 5 ) * q 3 p = q p / q = 1 / 3 the answer is a ."
Answer: a
Python program:
a = 1 + 3 
b = 4 + 2 
c = a - b
d = c + 1
Problem: if n is an integer and 101 n ^ 2 is less than or equal to 12100 , what is the greatest possible value of n ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "101 * n ^ 2 < = 12100 n ^ 2 < = 12100 / 101 which will be less than 121 since 12100 / 100 = 121 which is the square of 9 next closest value of n where n ^ 2 < = 121 is 10 ans d"
Answer: d
Python program:
a = 12100 / 101
b = math.sqrt(a)
c = math.floor(b)
Problem: how many minutes is it before 12 noon if 20 minutes ago it was 3 times as many minutes after 9 am ?
Options: a ) 40 , b ) 39 , c ) 42 , d ) 55 , e ) 29
Rationale: a 40 minutes , or 11.20 am
Answer: a
Python program:
a = 12 * const_60
b = 9 * const_60
c = a - b
d = c - 20
e = 3 + 1 
f = d / e
Problem: a bag holds 4 red marbles and 5 green marbles . if you removed two randomly selected marbles from the bag , without replacement , what is the probability that both would be red ?
Options: a ) 1 / 10 , b ) 1 / 6 , c ) 3 / 10 , d ) 2 / 5 , e ) 1 / 4
Rationale: "probability of selecting first red marble = 4 / 9 probability of selecting second red marble without replacement = 3 / 8 final probability = 4 / 9 * 3 / 8 = 1 / 6 the correct answer is b ."
Answer: b
Python program:
a = math.comb(2, 0)
b = 4 + 5 
c = math.comb(b, 4)
d = a / c
Problem: the sum of four consecutive even numbers is 140 . what would be the smallest number ?
Options: a ) 32 , b ) 88 , c ) 70 , d ) 123 , e ) 12
Rationale: "let the four consecutive even numbers be 2 ( x - 2 ) , 2 ( x - 1 ) , 2 x , 2 ( x + 1 ) their sum = 8 x - 4 = 140 = > x = 18 smallest number is : 2 ( x - 2 ) = 32 answer : a"
Answer: a
Python program:
a = 140 - 10
b = a - 2
c = b / 4
d = c + 2 
e = d + 2 
f = e ** 2
g = 140 - 10
h = g - 2
i = h / 4
j = i + 2 
k = j + 2 
l = k + 2 
m = l ** 2
n = f + m 
o = 140 - 10
p = o - 2
q = p / 4
r = q ** 2
s = 140 - 10
t = s - 2
u = t / 4
v = u + 2 
w = v ** 2
x = r + w 
y = n + x
Problem: a number is doubled and 15 is added . if the resultant is multiplied by 5 , it becomes 125 . what is that number ?
Options: a ) 5 , b ) 10 , c ) 8 , d ) none of these , e ) can not be determined
Rationale: "solution let the number be x . then , 5 ( 2 x + 15 ) ‹ = › 125 ‹ = › 2 x + 15 = 25 ‹ = › 2 x = 10 x = 5 . answer d"
Answer: d
Python program:
a = 3 * 15
b = 5 - a
c = 3 * 2
d = b / c
Problem: a train is 360 meter long is running at a speed of 75 km / hour . in what time will it pass a bridge of 140 meter length ?
Options: a ) 87 , b ) 69 , c ) 40 , d ) 72 , e ) 24
Rationale: "speed = 75 km / hr = 75 * ( 5 / 18 ) m / sec = 125 / 6 m / sec total distance = 360 + 140 = 500 meter time = distance / speed = 500 * ( 6 / 125 ) = 24 seconds answer : e"
Answer: e
Python program:
a = 360 + 140 
b = 75 * 1000
c = b / 3600
d = a / c
Problem: if k ^ 3 is divisible by 120 , what is the least possible value of integer k ?
Options: a ) 15 , b ) 30 , c ) 60 , d ) 90 , e ) 120
Rationale: "k ^ 3 = 120 * x = 2 ^ 3 * 3 * 5 * x the factors of k must at minimum include 2 * 3 * 5 = 30 . the answer is b ."
Answer: b
Python program:
a = 120 / 2
b = a / 2
Problem: population of a city in 20004 was 1000000 . if in 2005 there isan increment of 20 % , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45 % , then find the population of city atthe end of the year 2007
Options: a ) 1131000 , b ) 979923 , c ) 980241 , d ) 2356677 , e ) 1083875
Rationale: "required population = p ( 1 + r 1 / 100 ) ( 1 - r 2 / 100 ) ( 1 + r 3 / 100 ) = p ( 1 + 20 / 100 ) ( 1 - 35 / 100 ) ( 1 + 45 / 100 ) = 1131000 a"
Answer: a
Python program:
a = 20 / 100
b = 1 + a 
c = 35 / 100
d = 1 - c
e = b * d
f = 35 / 100
g = 1 + f 
h = e * g
i = 1000000 * h
Problem: sony and johnny caught 40 fishes . sony caught 4 times as many as johnny . how many fishes did johnny catch ?
Options: a ) 12 , b ) 16 , c ) 34 , d ) 38 , e ) 8
Rationale: s + j = 40 s = 4 * j j = 8 answer : e
Answer: e
Python program:
a = 4 + 1 
b = 40 / a
Problem: two digits in brother ' s age are the same as the digit in the sister ' s age , but in reverse order . in 20 9 years brother will be twice as old as sister will be then . what is the difference in their current age ?
Options: a ) 34 , b ) 50 , c ) 32 , d ) 28 , e ) 45
Rationale: brother ' s age = 10 x + y so sister ' s age = 10 y + x . . after 29 years , 10 x + y + 29 = 2 * ( 10 y + x + 29 ) . . . . so 29 + 19 y = 8 x . . . check for odd values of y , y = 1 satisfies the eqn with x = 6 . . . so ages are 61 and 16 and ans as found correctly by u is e . . 45
Answer: e
Python program:
a = 20 + 20 
b = 9 - 4
c = a + b
Problem: a man owns 1 / 3 of market reserch beauro buzness , and sells 3 / 5 of his shares for 2000 rs , what is the value of buzness ?
Options: a ) 40000 , b ) 60000 , c ) 10000 , d ) 25000 , e ) 50000
Rationale: "if value of business = x total sell ( 1 x / 3 ) ( 3 / 5 ) = 2000 - > x = 10000 answer : c"
Answer: c
Python program:
a = 1 / 3
b = 3 / 5
c = a * b
d = 2000 / c
Problem: a contest will consist of n questions , each of which is to be answered eithertrueorfalse . anyone who answers all n questions correctly will be a winner . what is the least value of n for which the probability is less than 1 / 100 that a person who randomly guesses the answer to each question will be a winner ?
Options: a ) 5 , b ) 10 , c ) 50 , d ) 100 , e ) 1000
Rationale: "a contest will consist of n questions , each of which is to be answered eithertrueorfalse . anyone who answers all n questions correctly will be a winner . what is the least value of n for which the probability is less than 1 / 1000 that a person who randomly guesses the answer to each question will be a winner ? a . 5 b . 10 c . 50 d . 100 e . 1000 soln : ans is b probability that one question is answered right is 1 / 2 . now for minimum number of questions needed to take probability less than 1 / 1000 is = > ( 1 / 2 ) ^ n < 1 / 100 n = 50 satisfies this . c"
Answer: c
Python program:
a = 1 / 100
b = 1000 * a
Problem: 15 binders can bind 1400 books in 21 days . how many binders will be required to bind 1600 books in 20 days ?
Options: a ) 14 , b ) 18 , c ) 24 , d ) 28 , e ) none of these
Rationale: "binders books days 15 1400 21 x 1600 20 x / 15 = ( 1600 / 1400 ) * ( 21 / 20 ) = > x = 18 answer : b"
Answer: b
Python program:
a = 1600 / 20
b = 15 * 21
c = 1400 / b
d = a / c
Problem: what is the smallest number which when increased by 3 is divisible by 18 , 70 , 100 and 84 ?
Options: a ) 5307 , b ) 5647 , c ) 5927 , d ) 6297 , e ) 6557
Rationale: "when increased by 3 , the number must include at least 2 ^ 2 * 3 ^ 2 * 5 ^ 2 * 7 = 6300 the answer is d ."
Answer: d
Python program:
a = math.lcm(18, 70)
b = math.lcm(100, 84)
c = math.lcm(a, b)
d = c + 3
Problem: find the compound ratio of ( 1 : 2 ) , ( 1 : 3 ) and ( 3 : 5 ) is
Options: a ) 1 : 10 , b ) 2 : 3 , c ) 3 : 4 , d ) 4 : 5 , e ) 3 : 2
Rationale: "required ratio = 1 / 2 * 1 / 3 * 3 / 5 = 1 / 10 = 1 : 10 answer is a"
Answer: a
Python program:
a = 1 / 2
b = 1 / 2
c = 1 / 2
d = b * c
e = a * d
Problem: the arithmetic mean and standard deviation of a certain normal distribution are 16.5 and 1.5 , respectively . what value is exactly 2 standard deviations less than the mean ?
Options: a ) 10.5 , b ) 11 , c ) 11.5 , d ) 12 , e ) 13.5
Rationale: "the value which isexactlytwo sd less than the mean is : mean - 2 * sd = 16.5 - 2 * 1.5 = 13.5 . answer : e ."
Answer: e
Python program:
a = 2 * 1
b = 16 - 5
Problem: find the value of 3 / 11 × [ ( 1 + 1 / 3 ) ( 1 + 1 / 4 ) … … … … . ( 1 + 1 / 120 ) ] is ?
Options: a ) 11 , b ) 12 , c ) 14 , d ) 15 , e ) 16
Rationale: "3 / 11 × [ ( 1 + 1 / 3 ) ( 1 + 1 / 4 ) . . . . . . . ( 1 + 1 / 120 ) ] 3 / 11 × [ 4 / 3 + 5 / 4 × . . . . . . . . 121 / 120 ] 3 / 11 × 4 / 3 × 5 / 4 × . . . . 121 / 120 121 / 11 = 11 . a )"
Answer: a
Python program:
a = 120 + 1 
b = a / 11
Problem: two cars are driving towards one another . the first car is traveling at a speed of 120 km / h , which is 28 % faster than the second car . if the distance between the cars is 855 km , how long will it takes the cars to meet ( in hours ) ?
Options: a ) 2.5 . , b ) 3 . , c ) 3.5 , d ) 4 . , e ) 4.5 .
Rationale: let s be the speed of the slower car . then the speed of the faster is 1.28 s 1.28 s = 120 s = 120 / 1.28 cumulative speed / rate = s + 1.28 s = 2.28 s time taken to meet = 855 / 2.28 s = 855 / 213.75 = 4 hrs answer : d
Answer: d
Python program:
a = 120 / 100
b = a * 28
c = 120 - b
d = 120 + c 
e = 855 / d
Problem: according to the directions on a packet of smoothie mix , 1 3 - ounce packet of smoothie mix is to be combined with 10 ounces of water to make a smoothie . how many 3 - ounce packets of smoothie mix are required to prepare 150 12 - ounce smoothies ?
Options: a ) 120 , b ) 150 , c ) 180 , d ) 240 , e ) 600
Rationale: "this question was n ' t particularly grueling , but i think it ' s the first where i had the opportunity to solve it via theory andinspectionthat many on this board suggest as strategy on the gmat . it actually came to me by accident . basically , if we thought that the 3 packets of powder were included in the 12 ounces of water , that would mean we would need 150 packets of smoothie mix ( along with 12 ( 150 ) ounces of water for a total of 150 packets . however , we know , after a more careful reading of the stimulus , that the 3 ounces are not included in the 12 ounces . as such , the answer has to be less than 150 packets , since 150 would be too much powder considering you already have 150 ( 12 ) ounces of water and need less packets than water to make a smoothie . as such , the only answer less than 150 is 120 , a . does this make sense ? or am i way off base ? b"
Answer: b
Python program:
a = 3 * 10
b = 150 + a
Problem: which fraction should be added to : 1 / ( 2 ã — 3 ) + 1 / ( 3 ã — 4 ) + 1 / ( 4 ã — 5 ) + . . . . . . . + 1 / ( 23 ã — 24 ) so that the result is equal to 1 ?
Options: a ) 7 / 24 , b ) 11 / 24 , c ) 13 / 24 , d ) 17 / 24 , e ) 19 / 24
Rationale: the given expression = 1 / ( 2 ã — 3 ) + 1 / ( 3 ã — 4 ) + 1 / ( 4 ã — 5 ) + . . . . . . + 1 / ( 23 ã — 24 ) = ( 1 / 2 - 1 / 3 ) + ( 1 / 3 - 1 / 4 ) + ( 1 / 4 - 1 / 5 ) + . . . . . . . . . . + ( 1 / 23 - 1 / 24 ) = 1 / 2 - 1 / 24 = 11 / 24 thus , the fraction we should add = 1 - 11 / 24 = 13 / 24 the answer is c .
Answer: c
Python program:
a = 3 + 10 
b = a / 24
Problem: of the land owned by a farmer , 90 percent was cleared for planting . of the cleared land , 80 percent was planted with barley and 10 percent of the cleared land was planted with potato . if the remaining 90 acres of cleared land was planted with tomato , how many acres did the farmer own ?
Options: a ) 850 , b ) 950 , c ) 1025 , d ) 975 , e ) 1000
Rationale: 80 % of 90 % = 72 % , 10 % 0 f 90 % = 9 % so the remaining 90 - 72 - 9 = 9 % = 90 acres or 10 % of 90 % = 9 % - - > 90 / 9 * 100 = 1000 acres answer ( e )
Answer: e
Python program:
a = 100 - 80
b = a - 10
c = b / 100
d = 90 / 100
e = c * d
f = 90 / e
Problem: if 4 xz + yw = 6 and xw + yz = 12 , what is the value of the expression ( 2 x + y ) ( 2 z + w ) ?
Options: a ) 9 . , b ) 30 . , c ) 15 . , d ) 16 . , e ) 18 .
Rationale: "( 2 x + y ) * ( 2 z + w ) = 6 + 2 ( 12 ) = 30 answer : b"
Answer: b
Python program:
a = 12 * 2
b = 4 + a
Problem: if one positive integer is greater than another positive integer by 3 , and the difference of their cubes is 63 , what is their sum ?
Options: a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1
Rationale: 1 ^ 3 = 1 2 ^ 3 = 8 3 ^ 3 = 27 4 ^ 3 = 64 the two numbers are 1 and 4 . the answer is a .
Answer: a
Python program:
a = 3 ** 3
b = 3 ** 3
c = b ** 2
d = 3 ** 3
e = 63 - d
f = e ** 2
g = c + f 
h = math.sqrt(g)
i = a + h 
j = 3 ** 2
k = j * 2
l = i / k
m = 3 ** 3
n = 3 ** 3
o = n ** 2
p = 3 ** 3
q = 63 - p
r = q ** 2
s = o + r 
t = math.sqrt(s)
u = m + t 
v = 3 ** 2
w = v * 2
x = u / w
y = x - 3
z = l + y