euclaise/mathqa_programs huggingface dataset:
Problem: tom opened a shop investing rs . 30000 . jose joined him 2 months later , investing rs . 45000 . they earned a profit of rs . 36000 after completion of one year . what will be jose ' s share of profit ?
Options: a ) 20000 , b ) 10000 , c ) 25000 , d ) 34000 , e ) 30000
Rationale: "sol = ~ s - so anju ’ s share = [ 5 / 9 ] x 36000 = 20000 a"
Answer: a
Python program:
a = 2 * 3
b = 2 * a
c = 30000 * b
d = 2 * 3
e = 2 * d
f = e - 2
g = 45000 * f
h = 2 * 3
i = 2 * h
j = 30000 * i
k = g + j 
l = c / k
m = 1 - l
n = 36000 * m
Problem: if 10 % of x = 20 % of y , then x : y is equal to ?
Options: a ) 2 : 6 , b ) 2 : 1 , c ) 7 : 1 , d ) 2 : 8 , e ) 2 : 2
Rationale: 10 % of x = 20 % of y 10 x / 100 = 20 y / 100 = > x / 10 = y / 5 x / y = 10 / 5 = 2 / 1 x : y = 2 : 1 . answer : b
Answer: b
Python program:
a = 20 / 10
Problem: in a certain math department , students are required to enroll in either calculus or trigonometry , each of which is offered in beginner and advanced courses . the number of students enrolled in trigonometry is 50 % greater than the number of students enrolled in calculus , and 70 % of calculus students are enrolled in the beginner course . if 4 / 5 of students are in the beginner courses , and one student is selected at random , what is the probability that a beginner trigonometry student is selected ?
Options: a ) 40 % , b ) 44 % , c ) 48 % , d ) 52 % , e ) 56 %
Rationale: "let x be the number of students in calculus . then the number of students in trigonometry is 1.5 x the number of students on beginner calculus is 0.7 x the number of students in beginner trigonometry is 4 / 5 * ( 2.5 x ) - 0.7 x = 1.3 x the percentage in beginner trigonometry is 1.3 x / 2.5 x = 52 % the answer is d ."
Answer: d
Python program:
a = 50 * 2
b = a + 50 
c = 50 * 2
d = b + c 
e = 4 / 5
f = d * e
g = f - 70
h = 50 * 2
i = h + 50 
j = 50 * 2
k = i + j 
l = g / k
m = 50 * 2
n = l * m
Problem: a and b can do a work in 12 days , b and c in 30 days and c and a in 36 days . in how many days will the work be completed , if all three of them work together ?
Options: a ) 180 / 15 , b ) 180 / 10 , c ) 180 / 13 , d ) 180 / 15 , e ) 180 / 11
Rationale: "one day work of a and b = 1 / 12 one day work of b and c = 1 / 30 one day work of c and a = 1 / 36 2 ( a + b + c ) = 1 / 12 + 1 / 30 + 1 / 36 2 ( a + b + c ) = 13 / 90 ( a + b + c ) = 13 / 180 number of days required = 180 / 13 days . answer : c"
Answer: c
Python program:
a = 1/(12)
b = 1/(30)
c = a + b 
d = 1/(36)
e = c + d 
f = e / 2
g = 1 / f
Problem: if the median of a list of numbers is m , the first quartile of the list is the median of the numbers in the list that are less than m . what is the first quartile of the list of numbers 42 , 24 , 30 , 22 , 28 , 19 , 33 and 35 ?
Options: a ) 33 , b ) 25 , c ) 27 , d ) 24 , e ) 23
Rationale: "it is given that a quartile is the middle number of all numbers less than median . . so lets arrange the number in ascending order - 42 , 24 , 30 , 22 , 28 , 19 , 33 and 35 19 , 22 , 24 , 28 , 30 , 33 , 35 , 42 . . . numbers less than median are 19 , 22 , 24 , 28 . . the median of these numbers = center of 22 and 24 = 23 e"
Answer: e
Python program:
a = 24 + 28 
b = a / 2
Problem: a and b can do a piece of work in 18 days ; band c can do it in 24 days a and c can do it in 36 days . in how many days will a , band c finish it together ?
Options: a ) 15 days , b ) 12 days , c ) 8 days , d ) 16 days , e ) 9 days
Rationale: sol . ( a + b ) ' s 1 day ' s work = ( 1 / 18 ) ( b + c ) ' s 1 day ' s work = ( 1 / 24 ) and ( a + c ) ' s 1 day ' s work = ( 1 / 36 ) adding , we get : 2 ( a + b + c ) ' s 1 day ' s work = ¬ ( 1 / 18 + 1 / 24 + 1 / 36 ) = 9 / 72 = 1 / 8 ( a + b + c ) ' s 1 day ' s work = 1 / 16 thus , a , band c together can finish the work in 16 days . ans : d
Answer: d
Python program:
a = 1/(18)
b = 1/(24)
c = a + b 
d = 1/(36)
e = c + d 
f = e / 2
g = 1 / f
Problem: what is the sum of all possible solutions to | x - 3 | ^ 2 + | x - 3 | = 30 ?
Options: a ) 4 , b ) 5 , c ) 3 , d ) 2 , e ) 1
Rationale: "denote | x - 3 | as y : y ^ 2 + y = 30 - - > y = - 6 or y = 5 . discard the first solution since y = | x - 3 | , so it ' s an absolute value and thus can not be negative . y = | x - 3 | = 5 - - > x = 8 or x = - 3 . the sum = 5 . answer : b ."
Answer: b
Python program:
a = 4 + 3 
b = 3 - 4
c = a + b
Problem: let the number which when multiplied by 12 is increased by 198 .
Options: a ) 18 , b ) 20 , c ) 26 , d ) 28 , e ) 30
Rationale: "solution let the number be x . then , 12 x - x = 198 ‹ = › 11 x = 198 x ‹ = › 18 . answer a"
Answer: a
Python program:
a = 12 - 1
b = 198 / a
Problem: 200 college students were asked in a survey if they preferred windows or mac brand computers . 70 students claimed that they preferred mac to windows brand computers . one third as many of the students who preferred mac to windows , equally preferred both brands . 80 of the students had no preference . how many of the students in the survey preferred windows to mac brand computers ?
Options: a ) 25 , b ) 50 , c ) 57 , d ) 60 , e ) 75
Rationale: "200 = 70 ( mac ) + x ( window ) + 80 ( both ) = > x = 50 answer : b"
Answer: b
Python program:
a = 200 - 80
b = a - 70
c = 200 - 80
d = c - 70
e = d / 3
f = b - e
Problem: a circle graph shows how the megatech corporation allocates its research and development budget : 14 % microphotonics ; 25 % home electronics ; 15 % food additives ; 29 % genetically modified microorganisms ; 8 % industrial lubricants ; and the remainder for basic astrophysics . if the arc of each sector of the graph is proportional to the percentage of the budget it represents , how many degrees of the circle are used to represent basic astrophysics research ?
Options: a ) 8 ° , b ) 10 ° , c ) 18 ° , d ) 33 ° , e ) 52 °
Rationale: "here all percentage when summed we need to get 100 % . as per data 14 + 25 + 15 + 29 + 8 = 91 % . so remaining 9 % is the balance for the astrophysics . since this is a circle all percentage must be equal to 360 degrees . 100 % - - - - 360 degrees then 9 % will be 33 degrees . . imo option d ."
Answer: d
Python program:
a = 14 + 25 
b = a + 15 
c = b + 29 
d = c + 8 
e = 100 - d
f = 3600 / 10
g = e * f
h = g / 100
Problem: two trains 140 m and 160 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time ( in seconds ) which they take to cross each other , is :
Options: a ) 9 , b ) 9.6 , c ) 10 , d ) 10.8 , e ) 7
Rationale: "explanation : relative speed = ( 60 + 40 ) km / hr = [ 100 x ( 5 / 18 ) ] m / sec = ( 250 / 9 ) m / sec . distance covered in crossing each other = ( 140 + 160 ) m = 300 m . required time = [ 300 x ( 9 / 250 ) ] sec = ( 54 / 5 ) sec = 10.8 sec . answer : d"
Answer: d
Python program:
a = 140 + 160 
b = 60 + 40 
c = b * const_0_2778
d = a / c
Problem: a certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996 . if total revenues from car sales and truck sales in 1997 were up 1 percent from 1996 , what is the ratio t of revenue from car sales in 1996 to revenue from truck sales in 1996 ?
Options: a ) 1 : 2 , b ) 4 : 5 , c ) 1 : 1 , d ) 3 : 2 , e ) 5 : 3
Rationale: a . . i have probably solved this question 3 - 4 times by now . . remember the answer . . 1 : 2
Answer: a
Python program:
a = 100 + 7 
b = 100 + 1 
c = a - b
d = 100 + 1 
e = 100 - 11
f = d - e
g = c / f
Problem: in a recent election , geoff received 0.5 percent of the 6,000 votes cast . to win the election , a candidate needed to receive more than x % of the vote . if geoff needed exactly 3,000 more votes to win the election , what is the value of x ?
Options: a ) 50 , b ) 50.5 , c ) 56 , d ) 60 , e ) 63
Rationale: word problems are tricky in somehow more than other problem because you have the additional step to translate . breaking the problem : geoff how many votes he receives ? ? 30 votes he needs 3571 more votes so : 30 + 3000 = 3030 now what ' s the problem wants ? ? a x % . . . . . . . . 3030 is what % of total votes 6000 . . . . . . . . translating : 3030 = x / 100 * 6000 - - - x = 50.5 % . . . . . . . . . . b
Answer: b
Python program:
a = 100 / 2
b = a + 0
Problem: if a ^ 3 is divisible by 240 what is the least possible value of integer a ?
Options: a ) 12 , b ) 30 , c ) 60 , d ) 90 , e ) 120
Rationale: 240 can be written as ( 2 ^ 4 ) * 3 * 5 . for a ^ 3 to be divisible by 240 it should contain atleast 2 ^ 4 and 3 and 5 in its factors . we can leave out option a because 12 doesnt have 5 as one of its factor . now if we check for option b , 30 can be written as 2 * 3 * 5 , hence 30 ^ 3 will have 3 as the maximum power of 2 , so we can leave out this option too . option c is the right answer if we follow the same method as we followed for other two previous options . 60 = ( 2 ^ 2 ) * 3 * 5 ; 60 ^ 3 = ( 2 ^ 6 ) * ( 3 ^ 3 ) * ( 5 ^ 3 ) . so it shows that 60 ^ 3 is divisible by 240 and hence the answer . answer : c
Answer: c
Python program:
a = 2 ** 3
b = 240 / a
c = b * 2
Problem: a goods train runs at a speed of 72 kmph and crosses a 250 m long platform in 26 seconds . what is the length of the goods train ?
Options: a ) 230 m , b ) 240 m , c ) 260 m , d ) 270 m , e ) 250 m
Rationale: "s = 250 + x / t 72 * 5 / 18 = 250 + x / 26 x = 270 answer : d"
Answer: d
Python program:
a = 72 * const_0_2778
b = a * 26
c = b - 250
Problem: the average of temperatures at noontime from monday to friday is 60 ; the lowest one is 50 , what is the possible maximum range of the temperatures ?
Options: a ) 50 , b ) 25 , c ) 40 , d ) 45 , e ) 75
Rationale: "average = 60 , sum of temperatures = 60 * 5 = 300 as the min temperature is 50 , max would be 300 - 4 * 50 = 100 - - > the range = 100 ( max ) - 50 ( min ) = 50 answer : a"
Answer: a
Python program:
a = 2 + 3 
b = 60 * a
c = 50 * 4
d = b - c
e = d - 50
Problem: find the area of a rhombus one side of which measures 20 cm and one diagonal is 26 cm .
Options: a ) 600 cm 2 , b ) 500 cm 2 , c ) 516 cm 2 , d ) 416 cm 2 , e ) 100 cm 2
Rationale: "explanation : let other diagonal = 2 x cm . since diagonals of a rhombus bisect each other at right angles , we have : ( 20 ) 2 = ( 12 ) 2 + ( x ) 2 = > x = √ ( 20 ) 2 – ( 12 ) 2 = √ 256 = 16 cm . _ i so , other diagonal = 32 cm . area of rhombus = ( 1 / 2 ) x ( product of diagonals ) = ( 1 / 2 × 26 x 32 ) cm 2 = 416 cm 2 answer : option d"
Answer: d
Python program:
a = 1 / 2
b = a * 26
c = 20 * 20
d = c * 4
e = 26 * 26
f = d - e
g = math.sqrt(f)
h = b * g
i = h + 26
Problem: what are the last two digits of ( 301 * 402 * 503 * 604 * 646 * 547 * 448 * 349 ) ^ 2
Options: a ) 96 , b ) 76 , c ) 56 , d ) 36 , e ) 16
Rationale: "( ( 301 * 402 * 503 * 604 * 646 ) * ( 547 * 448 * 349 ) ) ^ 2 if you observe above digits , last digit are : 1,2 , 3,4 , 6,7 , 8,9 ; 5 is missing ; so i have rearranged them so that multiplication will be easy for me as initial 4 digits have last two digits as 01 , 02,03 , 04,46 and final three as 47 * 48 * 49 . solving for only last two digits and multiplying them we get : ( ( 06 * 04 * 46 ) ( 56 * 49 ) ) ^ 2 = ( 44 * 44 ) ^ 2 = 36 ^ 2 = 76 hence answer is b"
Answer: b
Python program:
a = 100 / 4
b = 2 * 3
c = 1 - 2
d = b * c
e = 1 - 2
f = d * e
g = 1 - 2
h = f * g
i = a + h 
j = i * 4
Problem: if two of the 4 expressions x + y , x + 5 y , x - y , and 5 x - y are chosen at random , what is the probability t that their product will be of the form of x ^ 2 - ( by ) ^ 2 , where b is an integer ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) t = 1 / 6
Rationale: only ( x + y ) ( x - y ) pair will give the form x ^ 2 - ( by ) ^ 2 the probability of selecting these two pairs are 1 / 4 * 1 / 3 = 1 / 12 , assuming x + y is picked first , then x - y , but x - y can be picked first followed by x + y . so the probability t = 1 / 12 * 2 = 1 / 6 ans e
Answer: e
Python program:
a = math.factorial(4)
b = math.factorial(2)
c = math.factorial(2)
d = b * c
e = a / d
f = 1 / e
Problem: if n = 2.0767 and n * is the decimal obtained by rounding n to the nearest hundredth , what is the value of n * – n ?
Options: a ) - 0.0053 , b ) - 0.0003 , c ) 0.0007 , d ) 0.0047 , e ) 0.0033
Rationale: "n * = 2.08 n * - n = 2.08 - 2.0767 0.0033 answer : e"
Answer: e
Python program:
a = 2 * 10
b = a + 3 
c = b / 100
d = c / 100
e = 2 - 767
f = e - 2
Problem: list f consists of 12 consecutive integers . if - 4 is the least integer in list f , what is the range of positive integers in list f ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 11 , e ) 12
Rationale: since - 4 is the least integer in list f , then 7 is the largest integer in that list . thus the range of the positive integers in the list is 7 - 1 = 6 . answer : b .
Answer: b
Python program:
a = 12 / 2
Problem: a man is 32 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is ?
Options: a ) 16 , b ) 19 , c ) 15 , d ) 22 , e ) 30
Rationale: "let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . ( x + 32 ) + 2 = 2 ( x + 2 ) x + 34 = 2 x + 4 = > x = 30 . answer : e"
Answer: e
Python program:
a = 2 * 2
b = a - 2
c = 32 - b
d = 2 - 1
e = c / d
Problem: a man can row upstream at 8 kmph and downstream at 13 kmph . the speed of the stream is ?
Options: a ) 3 kmph , b ) 2.5 kmph , c ) 3.5 kmph , d ) 4.3 kmph , e ) 5 kmph
Rationale: "speed of stream = 1 / 2 ( 13 - 8 ) = 2.5 kmph answer is b"
Answer: b
Python program:
a = 8 + 13 
b = a / 2
Problem: a vessel of capacity 30 litres is fully filled with pure milk . nine litres of milk is removed from the vessel and replaced with water . nine litres of the solution thus formed is removed and replaced with water . find the quantity of pure milk in the final milk solution ?
Options: a ) 14.7 , b ) 2.9 , c ) 38.3 , d ) 78.3 , e ) 79.3
Rationale: "explanation : let the initial quantity of milk in vessel be t litres . let us say y litres of the mixture is taken out and replaced by water for n times , alternatively . quantity of milk finally in the vessel is then given by [ ( t - y ) / t ] ^ n * t for the given problem , t = 30 , y = 9 and n = 2 . hence , quantity of milk finally in the vessel = [ ( 30 - 9 ) / 30 ] ^ 2 ( 30 ) = 14.7 litres . answer : option a"
Answer: a
Python program:
a = 3 * 3
b = 30 - a
c = 3 * 3
d = 30 - c
e = d / 30
f = 3 * 3
g = e * f
h = b - g
Problem: the tax on a commodity is diminished by 20 % but its consumption is increased by 5 % . find the decrease percent in the revenue derived from it ?
Options: a ) 12 % , b ) 14 % , c ) 16 % , d ) 20 % , e ) 22 %
Rationale: "explanation : 100 * 100 = 10000 80 * 105 = 8400 10000 - - - - - - - 1600 100 - - - - - - - ? = 16 % c )"
Answer: c
Python program:
a = 100 + 5 
b = 100 - 20
c = a * b
d = c / 100
e = 100 - d
Problem: if 15 ! / 3 ^ x is an integer , what is the greatest possible value of x ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "15 - 5 * 3 12 - 4 * 3 9 - 3 * 3 6 - 2 * 3 3 - 1 * 3 hence max of 3 ^ 6 is allowed . imo d ."
Answer: d
Python program:
a = 15 / 3
b = 15 / 3
c = 3 / b
d = a + c
Problem: how many cubes of 50 cm edge can be put in a cubical box of 1 m edge .
Options: a ) 17 cm , b ) 10 cm , c ) 8 cm , d ) 6 cm , e ) 7 cm
Rationale: "number of cubes = 100 â ˆ — 100 â ˆ — 100 / 50 * 50 * 50 = 8 number of cubes = 100 â ˆ — 100 â ˆ — 10010 â ˆ — 10 â ˆ — 10 = 1000 note : 1 m = 100 cm answer : c"
Answer: c
Python program:
a = volume_cube / (
Problem: we have boxes colored either red or blue . in each blue box there is a fixed number of blueberries . in each red box there is a fixed number of strawberries . if we dispose of one blue box for one additional red box , the total number of berries would increase by 20 , and the difference between the total number of strawberries and the total number of blueberries would increase by 80 . each blue box contains how many blueberries ?
Options: a ) 25 , b ) 30 , c ) 35 , d ) 40 , e ) 45
Rationale: let x be the number of blueberries in each blue box . then there are x + 20 strawberries in each red box . x + ( x + 20 ) = 80 x = 30 the answer is b .
Answer: b
Python program:
a = 80 - 20
b = a / 2
Problem: a portion of the 90 % solution of chemicals was replaced with an equal amount of 20 % solution of chemicals . as a result , 40 % solution of chemicals resulted . what part of the original solution was replaced ?
Options: a ) 5 / 7 , b ) 6 / 7 , c ) 9 / 5 , d ) 13 / 9 , e ) 13 / 6
Rationale: this is a weighted average question . say x % of the solution was replaced - - > equate the amount of chemicals : 0.90 ( 1 - x ) + 0.2 * x = 0.4 - - > x = 5 / 7 . answer : a .
Answer: a
Python program:
a = 90 - 40
b = 90 - 20
c = a / b
Problem: in smithtown , the ratio of right - handed people to left - handed people is 3 to 1 and the ratio of men to women is 3 to 2 . if the number of right - handed men is maximized , then what s percent of all the people in smithtown are left - handed women ?
Options: a ) 50 % , b ) 40 % , c ) 25 % , d ) 20 % , e ) 10 %
Rationale: "looking at the ratio we can take total number of people = 20 . . ans 5 / 20 or 25 % c"
Answer: c
Python program:
a = 3 + 1 
b = 3 + 2 
c = a / b
d = 2 * c
e = 3 + 1 
f = 3 + 2 
g = e / f
h = 3 * g
i = 3 - h
j = d - i
k = 3 + 1 
l = j / k
m = l * 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 this son is
Options: a ) 21 years , b ) 22 years , c ) 23 years , d ) 24 years , e ) 26 years
Rationale: "explanation : let ' s son age is x , then father age is x + 24 . = > 2 ( x + 2 ) = ( x + 24 + 2 ) = > 2 x + 4 = x + 26 = > x = 22 years option b"
Answer: b
Python program:
a = 2 * 2
b = a - 2
c = 24 - b
d = 2 - 1
e = c / d
Problem: how many cubes of 10 cm edge can be put in a cubical box of 1 m edge
Options: a ) 10 , b ) 100 , c ) 1000 , d ) 10000 , e ) none of these
Rationale: "explanation : number of cubes = ( 100 x 100 x 100 ) / ( 10 x 10 x 10 ) = 1000 answer : c"
Answer: c
Python program:
a = volume_cube / (
Problem: each of the integers from 1 to 14 is written on the a seperate index card and placed in a box . if the cards are drawn from the box at random without replecement , how many cards must be drawn to ensure that the product of all the integers drawn is even ?
Options: a ) 19 , b ) 12 , c ) 11 , d ) 10 , e ) 8
Rationale: "out of the 14 integers : 7 are odd and 7 are even . if we need to make sure that the product of all the integers withdrawn is even then we need to make sure that we have at least one even number . in the worst case : 1 . we will end up picking odd numbers one by one , so we will pick all 7 odd numbers first 2 . 8 th number will be the first even number so we need to withdraw at least 8 numbers to make sure that we get one even number and the product of all the integers picked is even . so , answer will be 8 . ( e )"
Answer: e
Python program:
a = 14 / 2
b = a + 1
Problem: two trains of length 200 m and 300 m are 200 m apart . they start moving towards each other on parallel tracks , at speeds 36 kmph and 72 kmph . in how much time will the trains cross each other ?
Options: a ) 70 / 8 , b ) 70 / 7 , c ) 70 / 5 , d ) 70 / 3 , e ) 70 / 1
Rationale: "relative speed = ( 36 + 72 ) * 5 / 18 = 6 * 5 = 30 mps . the time required = d / s = ( 200 + 200 + 300 ) / 30 = 700 / 30 = 70 / 3 sec . answer : d"
Answer: d
Python program:
a = 36 + 72 
b = a * const_0_2778
c = 200 / b
Problem: a salesman ’ s terms were changed from a flat commission of 5 % on all his sales to a fixed salary of rs . 1200 plus 2.5 % commission on all sales exceeding rs . 4,000 . if his remuneration as per new scheme was rs . 1200 more than that by the previous schema , his sales were worth ?
Options: a ) 12028 , b ) 12000 , c ) 12019 , d ) 16000 , e ) 12012
Rationale: "[ 1200 + ( x - 4000 ) * ( 2.5 / 100 ) ] - x * ( 5 / 100 ) = 600 x = 16000 answer : d"
Answer: d
Python program:
a = 5 / 100
b = 1200 / a
Problem: i chose a number and divide it by 6 . then i subtracted 15 from the result and got 5 . what was the number i chose ?
Options: a ) 600 , b ) 700 , c ) 120 , d ) 900 , e ) none
Rationale: "solution : let xx be the number i chose , then x / 6 â ˆ ’ 15 = 5 x / 6 = 20 x = 120 answer c"
Answer: c
Python program:
a = 15 + 5 
b = a * 6
Problem: veena ranks 44 rd from the top in a class of 182 . what is her rank from the bottom if 22 students have failed the examination ?
Options: a ) 88 , b ) 108 , c ) 110 , d ) 90 , e ) 117
Rationale: "total student = 182 failed = 22 paasd student = 182 - 22 = 160 from bottom her rank is = 160 - 44 + 1 = 117 answer : e"
Answer: e
Python program:
a = 182 - 22
b = 44 - 1
c = a - b
d = c - 4
Problem: an alloy of copper and zinc contains copper and zinc in the ratio 5 : 4 . another alloy of copper and zinc contains copper and zinc in the ratio 3 : 6 . in what ratio should the two alloys be mixed so that the resultant alloy contains equal proportions of copper and zinc ?
Options: a ) 4 : 1 , b ) 6 : 1 , c ) 1 : 3 , d ) 2 : 1 , e ) 4 : 1
Rationale: let alloy _ 1 be x units , and let alloy _ 2 be y units . so , fraction of copper in alloy _ 1 = 5 x / 9 , and fraction of zinc in alloy _ 1 = 4 x / 9 . similarly , fraction of copper in alloy _ 2 = 3 y / 9 , and fraction of zinc in alloy _ 2 = 6 y / 9 . mixing them , we get copper = 5 x / 9 + 3 y / 9 ; zinc = 4 x / 9 + 6 y / 9 so , 5 x + 3 y = 4 x + 6 y - > x = 3 y - > x / y = 1 / 3 so , they must be mixed in the ratio 1 : 3 answer : c
Answer: c
Python program:
a = 3 + 6 
b = 5 / a
c = 3 / 6
d = b - c
e = 3 / 6
f = 3 + 6 
g = 3 / f
h = e - g
i = d / h
Problem: find the area of a parallelogram with base 26 cm and height 14 cm ?
Options: a ) 287 cm 2 , b ) 887 cm 2 , c ) 364 cm 2 , d ) 368 cm 2 , e ) 668 cm 2
Rationale: "area of a parallelogram = base * height = 26 * 14 = 364 cm 2 answer : c"
Answer: c
Python program:
a = 26 * 14
Problem: after decreasing 24 % in the price of an article costs rs . 532 . find the actual cost of an article ?
Options: a ) 118 , b ) 677 , c ) 700 , d ) 2688 , e ) 1991
Rationale: "cp * ( 76 / 100 ) = 532 cp = 7 * 100 = > cp = 700 answer : c"
Answer: c
Python program:
a = 24 / 100
b = 1 - a
c = 532 / b
Problem: a motorcyclist started riding at highway marker a , drove 120 miles to highway marker b , and then , without pausing , continued to highway marker c , where she stopped . the average speed of the motorcyclist , over the course of the entire trip , was 25 miles per hour . if the ride from marker a to marker b lasted 3 times as many hours as the rest of the ride , and the distance from marker b to marker c was half of the distance from marker a to marker b , what was the average speed , in miles per hour , of the motorcyclist while driving from marker b to marker c ?
Options: a ) 40 , b ) 45 , c ) 108 , d ) 55 , e ) 60
Rationale: "a - b = 120 miles b - c = 60 miles avg speed = 25 miles time taken for a - b 3 t and b - c be t avg speed = ( 120 + 60 ) / total time 25 = 180 / 4 t t = 108 b - c = 108 mph answer c"
Answer: c
Python program:
a = 120 / 2
b = a + 120 
c = b / 25
d = c / 4
e = 120 / 2
f = d * e
Problem: an engineer designed a ball so that when it was dropped , it rose with each bounce exactly one - half as high as it had fallen . the engineer dropped the ball from a 16 - meter platform and caught it after it had traveled 44.5 meters . how many times did the ball bounce ?
Options: a ) 4 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "division of total diatance travelled will be 16 + 16 + 8 + 4 + 0.5 ans : 4"
Answer: a
Python program:
a = 16 / 2
b = a / 2
Problem: of 70 players on a cricket team , 37 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?
Options: a ) 54 , b ) 55 , c ) 59 , d ) 71 , e ) 92
Rationale: "total = 90 thrower = 37 rest = 90 - 37 = 33 left handed = 33 / 3 = 11 right handed = 22 if all thrower are right handed then total right handed is 37 + 22 = 59 so c . 59 is the right answer"
Answer: c
Python program:
a = 1 / 3
b = 1 - a
c = 70 - 37
d = b * c
e = 37 + d