euclaise/mathqa_programs huggingface dataset:
Problem: the prices of tea and coffee per kg were the same in june . in july the price of coffee shot up by 20 % and that of tea dropped by 20 % . if in july , a mixture containing equal quantities of tea and coffee costs 40 / kg . how much did a kg of coffee cost in june ?
Options: a ) 40 , b ) 60 , c ) 80 , d ) 100 , e ) 120
Rationale: "let the price of tea and coffee be x per kg in june . price of tea in july = 1.2 x price of coffee in july = 0.8 x . in july the price of 1 / 2 kg ( 400 gm ) of tea and 1 / 2 kg ( 400 gm ) of coffee ( equal quantities ) = 40 1.2 x ( 1 / 2 ) + 0.8 x ( 1 / 2 ) = 40 = > x = 40 thus proved . . . option a ."
Answer: a
Python program:
a = 20 / 100
b = 1 - a
c = 20 / 100
d = c + 1 
e = b * d
f = 40 / e
Problem: solve below question 4 x + 1 = 37
Options: a ) - 8 , b ) - 9 , c ) - 5 , d ) 9 , e ) 1
Rationale: 1 . subtract 1 from both sides : 4 x + 1 - 1 = 37 - 1 2 . simplify both sides : 4 x = 36 3 . divide both sides by 4 : 4 . simplify both sides : x = 9 d
Answer: d
Python program:
a = 37 + 1 
b = negate / (
Problem: thabo owns exactly 220 books , and each book is either paperback fiction , paperback nonfiction , or hardcover nonfiction . if he owns 20 more paperback nonfiction books than hardcover nonfiction books , and twice as many paperback fiction books as paperback nonfiction books , how many hardcover books nonfiction books does thabo own ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: "i think we can use double - matrix method and solve using only one variable . our goal is to find the number of hardcover nonfiction books . let that number be x . we are given that all 140 books are either paperback fiction , paperback nonfiction , or hardcover nonfiction . this implies that number of hardcover fiction books is 0 . double - matrix : p = paperback ; h = hardcover ; f = fiction ; nf = nonfiction p h total f 2 x + 40 0 nf x + 20 x total 3 x + 60 x 220 3 x + 60 + x = 220 x = 40 answer ( d . )"
Answer: d
Python program:
a = 220 + 20 
b = a / 4
c = b - 20
Problem: 10 men do a work in 10 days . how many men are needed to finish the work in 5 days ?
Options: a ) 50 , b ) 20 , c ) 30 , d ) 10 , e ) 15
Rationale: "men required to finish the work in 5 days = 10 * 10 / 5 = 20 answer is b"
Answer: b
Python program:
a = 10 * 10
b = a / 5
Problem: the average age of a family of 6 members is 28 years . if the age of the youngest member is 7 years , what was the average age of the family at the birth of the youngest member ?
Options: a ) 15 , b ) 18 , c ) 21 , d ) 12 , e ) 19
Rationale: "present age of total members = 6 x 28 = 168 7 yrs back their ages were = 6 x 7 = 42 ages at the birth of youngest member = 168 - 42 = 126 therefore , avg age at the birth of youngest member = 126 / 6 = 21 . answer : c"
Answer: c
Python program:
a = 6 * 28
b = a - 7
c = b / 4
d = c - 7
Problem: there are 84 supermarkets in the fgh chain . all of them are either in the us or canada . if there are 14 more fgh supermarkets in the us than in canada , how many fgh supermarkets are there in the us ?
Options: a ) 20 , b ) 31 , c ) 42 , d ) 49 , e ) 64
Rationale: x + ( x - 14 ) = 84 - - > x = 49 . answer : d .
Answer: d
Python program:
a = 84 + 14 
b = a / 2
Problem: find out the square of a number which when doubled exceeds its one eighth by 15 ?
Options: a ) 16 , b ) 25 , c ) 19 , d ) 64 , e ) 17
Rationale: "let the number be p , then the square will be p ^ 2 according to question : 2 p = ( p / 8 ) + 15 = > 16 p = p + 120 = > p = 8 p ^ 2 = 8 ^ 2 = 64 . answer : d"
Answer: d
Python program:
a = 4 + 1 
b = 1 / a
c = 2 - b
d = 15 / c
e = d ** 2
Problem: the h . c . f . of two numbers is 5 and their l . c . m . is 150 . if one of the numbers is 25 , then the other is :
Options: a ) 30 , b ) 28 , c ) 24 , d ) 20 , e ) 35
Rationale: "product of two nos = product of hcf and lcm let one number = x = > 25 * x = 5 * 150 x = 5 * 150 / 25 = 30 answer a"
Answer: a
Python program:
a = 5 * 25
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 5 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 ) 47 / 5 , b ) 13 , c ) 17 , d ) 21 , e ) 23
Rationale: "let a contains a , b contains b liters so , ( a - 4 ) / ( b + 4 ) = 1 / 3 . . . . . . . ( 1 ) again , ( b - 5 ) / ( a + 5 ) = 1 / 2 . . . . . . . . . . ( 2 ) from ( 1 ) ( 2 ) we find a = 47 / 5 ans : ( 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: a sporting good store sells one type of baseball bat and one type of baseball . the cost for 2 bats and 4 balls is $ 220 . the cost for 1 bat and 6 balls is $ 190 , as well . if someone were to buy an equal number of bats and balls , at most how many bats can he purchase if he has a budget of $ 270 for the purchase ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "imo it should be c that is 4 reason : formed an equation . . . bat = b ball = c 2 b + 4 c = 220 1 b + 6 c = 190 solving both we get b that is bat = 70 and c that is ball = 20 new equation 270 to be divided in equal 3 b + 3 c = 270 3 * 70 + 3 * 20 = 270 210 + 60 = 270"
Answer: c
Python program:
a = 220 / 2
b = 190 - a
c = b / 4
d = 6 * c
e = 190 - d
f = 220 / 2
g = 190 - f
h = g / 4
i = e + h 
j = 270 / i
Problem: in a coconut grove , ( x + 2 ) trees yield 30 nuts per year , x trees yield 120 nuts per year and ( x – 2 ) trees yield 180 nuts per year . if the average yield per year per tree be 100 , find x .
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 10
Rationale: "( x + 2 ) × 30 + x × 120 + ( x − 2 ) × 180 / ( x + 2 ) + x + ( x − 2 ) = 100 ⇒ 330 x − 300 / 3 x = 100 ⇒ 30 x = 300 ⇒ x = 10 answer e"
Answer: e
Python program:
a = 180 * 2
b = 30 * 2
c = a - b
d = 30 + 120 
e = d + 180 
f = 100 * 3
g = e - f
h = c / g
Problem: a football player scores 2 goals in his fifth match thus increasing his average goals score by 0.3 . the total number of goals in his 5 matches would be
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , 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 gohigherorlowerwith your next test . here , i ' ll start with answer a = 4 goals if . . . . total goals = 4 goals 5 th game = 2 goals 1 st 4 games = 2 goals avg . for 1 st 4 games = 2 / 4 = 0.5 goal / game avg . for all 5 games = 4 / 5 = 0.8 goals / game this is an exact match for what we ' re told in the prompt , so answer a must be the answer ."
Answer: a
Python program:
a = 4 * 2
b = 4 * 5
c = b * 0
d = a - c
e = d + 2
Problem: a salt solution contains 15 grams of salt per 1000 cubic centimeters of solution . if 25 cubic centimeters of the solution were poured into an empty container , how many grams of salt would be in the container ?
Options: a ) 0.550
b ) 0.350
c ) 0.450
d ) 0.700
e ) 0.375
Rationale: we are given that a salt solution contains 15 grams of salt per 1000 cubic centimeters of solution . since we are dealing with a solution , we know that the grams of salt is proportional to the number of cubic centimeters of solution . thus , to determine how many grams of salt would be in the container when we have 25 cubic centimeters of solution , we can set up a proportion . we can say : “ 15 grams of salt is to 1000 cubic centimeters of solution as x grams of salt is to 25 cubic centimeters of solution . ” let ’ s now set up the proportion and solve for x . 15 / 1000 = x / 25 when we cross multiply we obtain : ( 15 ) ( 25 ) = 1000 x 375 = 1000 x 0.375 = x there are 0.375 grams of salt in the solution in the container . the answer is e .
Answer: e
Python program:
a = 15 * 25
b = a / 1000
Problem: jennifer had $ 120 to spend on herself . she spent 1 / 5 of the money on a sandwich , 1 / 6 for a ticket to a museum , and 1 / 2 of it on a book . how much money does jennifer have left over ?
Options: a ) $ 16 , b ) $ 14 , c ) $ 5 , d ) $ 15 , e ) $ 0
Rationale: "1 / 5 x $ 120 = $ 24 for sandwich 1 / 6 x $ 120 = $ 20 for museum 1 / 2 x $ 120 = $ 60 for book $ 24 + $ 20 + $ 60 = $ 104 spent $ 120 - $ 104 = $ 16 left over correct answer a"
Answer: a
Python program:
a = 1 / 5
b = 120 * a
c = 1 / 6
d = 120 * c
e = b + d 
f = 1 / 2
g = 120 * f
h = e + g 
i = 120 - h
Problem: if the sum of two numbers is 55 and the h . c . f . and l . c . m of these numbers are 5 and 120 respectively , then the sum of the reciprocals of the numbers is equal to :
Options: a ) 55 / 601 , b ) 601 / 55 , c ) 11 / 120 , d ) 120 / 11 , e ) 120 / 13
Rationale: "given a + b = 55 , hcm and lcm is 5 and 120 axb = lcmx hcf 600 = 120 x 5 1 / a + 1 / b = a + b / ab = > 55 / 600 = > 11 / 120 answer : c"
Answer: c
Python program:
a = 55 / 5
b = a / 120
Problem: the banker ' s gain on a bill due due 1 year hence at 12 % per annum is rs . 7.8 . the true discount is
Options: a ) rs . 72 , b ) rs . 65 , c ) rs . 54 , d ) rs . 50 , e ) none
Rationale: "solution t . d = [ b . g x 100 / r x t ] = rs . ( 7.8 x 100 / 12 x 1 ) = rs . 65 . answer b"
Answer: b
Python program:
a = 12 / 100
b = 7 / 8
Problem: a man engaged a servant on the condition that he would pay him rs . 900 and a uniform after 1 year service . he served only for 9 months and receiveduniform and rs . 650 , find the priceof the uniform ?
Options: a ) rs . 90 , b ) rs . 100 , c ) rs . 120 , d ) rs . 150 , e ) rs . 160
Rationale: "9 / 12 = 3 / 4 * 900 = 675 650 - - - - - - - - - - - - - 25 1 / 4 - - - - - - - - 25 1 - - - - - - - - - ? = > rs . 100 b"
Answer: b
Python program:
a = 1 * 900
b = 3 * 4
c = b * 9
d = a - c
e = 3 * 4
f = e * 1
g = d / f
h = g * 4
Problem: 2 men and 4 boys can complete a work in 4 days . 5 men and 6 boys can complete the same work in 3 days . the work done by 2 boys is equal to the work of how many men ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: exp : ( 2 m + 4 b ) ’ s one day ’ s work = 1 / 4 ( 5 m + 6 b ) ’ s one day ’ s work = 1 / 3 = > ( 8 m + 16 b ) ’ s one day ’ s work = ( 15 m + 18 b ) ’ s one day ’ s work = > 7 men ’ s work = 2 boy ’ s work so , we should be employ 5 more men to be completed the work . answer : b
Answer: b
Python program:
a = 5 * 4
b = 3 * 4
c = a - b
d = 5 * 4
e = 3 * 4
f = d - e
g = c / f
h = 5 * g
Problem: the sides of a rectangular field are in the ratio 3 : 4 . if the area of the field is 10092 sq . m , the cost of fencing the field @ 25 paise per metre is
Options: a ) rs . 55.50 , b ) rs . 67.50 , c ) rs . 86.50 , d ) rs . 101.50 , e ) none of these
Rationale: "solution let length = ( 3 x ) metres and breadth = ( 4 x ) metres . then , 3 x × 4 x = 10092 ⇔ 12 x 2 = 10092 ⇔ x 2 = 841 ⇔ x = 29 . so , length = 87 m and breadth = 116 m . perimeter = [ 2 ( 87 + 116 ) ] m = 406 m . ∴ cost of fencing = rs . ( 0.25 × 406 ) = rs . 101.50 . answer d"
Answer: d
Python program:
a = 3 * 4
b = 10092 / a
c = math.sqrt(b)
d = 3 * c
e = 3 * 4
f = 10092 / e
g = math.sqrt(f)
h = 4 * g
i = rectangle_perimeter * (
j = i / 25
Problem: of 1000 surveyed students , 20 % of those who read book a also read book b and 25 % of those who read book b also read book a . if each student read at least one of the books , what is the difference between the number of students who read only book a and the number of students who read only book b ?
Options: a ) 120 , b ) 125 , c ) 130 , d ) 145 , e ) 155
Rationale: "say the number of students who read book a is a and the number of students who read book b is b . given that 20 % of those who read book a also read book b and 25 % of those who read book b also read book a , so the number of students who read both books is 0.2 a = 0.25 b - - > a = 1.25 b . since each student read at least one of the books then { total } = { a } + { b } - { both } - - > 1000 = 1.25 b + b - 0.25 b - - > b = 500 , a = 1.25 b = 625 and { both } = 0.25 b = 125 . the number of students who read only book a is { a } - { both } = 625 - 125 = 500 ; the number of students who read only book b is { b } - { both } = 500 - 125 = 375 the difference is 500 - 375 = 125 . answer : b ."
Answer: b
Python program:
a = 25 / 100
b = 20 / 100
c = a / b
d = c + 1 
e = 25 / 100
f = d - e
g = 1000 / f
h = 25 / 100
i = 20 / 100
j = h / i
k = g * j
l = 20 / 100
m = 1 - l
n = k * m
o = 25 / 100
p = 20 / 100
q = o / p
r = q + 1 
s = 25 / 100
t = r - s
u = 1000 / t
v = 25 / 100
w = 1 - v
x = u * w
y = n - x
Problem: a and b finish the job in 15 days . while a , b and c can finish it in 3 days . c alone will finish the job in
Options: a ) 4.75 days , b ) 3.75 days , c ) 6.50 days , d ) 7.50 days , e ) 5.50 days
Rationale: "explanation : 3 = ( 15 * x ) / ( 15 + x ) 45 + 3 x = 15 x 12 x = 45 x = 3.75 answer : option b"
Answer: b
Python program:
a = 3 * 15
b = 15 - 3
c = a / b
Problem: the sum of 3 integers a , b and c is 60 . a is one third of the sum of b and c and b is one fifth of the sum of a and c . what is c ?
Options: a ) 40 , b ) 45 , c ) 35 , d ) 50 , e ) 55
Rationale: a is one third of the sum of b and c . . or a = 1 / 3 ( b + c ) . . . but a + b + c = 60 so 1 / 3 ( b + c ) + b + c = 60 4 ( b + c ) / 3 = 60 b + c = 60 * 3 / 4 = 45 a = 60 - 45 = 15 2 ) b is one fifth of the sum of a and c or b = 1 / 5 ( a + c ) . . . but a + b + c = 60 so 1 / 5 ( a + c ) + a + c = 60 a + c = 60 * 5 / 6 = 50 but a = 15 , so c = 50 - 15 = 35 answer : c
Answer: c
Python program:
a = 1/(3)
b = a * 60
c = 1 + 4 
d = 1/(c)
e = d * 60
f = b + e 
g = f + 3
Problem: the instructions state that cheryl needs 5 / 11 square yards of one type of material and 2 / 3 square yards of another type of material for a project . she buys exactly that amount . after finishing the project , however , she has 25 / 55 square yards left that she did not use . what is the total amount of square yards of material cheryl used ?
Options: a ) 1 / 12 , b ) 1 / 9 , c ) 1 2 / 3 , d ) 2 / 3 , e ) 2 1 / 9
Rationale: "total bought = 5 / 11 + 2 / 3 left part 25 / 55 - - - > 5 / 11 so used part 5 / 11 + 2 / 3 - 5 / 11 = 2 / 3 ans d"
Answer: d
Python program:
a = 5 / 11
b = 2 / 3
c = a + b 
d = 25 / 55
e = c - d
Problem: in a class of 87 students 41 are taking french , 22 are taking german . of the students taking french or german , 9 are taking both courses . how many students are not enrolled in either course ?
Options: a ) 6 , b ) 15 , c ) 24 , d ) 33 , e ) 54
Rationale: formula for calculating two overlapping sets : a + b - both + not ( a or b ) = total so in our task we have equation : 41 ( french ) + 22 ( german ) - 9 ( both ) + not = 87 54 + not = 87 not = 87 - 54 = 33 so answer is d
Answer: d
Python program:
a = 41 + 22 
b = a - 9
c = 87 - b
Problem: what is the least positive integer x for which ( x ^ 2 ) + 164 is divisible by 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , and 11 ?
Options: a ) 27556 , b ) 800 , c ) 796 , d ) 87 , e ) 166
Rationale: 2 = 2 3 = 3 4 = 2 * 2 5 = 5 6 = 2 * 3 7 = 7 8 = 2 * 2 * 2 9 = 3 * 3 10 = 2 * 5 11 = 11 so ( x ^ 2 ) + 164 = ( 2 * 2 * 2 * 3 * 3 * 5 * 7 * 11 ) = 27720 . then ( x ^ 2 ) = 27556 . then x = 166 , which is option e .
Answer: e
Python program:
a = math.lcm(2, 3)
b = math.lcm(a, 4)
c = math.lcm(b, 5)
d = math.lcm(c, 6)
e = math.lcm(d, 7)
f = math.lcm(e, 8)
g = math.lcm(f, 9)
h = math.lcm(g, 11)
i = h - 164
j = math.sqrt(i)
Problem: the cross - section of a cannel is a trapezium in shape . if the cannel is 16 m wide at the top and 4 m wide at the bottom and the area of cross - section is 700 sq m , the depth of cannel is ?
Options: a ) 76 , b ) 28 , c ) 27 , d ) 80 , e ) 70
Rationale: "1 / 2 * d ( 16 + 4 ) = 700 d = 70 answer : e"
Answer: e
Python program:
a = 16 + 4 
b = a / 2
c = 700 / b
d = c / 4
e = d / 2
Problem: two equal triangles constitute rhombus a . if the diagonals of rhombus are 15 cm and 20 cm long . what is the area of each triangle ?
Options: a ) 300
b ) 150
c ) 75
d ) 40
e ) 20
Rationale: area of rhombus = 0.5 x 15 x 20 = 150 cm â ² area of triangle = 150 / 2 = 75 cm â ² answer : c
Answer: c
Python program:
a = 15 * 20
b = a / 4
Problem: there is a total of 84 marbles in a box , each of which is red , green , blue , or white . if one marble is drawn from the box at random , the probability that it will be white is 1 / 4 and the probability that it will be green is 1 / 7 . what is the probability that the marble will be either red or blue ?
Options: a ) 4 / 7 , b ) 9 / 14 , c ) 11 / 14 , d ) 17 / 28 , e ) 23 / 28
Rationale: "p ( red or blue ) = 1 - p ( white ) - p ( green ) = 28 / 28 - 7 / 28 - 4 / 28 = 17 / 28 the answer is d ."
Answer: d
Python program:
a = 1 / 4
b = 1 / 7
c = a + b 
d = 1 - c
Problem: if the side length of square b is four times that of square a , the area of square b is how many times the area of square a ?
Options: a ) 20
b ) 16
c ) 12
d ) 8
e ) 4
Rationale: let x be the side length of square a . then the area of square a is x ^ 2 . the area of square b is ( 4 x ) ^ 2 = 16 x ^ 2 . the answer is b .
Answer: b
Python program:
a = 4 * 4
Problem: two trains of equal are running on parallel lines in the same direction at 50 km / hr and 36 km / hr . the faster train passes the slower train in 36 sec . the length of each train is ?
Options: a ) 70 m , b ) 72 m , c ) 80 m , d ) 82 m , e ) 84 m
Rationale: "let the length of each train be x m . then , distance covered = 2 x m . relative speed = 50 - 36 = 14 km / hr . = 14 * 5 / 18 = 35 / 9 m / sec . 2 x / 36 = 35 / 9 = > x = 70 . answer : a"
Answer: a
Python program:
a = 50 - 36
b = a * 1000
c = b / 3600
d = 36 * c
e = d / 2
Problem: a dog takes 3 leaps for every 7 leaps of a hare . if one leap of the dog is equal to 3 leaps of the hare , the ratio of the speed of the dog to that of the hare is :
Options: a ) 9 : 7 , b ) 9 : 9 , c ) 9 : 6 , d ) 9 : 1 , e ) 9 : 2
Rationale: "explanation : dog : hare = ( 3 * 3 ) leaps of hare : 7 leaps of hare = 9 : 7 . answer : a ) 9 : 7"
Answer: a
Python program:
a = 3 * 3
b = a / 7
Problem: what is the dividend . divisor 17 , the quotient is 9 and the remainder is 5 ?
Options: a ) 150 , b ) 152 , c ) 154 , d ) 158 , e ) 144
Rationale: "d = d * q + r d = 17 * 9 + 5 d = 153 + 5 d = 158"
Answer: d
Python program:
a = 17 * 9
b = a + 5
Problem: circular gears p and q start rotating at the same time at constant speeds . gear p makes 10 revolutions per minute and gear q makes 40 revolutions per minute . how many seconds after the gears start rotating will gear q have made exactly 2 more revolutions than gear p ?
Options: a ) 4 , b ) 8 , c ) 10 , d ) 12 , e ) 15
Rationale: "gear q makes 30 more revolutions each 60 seconds . the time to make 2 = 30 / 15 more revolutions is 60 / 15 = 4 seconds . the answer is a ."
Answer: a
Python program:
a = 40 / const_60
b = 10 / const_60
c = a - b
d = 2 / c
Problem: a and b together can do a piece of work in 3 days . if a alone can do the same work in 20 days , then b alone can do the same work in ?
Options: a ) 0.28 days , b ) 0.45 days , c ) 0.55 days , d ) 0.25 days , e ) 0.15 days
Rationale: "b = 1 / 2 – 1 / 20 = 0.28 days answer : a"
Answer: a
Python program:
a = 1/(3)
b = 1/(20)
c = a - b
d = 1/(c)
Problem: the hcf of two numbers is 62 and the other two factors of their lcm are 11 and 12 . what is the largest number .
Options: a ) 462 , b ) 744 , c ) 480 , d ) 504 , e ) 555
Rationale: "explanation : hcf of the two numbers = 62 hcf will be always a factor of lcm 62 is factor of lcm other two factors are 11 & 12 then the numbers are ( 62 * 11 ) and ( 62 x 12 ) = 682 and 744 answer : option b"
Answer: b
Python program:
a = 62 * 12
Problem: a and b can do a piece of work in 45 days and 40 days respectively . they began to do the work together but a leaves after some days and then b completed the remaining work in 23 days . the number of days after which a left the work was ?
Options: a ) 12 , b ) 11 , c ) 10 , d ) 9 , e ) 8
Rationale: let the total units of work to be done be 360 . the units of work done by a in a single day = 8 similarly , the units of work done by b in a single day = 9 . a and b ’ s one day work = 17 units a and b worked together for some days = 17 x ( assume ) b ’ s work alone for 23 days = 23 x 9 = 207 so , the work done by a and b together = ( 360 - 207 ) = 153 units therefore , 17 x = 153 = > 9 units therefore , the number of days after which a left the work was 9 days . answer : d
Answer: d
Python program:
a = 23 / 40
b = 1 - a
c = 1 / 45
d = 1 / 40
e = c + d 
f = b / e
Problem: teas worth rs . 126 per kg and rs . 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . if the mixture is worth rs 152 per kg , the price of the third variety per kg will be ?
Options: a ) rs . 147.50 , b ) rs . 785.50 , c ) rs . 174.50 , d ) rs . 258.50 , e ) none of these
Rationale: "explanation : since first and second varieties are mixed in equal proportions . so , their average price = rs . ( 126 + 135 ) / 2 . = > rs . 130.50 . so , the mixture is formed by mixing two varieties , one at rs . 130.50 per kg and the other at say , rs . x per kg in the ratio 2 : 2 , i . e . , 1 : 1 . we have to find x . by the rule of alligation , we have : cost of 1 kg cost of 1 kg of 1 st kind of 2 nd kind ( rs . 130.50 ) ( rs . x ) \ / mean price ( rs . 152 ) / \ x â ˆ ’ 152 22.50 = > x â ˆ ’ ( 152 / 22.50 ) = 1 . = > x â ˆ ’ 152 = 22.50 . = > x = 174.50 rs . answer : c"
Answer: c
Python program:
a = 1 + 1 
b = a + 2 
c = 152 * b
d = 126 + 135 
e = c - d
f = e / 2
Problem: when positive integer n is divided by 3 , the remainder is 1 . when n is divided by 8 , the remainder is 5 . what is the smallest positive integer p , such that ( n + p ) is a multiple of 15 ?
Options: a ) 1 , b ) 2 , c ) 5 , d ) 19 , e ) 20
Rationale: "when positive integer n is divided by 3 , the remainder is 1 i . e . , n = 3 x + 1 values of n can be one of { 1 , 4 , 7 , 10 , 13 , 16 , 19 , 22 . . . . . . . . . . . . . . 49 , 52 , 59 . . . . . . . . . . . . . . . . . . } similarly , when n is divided by 8 , the remainder is 5 . . i . e . , n = 7 y + 5 values of n can be one of { 5 , 13 , 21 , 29 , 37 , 45 , 53 , 61 . . . . . . . . } combining both the sets we get n = { 13 , 37 , . . . . . . . . . . . } what is the smallest positive integer p , such that ( n + p ) is a multiple of 15 or 15 x in case of n = 13 p = 2 so for min value of p , we take min value of n . b is the answer ."
Answer: b
Python program:
a = 15 - reminder
Problem: what are the last two digits of ( 301 * 402 * 502 * 604 * 646 * 547 * 448 * 349 ) ^ 2
Options: a ) 96 , b ) 76 , c ) 56 , d ) 36 , e ) 16
Rationale: "( ( 301 * 402 * 502 * 604 * 646 ) * ( 547 * 448 * 349 ) ) ^ 2 if you observe above digits , last digit are : 1,2 , 2,4 , 6,7 , 8,9 ; 3 & 5 are missing ; so i have rearranged them so that multiplication will be easy for me as initial 4 digits have last two digits as 01 , 02,02 , 04,46 and final three as 47 * 48 * 49 . solving for only last two digits and multiplying them we get : ( ( 04 * 04 * 46 ) ( 56 * 49 ) ) ^ 2 = ( 36 * 44 ) ^ 2 = 84 ^ 2 = 56 hence answer is c"
Answer: c
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: p runs 25 % faster than q so p gives q a 60 meter head start . if the race ends in a tie , how far ( in meters ) did p run in the race ?
Options: a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) 500
Rationale: "let d be the race distance that p ran . let t be the time it took to complete the race . let v be q ' s speed . t = d / 1.25 v = ( d - 60 ) / v d = 1.25 d - 75 0.25 d = 75 d = 300 meters . the answer is c ."
Answer: c
Python program:
a = 60 * 100
b = a / 25
c = b + 60