euclaise/mathqa_programs huggingface dataset:
Problem: krishan and nandan jointly started a business . krishan invested 4 times as nandan did and invested his money for trible time as compared to nandan . if the gain is proportional to the money invested and the time for which the money is invested and the total gain was rs . 26000 , find the nandan ' s earning .
Options: a ) 4000 , b ) 1000 , c ) 5000 , d ) 3000 , e ) 2000
Rationale: 4 : 1 3 : 1 - - - - - - 12 : 1 13 - - - - - rs . 26000 1 - - - - - ? = > rs . 26000 / 13 = rs . 2000 answer : e
Answer: e
Python program:
a = 3 * 4
b = a + 1 
c = 26000 / b
Problem: what is the 21 th digit to the right of the decimal point in the decimal expansion of 1 / 37 ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 7 , e ) 9
Rationale: "1 / 37 = 0.027027 . . . so , we have a repeating cycle of 027 . every third digit ( 3 rd , 6 th , 9 th , . . . ) to the right of the decimal point is 7 , thus 21 st digit to the right of the decimal point is also 7 . answer : d ."
Answer: d
Python program:
a = 1 / 37
Problem: two brothers ram and ravi appeared for an exam . the probability of selection of ram is 2 / 7 and that of ravi is 1 / 5 . find the probability that both of them are selected .
Options: a ) 2 / 35 , b ) 2 / 3 , c ) 7 / 35 , d ) 5 / 7 , e ) 7 / 5
Rationale: "let a be the event that ram is selected and b is the event that ravi is selected . p ( a ) = 2 / 7 p ( b ) = 1 / 5 let c be the event that both are selected . p ( c ) = p ( a ) x p ( b ) as a and b are independent events : = 2 / 7 x 1 / 5 = 2 / 35 answer : a"
Answer: a
Python program:
a = 2 / 7
b = 1 / 5
c = a * b
Problem: if a rectangular billboard has an area of 104 square feet and a perimeter of 42 feet , what is the length of each of the longer sides ?
Options: a ) 4 , b ) 7 , c ) 8 , d ) 13 , e ) 26
Rationale: "this question can be solved algebraically or by testing the answers . we ' re told that a rectangle has an area of 104 and a perimeter of 42 . we ' re asked for the length of one of the longer sides of the rectangle . since the answers are all integers , and the area is 104 , the shorter side will almost certainly be less than 10 ( since 10 x 10 = 100 , but we ' re not dealing with a square ) . answer b ( 7 ) does not divide evenly into 104 , so the correct answer is probably a or c . let ' s test answer c : 8 if . . . the shorter side = 8 . . . the area = 104 . . . . 104 / 8 = 13 = the longer side perimeter = 8 + 8 + 13 + 13 = 42 d"
Answer: d
Python program:
a = 42 / 2
b = 42 / 2
c = b ** 2
d = 4 * 104
e = c - d
f = math.sqrt(e)
g = a - f
h = g / 2
Problem: a cricket bat is sold for $ 900 , making a profit of $ 75 . the profit percentage would be
Options: a ) 9 % , b ) 12 % , c ) 10 % , d ) 36 % , e ) 40 %
Rationale: "75 / ( 900 - 75 ) = 75 / 825 = 0.9 bit more than 9 % . answer : a"
Answer: a
Python program:
a = 900 - 75
b = 75 / a
c = b * 100
Problem: if 4 ^ ( 2 x + 2 ) = 16 ^ ( 3 x − 1 ) , what is the value of x ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: 2 ^ ( 4 x + 4 ) = 2 ^ ( 12 x - 4 ) 4 x + 4 = 12 x − 4 x = 1 answer b
Answer: b
Python program:
a = 2 + 2 
b = 4 / a
Problem: the product of three consecutive numbers is 720 . then the sum of the smallest two numbers is ?
Options: a ) 11 , b ) 15 , c ) 17 , d ) 38 , e ) 56
Rationale: "product of three numbers = 720 720 = 8 * 9 * 10 so , the three numbers are 8 , 9 and 10 . and sum of smallest of these two = 8 + 9 = 17 . answer : option c"
Answer: c
Python program:
a = 2 ** 4
b = math.factorial(720)
c = a * b
Problem: you collect pens . suppose you start out with 25 . mike gives you another 22 pens . since her father makes pens , cindy decides to double your pens . since you ' re nice , you give sharon 19 pens . how many pens do you have at the end ?
Options: a ) 39 , b ) 40 , c ) 41 , d ) 75 , e ) 43
Rationale: "solution start with 25 pens . mike gives you 22 pens : 25 + 22 = 47 pens . cindy doubles the number of pens you have : 47 ã — 2 = 94 pens . sharon takes 19 pens from you : 94 - 19 = 75 pens . so you have 75 at the end . correct answer : d"
Answer: d
Python program:
a = 22 + 25 
b = a * 2
c = b - 19
Problem: the population of a town increased from 1 , 45,000 to 2 , 30,500 in a decade . the average percent increase of population per year is :
Options: a ) 4.37 % , b ) 5.8 % , c ) 6.8 % , d ) 8.75 % , e ) none
Rationale: "explanation : increase in 10 years = ( 230500 - 145000 ) = 85500 . increase % = ( 85500 / 145000 x 100 ) % = 58 % . required average = ( 58 / 10 ) % = 5.8 % . answer : option b"
Answer: b
Python program:
a = 10 * 1000
b = a * 10
c = b - 1000
d = c - 1000
e = 2 + 3 
f = e * 100
g = d - f
h = 3 + 4 
i = h * 10
j = 2 + 3 
k = i + j 
l = k * 1000
m = g / l
n = m - 1
o = n / 10
p = o * 100
q = p + 4
Problem: in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the sport formulation , the ratio of flavoring to corn syrup is three times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of the sport formulation contains 1 ounces of corn syrup , how many ounces of water does it contain ?
Options: a ) 15 , b ) 30 , c ) 45 , d ) 60 , e ) 90
Rationale: "standard : fl : corn s : water = 1 : 12 : 30 sport : fl : corn s : water = 3 : 12 : 180 this simplifies to 1 : 4 : 60 if the large bottle has a capacity of x ounces , then 4 x / 65 = 1 . so , x = 65 / 4 ounces . water = ( 60 / 65 ) * ( 65 / 4 ) = 15 ounces . ans a"
Answer: a
Python program:
a = 1 / 12
b = a * 3
c = 1 / 30
d = c / 2
e = b / d
f = e * 1
Problem: in a certain animal shelter , the ratio of the number of dogs to the number of cats is 15 to 7 . if 8 additional cats were to be taken in by the shelter , the ratio of the number of dogs to the number of cats would be 15 to 11 . how many dogs are in the shelter ?
Options: a ) 15 , b ) 25 , c ) 30 , d ) 45 , e ) 60
Rationale: "this ratio question can be solved in a couple of different ways . here ' s an algebraic approach . . . we ' re told that the ratio of the number of dogs to the number of cats is 15 : 7 . we ' re then told that 8 more cats are added to this group and the ratio becomes 15 : 11 . we ' re asked for the number of dogs . algebraically , since the number of dogs is a multiple of 15 and the number of cats is a multiple of 7 , we can write this initial relationship as . . . 15 x / 7 x when we add the 18 cats and factor in the ' ending ratio ' , we have an equation . . . . 15 x / ( 7 x + 8 ) = 15 / 11 here we have 1 variable and 1 equation , so we can solve for x . . . . ( 15 x ) ( 11 ) = ( 7 x + 8 ) ( 15 ) ( x ) ( 11 ) = ( 7 x + 8 ) ( 1 ) 11 x = 7 x + 8 4 x = 8 x = 2 with this x , we can figure out the initial number of dogs and cats . . . initial dogs = 15 x = 15 ( 2 ) = 30 final answer : c"
Answer: c
Python program:
a = 7 * 8
b = 11 - 7
c = a / b
d = c / 7
e = d * 15
Problem: the number 523 fbc is divisible by 7 , 89 . then what is the value of f * b * c
Options: a ) 504 , b ) 532 , c ) 210 , d ) 180 , e ) 280
Rationale: lcm of 7 , 8 and 9 is 504 , thus 523 fbc must be divisible by 504 . 523 fbc = 523000 + fbc 523000 divided by 504 gives a remainder of 352 . hence , 352 + fbc = k * 504 . k = 1 fbc = 152 - - > f * b * c = 10 k = 2 fbc = 656 - - > f * b * c = 180 as fbc is three digit number k can not be more than 2 . two answers ? well only one is listed in answer choices , so d . answer : d .
Answer: d
Python program:
a = 523 / 4
b = 523 / 4
c = a + b 
d = c / 2
e = 4 + 1 
f = e * 10
g = d + f
Problem: the toll t , in dollars , for a truck using a certain bridge is given by the formula t = 1.50 + 0.50 ( x − 2 ) , where x is the number of axles on the truck . what is the toll for an 18 - wheel truck that has 2 wheels on its front axle and 2 wheels on each of its other axles ?
Options: a ) $ 2.50 , b ) $ 3.00 , c ) $ 3.50 , d ) $ 4.00 , e ) $ 5.00
Rationale: "number of wheels in truck = 18 number of wheels on its front axle = 2 number of wheels remaining = 16 number of axles remaining axles = 16 / 2 = 8 total number of axles = 9 t = 1.50 + 0.50 ( 9 − 2 ) = 1.50 + . 5 * 7 = 1.5 + 1.5 = 5 $ answer e"
Answer: e
Python program:
a = 18 - 2
b = a / 2
c = b + 1 
d = c - 2
e = 0 * 50
f = 1 + 50
Problem: indu gave bindu rs . 5000 on compound interest for 2 years at 4 % per annum . how much loss would indu has suffered had she given it to bindu for 2 years at 4 % per annum simple interest ?
Options: a ) 8 , b ) 2 , c ) 9 , d ) 5 , e ) 1
Rationale: "5000 = d ( 100 / 4 ) 2 d = 8 answer : a"
Answer: a
Python program:
a = 4 / 100
b = 1 + a 
c = b ** 2
d = 5000 * c
e = d - 5000
f = 4 / 100
g = 5000 * f
h = g * 2
i = e - h
Problem: a sum of money at simple interest amounts to $ 700 in 3 years and to $ 764 in 4 years . the sum is :
Options: a ) $ 508 , b ) $ 698 , c ) $ 398 , d ) $ 549 , e ) $ 675
Rationale: "a $ 508 s . i . for 1 year = $ ( 764 - 700 ) = $ 64 . s . i . for 3 years = $ ( 64 x 3 ) = $ 192 . principal = $ ( 700 - 192 ) = $ 508 ."
Answer: a
Python program:
a = 764 - 700
b = a * 3
c = b / 4
d = 700 - c
Problem: how many factors does 34 ^ 2 have ?
Options: a ) 2 , b ) 8 , c ) 20 , d ) 25 , e ) 26
Rationale: "36 ^ 2 = 6 * 6 * 6 * 6 = 2 ^ 4 * 3 ^ 4 total factors = ( 4 + 1 ) * ( 4 + 1 ) = 5 * 4 = 20 answer c ."
Answer: c
Python program:
a = 10 * 2
b = 34 / a
Problem: how many positive integers between 1 and 100 are there such that they are multiples of 15 ?
Options: a ) 5 , b ) 4 , c ) 7 , d ) 1 , e ) 6
Rationale: "multiples of 15 = 15 , 30,45 , - - - - - 90 number of multiples of 15 = > 90 - 15 / 15 + 1 = 6 answer is e"
Answer: e
Python program:
a = 100 - 1
b = a / 15
Problem: a man walking at a rate of 10 km / hr crosses a bridge in 3 minutes . the length of the bridge is ?
Options: a ) 500 , b ) 650 , c ) 250 , d ) 111 , e ) 236
Rationale: "speed = 10 * 5 / 18 = 50 / 18 m / sec distance covered in 5 minutes = 50 / 18 * 5 * 60 = 500 m answer is a"
Answer: a
Python program:
a = 10 * 1000
b = a / const_60
c = b * 3
Problem: how many paying stones , each measuring 3 * 2 m are required to pave a rectangular court yard 15 m long and 6 m board ?
Options: a ) 99 , b ) 18 , c ) 26 , d ) 15 , e ) 12
Rationale: "15 * 6 = 3 * 2 * x = > x = 15 answer : d"
Answer: d
Python program:
a = rectangle_area / (
Problem: on a partly cloudy day , derek decides to walk back from work . when it is sunny , he walks at a speed of s miles / hr ( s is an integer ) and when it gets cloudy , he increases his speed to ( s + 1 ) miles / hr . if his average speed for the entire distance is 2.8 miles / hr , what fraction w of the total distance did he cover while the sun was shining on him ?
Options: a ) 1 / 4 , b ) 4 / 5 , c ) 1 / 5 , d ) 1 / 6 , e ) 1 / 7
Rationale: if s is an integer and we know that the average speed is 2.8 , s must be = 2 . that meanss + 1 = 3 . this implies that the ratio of time for s = 2 is 1 / 4 of the total time . the formula for distance / rate is d = rt . . . so the distance travelled when s = 2 is 2 t . the distance travelled for s + 1 = 3 is 3 * 4 t or 12 t . therefore , total distance covered while the sun was shining over him is w = 2 / 14 = 1 / 7 . answer : e
Answer: e
Python program:
a = math.lcm(2, 3)
b = a / 2
c = b - 2
Problem: what number has a 15 : 1 ratio to the number 10 ?
Options: a ) 130 , b ) 100 , c ) 200 , d ) 150 , e ) 120
Rationale: "15 : 1 = x : 10 x = 10 * 15 x = 150 answer : d"
Answer: d
Python program:
a = 10 * 15
Problem: if a and b are positive integers and ( 2 ^ a ) ^ b = 2 ^ 7 , what is the value of 2 ^ a * 2 ^ b ?
Options: a ) 16 , b ) 32 , c ) 64 , d ) 256 , e ) 128
Rationale: "2 ^ ab = 2 ^ 7 therefore ab = 7 either a = 1 or 7 or b = 7 or 1 therefore 2 ^ a * 2 ^ b = 2 ^ ( a + b ) = 2 ^ 8 = 256 d"
Answer: d
Python program:
a = 2 ** 3
b = a * 2
Problem: a man is 30 years older than his son . in four years , his age will be twice the age of his son . the present age of this son is
Options: a ) 22 years , b ) 23 years , c ) 24 years , d ) 25 years , e ) 26 years
Rationale: "explanation : let ' s son age is x , then father age is x + 30 . = > 2 ( x + 4 ) = ( x + 30 + 4 ) = > 2 x + 8 = x + 34 = > x = 26 years answer : option e"
Answer: e
Python program:
a = 2 * 2
b = a - 2
c = 30 - b
d = 2 - 1
e = c / d
Problem: the sum of the fourth and twelfth term of an arithmetic progression is 20 . what is the sum of the first 17 terms of the arithmetic progression ?
Options: a ) 300 , b ) 120 , c ) 150 , d ) 170 , e ) 270
Rationale: "n th term of a . p . is given by a + ( n - 1 ) d 4 th term = a + 3 d 12 th term = a + 11 d given a + 3 d + a + 11 d = 20 - - > 2 a + 14 d = 20 - - > a + 7 d = 10 sum of n term of a . p = n / 2 [ 2 a + ( n - 1 ) d ] subsitiuing n = 17 . . . we get 17 / 2 [ 2 a + 14 d ] = 17 [ a + 7 d ] = 17 * 10 = 170 . . . answer is d . . ."
Answer: d
Python program:
a = 20 * 17
b = a / 2
Problem: a man invests rs . 4,000 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 . 4000 at 5 % per annum = ( 4000 × 5 × 1 ) / 100 = rs . 200 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 = ( 4000 + x ) × 6 × 1 / 100 . = > 200 + 2 x / 25 = ( 4000 + x ) × 6 × 1 / 100 . = > 20000 + 8 x = ( 4000 + x ) × 6 . = > 20000 + 8 x = 24000 + 6 x . = > 2 x = 4000 . = > x = 2000 . answer : d"
Answer: d
Python program:
a = 8 * 1000
b = 6 - 5
c = 8 - 6
d = b / c
e = a * d
Problem: a cab driver 5 days income was $ 400 , $ 250 , $ 650 , $ 400 , $ 500 . then his average income is ?
Options: a ) $ 400 , b ) $ 420 , c ) $ 440 , d ) $ 460 , e ) $ 480
Rationale: "avg = sum of observations / number of observations avg income = ( 400 + 250 + 650 + 400 + 500 ) / 5 = 440 answer is c"
Answer: c
Python program:
a = 400 + 250 
b = a + 650 
c = b + 400 
d = c + 500 
e = d / 5
Problem: calculate the time it will take for a train that is 120 meter long to pass a bridge of 160 meter length , if the speed of the train is 40 km / hour ?
Options: a ) 21.2 seconds , b ) 25.2 seconds , c ) 29.2 seconds , d ) 35.2 seconds , e ) 11.2 seconds
Rationale: speed = 40 km / hr = 40 * ( 5 / 18 ) m / sec = 11.1111 m / sec total distance = 120 + 160 = 280 meter time = distance / speed = 280 * ( 1 / 11.1111 ) = 25.2 seconds answer : b
Answer: b
Python program:
a = 120 + 160 
b = 40 / const_3_6
c = a / b
Problem: the banker ' s gain on a sum due 6 years hence at 12 % per annum is rs . 540 . what is the banker ' s discount ?
Options: a ) 1240 , b ) 1120 , c ) 1190 , d ) 1290 , e ) none of these
Rationale: "explanation : td = ( bg × 100 ) / tr = ( 540 × 100 ) / ( 6 × 12 ) = ( 90 × 100 ) / 12 = ( 15 × 100 ) 2 / = rs . 750 bg = bd – td = > 540 = bd - 750 = > bd = 540 + 750 = 1290 answer : option d"
Answer: d
Python program:
a = 540 * 100
b = 12 * 6
c = a / b
d = 540 + c
Problem: a and b can together finish a work in 30 days . they worked together for 20 days and then b left . after another 20 days , a finished the remaining work . in how many days a alone can finish the job ?
Options: a ) 40 , b ) 50 , c ) 54 , d ) 60 , e ) none of these
Rationale: "( a + b ) ' s 20 days work = ( 1 / 30 * 20 ) = 2 / 3 . remaining work = ( 1 - 2 / 3 ) = 1 / 3 . now , 1 / 3 work is done by a in 20 days . whole work will be done by a in ( 20 * 3 ) = 60 days . correct option : d"
Answer: d
Python program:
a = 20 * 30
b = 30 - 20
c = a / b
Problem: how many numbers between 190 and 580 are divisible by 4,5 and 6 ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: every such number must be divisible by l . c . m of 4 , 5,6 i . e , 60 . such numbers are 240,300 , 360,420 , 480,540 . clearly , there are 6 such numbers answer : a
Answer: a
Python program:
a = 4 + 1 
b = math.lcm(4, a)
c = math.lcm(b, 6)
d = 580 / c
e = math.floor(d)
f = 4 + 1 
g = math.lcm(4, f)
h = math.lcm(g, 6)
i = 190 / h
j = math.floor(i)
k = e - j
Problem: a 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 24 sec . what is the length of the platform ?
Options: a ) 389 m , b ) 350 m , c ) 187.5 m , d ) 299 m , e ) 219.5 m
Rationale: "speed = 300 / 24 = 25 / 2 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 39 = 25 / 2 = > x = 187.5 m . answer : c"
Answer: c
Python program:
a = speed * (
b = a - 39
Problem: what percent is 3 % of 5 % ?
Options: a ) 60 % , b ) 50 % , c ) 75 % , d ) 45 % , e ) 30 %
Rationale: "required percentage = 3 % / 5 % * 100 = 3 / 5 * 100 = 60 % answer is a"
Answer: a
Python program:
a = 3 / 5
b = a * 100
Problem: when positive integer x is divided by positive integer y , the result is 59.32 . what is the sum t of all possible 2 - digit remainders for x / y ?
Options: a ) 560 , b ) 616 , c ) 672 , d ) 728 , e ) 784
Rationale: "ans b 616 . . . remainders = . 32 = 32 / 100 = 8 / 25 = 16 / 50 and so on . . so two digit remainders are 16 + 24 + 32 + . . . . + 96 . . t = 8 ( 2 + 3 + 4 . . . . + 12 ) = 616 . b"
Answer: b
Python program:
a = math.floor(2)
b = 2 - a
c = 59 / 32
Problem: perimeter of an equilateral and isosceles is 45 and 40 respectively . at least one of the sides of isosceles is equal to the equilateral . what ' s the base of isosceles triangle ?
Options: a ) 7
b ) 8
c ) 9
d ) 10
e ) 11
Rationale: 10 units as other 2 sides will be 15,15 units . answer : d
Answer: d
Python program:
a = 45 / 3
b = a * 2
c = 40 - b
Problem: kamal obtained 76 , 60 , 82 , 67 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 65 , b ) 69 , c ) 74 , d ) 75 , e ) none
Rationale: "sol . average = 76 + 60 + 82 + 67 + 85 / 5 ) = ( 375 / 5 ) = 74 . answer c"
Answer: c
Python program:
a = 76 + 60 
b = a + 82 
c = b + 67 
d = c + 85 
e = 1 + 4 
f = d / e
Problem: a train covers a distance of 12 km in 10 min . if it takes 16 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 320 m , b ) 188 m , c ) 120 m , d ) 178 m , e ) 189 m
Rationale: "speed = ( 12 / 10 * 60 ) km / hr = ( 72 * 5 / 18 ) m / sec = 20 m / sec . length of the train = 20 * 16 = 320 m . answer : a"
Answer: a
Python program:
a = 12 / 10
b = a - 16
c = 12 / b
Problem: if 12 men and 16 boys can do a piece of work in 5 days and 13 men together will 24 boys can do it in 4 days . compare the daily work done by a man with that of a boy .
Options: a ) 2 : 9 , b ) 2 : 1 , c ) 2 : 7 , d ) 2 : 5 , e ) 2 : 2
Rationale: "12 m + 16 b - - - - - 5 days 13 m + 24 b - - - - - - - 4 days 60 m + 80 b = 52 m + 96 b 8 m = 16 b = > 1 m = 2 b m : b = 2 : 1 answer : b"
Answer: b
Python program:
a = 4 * 24
b = 5 * 16
c = a - b
d = 5 * 12
e = 4 * 13
f = d - e
g = c / f
Problem: what least value should be replaced by * in 223 * 431 so the number become divisible by 9
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "explanation : trick : number is divisible by 9 , if sum of all digits is divisible by 9 , so ( 2 + 2 + 3 + * + 4 + 3 + 1 ) = 15 + * should be divisible by 9 , 15 + 3 will be divisible by 9 , so that least number is 3 . answer : option a"
Answer: a
Python program:
a = 431 - 431
b = 431 - a
Problem: the cost price of a radio is rs . 1340 and it was sold for rs . 1210 , find the loss % ?
Options: a ) 18 % , b ) 9 % , c ) 22 % , d ) 24 % , e ) 21
Rationale: "1340 - - - - 130 100 - - - - ? = > 9 % answer : b"
Answer: b
Python program:
a = 1340 - 1210
b = a / 1340
c = b * 100
Problem: the probability that a number selected at random from the first 50 natural numbers is a composite number is ?
Options: a ) 17 / 65 , b ) 17 / 25 , c ) 17 / 28 , d ) 17 / 65 , e ) 17 / 39
Rationale: "the number of exhaustive events = ⁵ ⁰ c ₁ = 50 . we have 15 primes from 1 to 50 . number of favourable cases are 34 . required probability = 34 / 50 = 17 / 25 . answer : b"
Answer: b
Python program:
a = 6 * 3
b = a - 1
c = b * 2
d = c / 50
Problem: if x : y = 4 : 7 , find the value of ( 6 x + 2 y ) : ( 5 x – y )
Options: a ) 7 : 13 , b ) 38 : 7 , c ) 3 : 13 , d ) 2 : 3 , e ) 38 : 13
Rationale: explanation : given : x / y = 4 / 7 ( 6 x + 2 y ) : ( 5 x – y ) = ( 6 * 4 + 2 * 7 ) : ( 5 * 4 – 7 ) 38 : 13 answer : e
Answer: e
Python program:
a = 6 ** 2
b = a + 2 
c = 4 + 7 
d = c + 2 
e = b / d
Problem: ritesh and co . generated revenue of rs . 2,500 in 2006 . this was 12.5 % of its gross revenue . in 2007 , the gross revenue grew by rs . 2,500 . what is the percentage increase in the revenue in 2007 ?
Options: a ) 12.5 % , b ) 20 % , c ) 25 % , d ) 50 % , e ) none of these
Rationale: "explanation : given , ritesh and co . generated revenue of rs . 2,500 in 2006 and that this was 12.5 % of the gross revenue . hence , if 2500 is 12.5 % of the revenue , then 100 % ( gross revenue ) is : = > ( 100 / 12.5 ) × 2500 . = > 20,000 . hence , the total revenue by end of 2007 is rs . 10,000 . in 2006 , revenue grew by rs . 2500 . this is a growth of : = > ( 2500 / 20000 ) × 100 . = > 12.5 % . answer : a"
Answer: a
Python program:
a = 1 + 4 
b = 2 * a
c = b * 100
d = 2 * c
e = 1 + 4 
f = e * 100
g = d + f 
h = 1 + 4 
i = 2 * h
j = i * 100
k = 2 + 4 
l = k * 100
m = j + l 
n = 12 / 5
o = m / n
p = g / o
q = p * 100
Problem: according to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . how many 15 - ounce cans of the concentrate are required to prepare 200 6 - ounce servings of orange juice ?
Options: a ) 25 , b ) 34 , c ) 50 , d ) 20 , e ) 100
Rationale: "orange juice concentrate : water : : 1 : 3 total quantity of orange juice = 200 * 6 = 1200 oz so orange juice concentrate : water : : 300 oz : 900 oz no . of 15 oz can = 300 oz / 15 oz = 20 answer d , 20 cans"
Answer: d
Python program:
a = 6 * 200
b = 200 / 10
c = a / b
Problem: the difference between compound interest and simple interest on an amount of $ 15,000 for 2 years is $ 96 . what is the rate of interest per annum ?
Options: a ) 6 % , b ) 7 % , c ) 9 % , d ) 8 % , e ) 5 %
Rationale: "[ 15000 x ( 1 + r / 100 ) ^ 2 - 15000 ] - [ ( 15000 x r x 2 ) / 100 ] = 96 = = > 15000 [ ( 1 + r / 100 ) ^ 2 - 1 - 2 r / 100 ] = 96 = = > 15000 [ ( ( 100 + r ) ^ 2 - 10000 - ( 200 x r ) ) / 10000 ] = 96 = = > r ^ 2 = ( 96 x 2 ) / 3 = 64 = = > r = 8 . rate = 8 % answer d ) 8 %"
Answer: d
Python program:
a = 15 / 0
b = 1 + a 
c = b ** 2
d = 15 / 0
e = 2 * d
f = 1 + e 
g = c - f
h = 96 / g
Problem: if x + y = 14 , x - y = 60 , for integers of x and y , x = ?
Options: a ) 37 , b ) 35 , c ) 25 , d ) 20 , e ) 42
Rationale: "x + y = 14 x - y = 60 2 x = 74 x = 37 answer is a"
Answer: a
Python program:
a = 14 + 60 
b = a / 2
Problem: if in a race of 100 m , a covers the distance in 20 seconds and b in 25 seconds , then a beats b by :
Options: a ) 20 m , b ) 16 m , c ) 11 m , d ) 10 m , e ) 15 m
Rationale: "explanation : the difference in the timing of a and b is 5 seconds . hence , a beats b by 5 seconds . the distance covered by b in 5 seconds = ( 100 * 5 ) / 25 = 20 m hence , a beats b by 20 m . answer a"
Answer: a
Python program:
a = 25 - 20
b = a / 25
c = b * 100
Problem: the speed of a car is 90 km in the first hour and 30 km in the second hour . what is the average speed of the car ?
Options: a ) 50 kmph , b ) 60 kmph , c ) 75 kmph , d ) 85 kmph , e ) 90 kmph
Rationale: "explanation : s = ( 90 + 30 ) / 2 = 60 kmph b )"
Answer: b
Python program:
a = 90 + 30 
b = a / 2
Problem: suzie ’ s discount footwear sells all pairs of shoes for one price and all pairs of boots for another price . on monday the store sold 22 pairs of shoes and 16 pairs of boots for $ 580 . on tuesday the store sold 8 pairs of shoes and 32 pairs of boots for $ 800 . how much more do pairs of boots cost than pairs of shoes at suzie ’ s discount footwear ?
Options: a ) $ 10.50 , b ) $ 12.50 , c ) $ 11.50 , d ) $ 16.50 , e ) $ 9.50
Rationale: "let x be pair of shoes and y be pair of boots . 22 x + 16 y = 580 . . . eq 1 8 x + 32 y = 800 . . . . eq 2 . now multiply eq 1 by 2 and sub eq 2 . 44 x = 1160 8 x = 800 . 36 x = 360 = > x = 10 . sub x in eq 2 . . . . we get 80 + 32 y = 800 . . . then we get 32 y = 720 then y = 22.50 differenece between x and y is 12.50 answer : b"
Answer: b
Python program:
a = 580 * 2
b = a - 800
c = 22 * 2
d = c - 8
e = b / d
f = 22 * e
g = 580 - f
h = g / 16