euclaise/mathqa_programs huggingface dataset:
Problem: the average ( arithmetic mean ) of the 5 positive integers k , m , r , s , and t is 18 , and k < m < r < s < t . if t is 40 , what is the greatest possible value of the median of the 5 integers ?
Options: a ) 16 , b ) 23 , c ) 19 , d ) 20 , e ) 22
Rationale: "we need to find the median which is the third value when the numbers are in increasing order . since k < m < r < s < t , the median would be r . the average of the positive integers is 18 which means that in effect , all numbers are equal to 18 . if the largest number is 40 , it is 22 more than 18 . we need r to be maximum so k and m should be as small as possible to get the average of 16 . since all the numbers are positive integers , k and m can not be less than 1 and 2 respectively . 1 is 17 less than 18 and 2 is 16 less than 18 which means k and m combined are 33 less than the average . 40 is already 22 more than 18 and hence we only have 33 - 22 = 11 extra to distribute between r and s . since s must be greater than r , r can be 18 + 5 = 23 and s can be 18 + 6 = 24 . so r is 23 answer ( b )"
Answer: b
Python program:
a = 18 * 5
b = a - 40
c = b / 2
d = c - 2
Problem: how many positive integers less than 7,000 are there in which the sum of the digits equals 5 ?
Options: a ) 52 , b ) 54 , c ) 56 , d ) 58 , e ) 60
Rationale: "basically , the question asks how many 4 digit numbers ( including those in the form 0 xxx , 00 xx , and 000 x ) have digits which add up to 5 . think about the question this way : we know that there is a total of 5 to be spread among the 4 digits , we just have to determine the number of ways it can be spread . let x represent a sum of 1 , and | represent a seperator between two digits . as a result , we will have 5 x ' s ( digits add up to the 5 ) , and 3 | ' s ( 3 digit seperators ) . so , for example : xx | x | x | x = 2111 | | xxx | xx = 0032 etc . there are 8 c 3 ways to determine where to place the separators . hence , the answer is 8 c 3 = 56 . c"
Answer: c
Python program:
a = 4 + 5 
b = a - 1
c = math.factorial(b)
d = math.factorial(5)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: 4 / [ ( 1 / 0.03 ) + ( 1 / 0.37 ) ] = ?
Options: a ) 0.004 , b ) 0.11111 , c ) 2.775 , d ) 3.6036 , e ) 36.036
Rationale: "approximate . 1 / . 03 = 100 / 3 = 33 1 / . 37 = 100 / 37 = 3 denominator becomes 33 + 3 = 36 4 / 36 = . 1111 answer ( b )"
Answer: b
Python program:
a = 4 / 0
b = 4 / 0
c = a + b 
d = 1/(c)
Problem: by selling 16 pencils for a rupee a man loses 28 % . how many for a rupee should he sell in order to gain 28 % ?
Options: a ) 8 , b ) 9 , c ) 7 , d ) 6 , e ) 4
Rationale: "72 % - - - 16 128 % - - - ? 72 / 128 * 16 = 9 answer : b"
Answer: b
Python program:
a = 100 + 28 
b = 100 - 28
c = 1 / b
d = a * c
e = 1 / d
f = e * 16
Problem: if the radius of a circle is diminished by 10 % , then the area is diminished by :
Options: a ) 200 % , b ) 210 % , c ) 300 % , d ) 310 % , e ) none of these
Rationale: "explanation : let the original radius be r cm . new radius = 2 r area = π r 2 new area = π 2 r 2 = 4 π r 2 increase in area = ( 4 π r 2 − π r 2 ) = 3 π r 2 increase percent = 3 π r 2 / π r 2 ∗ 100 = 300 % option c"
Answer: c
Python program:
a = 100 / 100
b = 100 / 100
c = 10 / 100
d = b - c
e = d ** 2
f = a - e
g = f * 100
Problem: a parking garage rents parking spaces for $ 10 per week or $ 24 per month . how much does a person save in a year by renting by the month rather than by the week ?
Options: a ) $ 140 , b ) $ 160 , c ) $ 220 , d ) $ 232 , e ) $ 260
Rationale: "10 $ per week ! an year has 52 weeks . annual charges per year = 52 * 10 = 520 $ 30 $ per month ! an year has 12 months . annual charges per year = 12 * 24 = 288 $ 520 - 288 = 232 ans d"
Answer: d
Python program:
a = 3 + 2 
b = 10 * a
c = b + 2 
d = c * 10
e = 24 * 12
f = d - e
Problem: a boat running downstream covers a distance of 12 km in 2 hours while for covering the same distance upstream , it takes 3 hours . what is the speed of the boat in still water ?
Options: a ) 8 kmph , b ) 5 kmph , c ) 4 kmph , d ) 6 kmph , e ) 7 kmph
Rationale: "speed downstream = 12 / 2 = 6 kmph speed upstream = 12 / 3 = 4 kmph speed of the boat in still water = 6 + 4 / 2 = 5 kmph answer : b"
Answer: b
Python program:
a = 12 / 2
b = 12 / 3
c = a + b 
d = c / 2
Problem: what is the area of a square field whose diagonal of length 20 m ?
Options: a ) 288
b ) 289
c ) 200
d ) 112
e ) 178
Rationale: d 2 / 2 = ( 20 * 20 ) / 2 = 200 answer : c
Answer: c
Python program:
a = square_area / (
Problem: a sum of rs . 12,500 amounts to rs . 15,500 in 4 years at the rate of simple interest . what is the rate of interest ?
Options: a ) 3 % , b ) 4 % , c ) 5 % , d ) 6 % , e ) 7 %
Rationale: s . i . = rs . ( 15500 - 12500 ) = rs . 3000 . rate = ( 100 x 3000 ) / ( 12500 x 4 ) % = 6 % answer : d
Answer: d
Python program:
a = 2 + 3 
b = a * 3
c = 2 + 3 
d = c * 2
e = d * 100
f = b * e
g = 2 + 3 
h = g * 100
i = f + h 
j = 3 * 4
k = 2 + 3 
l = k * 2
m = l * 100
n = j * m
o = 2 + 3 
p = o * 100
q = n + p 
r = i - q
s = 3 * 4
t = 2 + 3 
u = t * 2
v = u * 100
w = s * v
x = 2 + 3 
y = x * 100
z = w + y 
A = r / z
B = A / 4
C = B * 100
Problem: ravi purchased a refrigerator and a mobile phone for rs . 15000 and rs . 8000 respectively . he sold the refrigerator at a loss of 4 percent and the mobile phone at a profit of 10 percent . overall he make a .
Options: a ) loss of rs . 200 , b ) loss of rs . 100 , c ) profit of rs . 100 , d ) profit of rs . 200 , e ) none of these
Rationale: "let the sp of the refrigerator and the mobile phone be rs . r and rs . m respectively . r = 15000 ( 1 - 4 / 100 ) = 15000 - 600 m = 8000 ( 1 + 10 / 100 ) = 8000 + 800 total sp - total cp = r + m - ( 15000 + 8000 ) = - 600 + 800 = rs . 200 as this is positive , an overall profit of rs . 200 was made . answer : d"
Answer: d
Python program:
a = 4 / 100
b = 1 - a
c = 15000 * b
d = 10 / 100
e = 1 + d 
f = 8000 * e
g = c + f 
h = 15000 + 8000 
i = g - h
Problem: tim came second in math . when his mother asked him how much he had scored , he answered that he got the sum of the first 8 even numbers . his mother immediately worked out the answer . how much had he scored in math ?
Options: a ) 80 , b ) 90 , c ) 30 , d ) 72 , e ) 60
Rationale: d 72 sum = ( n x n ) + n hence , 8 x 8 = 64 + 8 = 72
Answer: d
Python program:
a = 8 + 1 
b = a * 8
Problem: a and b can do a work in 5 days , b and c in 15 days and c and a in 25 days . in how many days will the work be completed , if all three of them work together ?
Options: a ) 26 / 18 , b ) 42 / 15 , c ) 48 / 63 , d ) 12 / 36 , e ) 150 / 23
Rationale: "one day work of a and b = 1 / 5 one day work of b and c = 1 / 15 one day work of c and a = 1 / 25 2 ( a + b + c ) = 1 / 5 + 1 / 15 + 1 / 25 2 ( a + b + c ) = 23 / 75 ( a + b + c ) = 23 / 150 number of days required = 150 / 23 days . answer : e"
Answer: e
Python program:
a = 1/(5)
b = 1/(15)
c = a + b 
d = 1/(25)
e = c + d 
f = e / 5
g = 1 / f
Problem: 22 percent of 300
Options: a ) 50 , b ) 55 , c ) 62 , d ) 77 , e ) 66
Rationale: 1 % of 300 = 3 22 % of 300 = 22 * 3 = 66 answer : e
Answer: e
Python program:
a = 22 * 300
b = a / 100
Problem: working individually , allison can sew dresses for 9 hours and al can sew dresses in 12 hours . if allison and al work together but independently at the task for 3 hours , at which point al leaves , how many remaining hours will it take allison to complete the task alone ?
Options: a ) 45 / 12 , b ) 23 / 12 , c ) 40 / 33 , d ) 34 / 12 , e ) 43 / 5
Rationale: in first 3 hrs al will finish 3 / 12 = 1 / 4 of work and allison will finish 3 / 9 = 1 / 3 work so total 1 / 4 + 1 / 3 = 7 / 12 work is finished and 1 - 7 / 12 = 5 / 12 work remaining . now allison will take ( 5 / 12 ) * 9 = 45 / 12 hrs to finish it . so answer is a .
Answer: a
Python program:
a = 1 / 9
b = 1 / 12
c = a + b 
d = c * 3
e = 1 - d
f = 1 / 9
g = e / f
Problem: 3 friends are planning to attend a concert . if another friend also goes with them , they will get a group discount on their tickets . if the new total price of the tickets with the group discount is the same as the original total price of the tickets without the group discount , how much is the discount ?
Options: a ) 5 % , b ) 10 % , c ) 20 % , d ) 25 % , e ) 33 %
Rationale: let x be the original price of one ticket . the total original cost is 3 x . the new cost is 4 y , where y is the discounted price of one ticket . 3 x = 4 y y = 3 x / 4 = 0.75 x which is a discount of 25 % . the answer is d .
Answer: d
Python program:
a = 3 + 1 
b = 3 / a
c = 1 - b
d = c * 100
Problem: the true discount on a bill of rs . 540 is rs . 90 . the banker ' s discount is :
Options: a ) rs . 60 , b ) rs . 108 , c ) rs . 110 , d ) rs . 112 , e ) rs . 122
Rationale: "p . w . = rs . ( 540 - 90 ) = rs . 450 . s . i . on rs . 450 = rs . 90 . s . i . on rs . 540 = rs . ( 90 / 450 ) x 540 = rs . 108 . b . d . = rs . 108 . answer : b"
Answer: b
Python program:
a = 540 - 90
b = 90 / a
c = b * 540
Problem: when positive integer x is divided by positive integer y , the remainder is 3 . if x / y = 96.15 , what is the value of y ?
Options: a ) 96 , b ) 75 , c ) 48 , d ) 25 , e ) 20
Rationale: by the definition of a remainder , the remainder here is equal to 3 / y . the remainder in decimal form is given as . 15 therefore , 3 / y = . 15 solve for y and get 20 . e
Answer: e
Python program:
a = math.floor(96, 15)
b = 96 - 15
c = 3 / b
Problem: fetched a total simple interest of rs . 4216.25 at the rate of 9 p . c . p . a . in 5 years . what is the sum ?
Options: a ) rs . 8928 , b ) rs . 89228 , c ) rs . 8911 , d ) rs . 8925 , e ) rs . 8922
Rationale: explanation : principal = rs . = rs . = rs . 8925 answer : d
Answer: d
Python program:
a = 4216 * 25
b = 9 * 5
c = a / b
Problem: the average of 10 numbers is calculated as 15 . it is discovered later on that while calculating the average , one number namely 36 was wrongly read as 26 . the correct average is ?
Options: a ) 16 , b ) 18 , c ) 19 , d ) 22 , e ) 24
Rationale: "explanation : 10 * 15 + 36 – 26 = 160 / 10 = 16 a )"
Answer: a
Python program:
a = 36 - 26
b = a / 10
c = 15 + b
Problem: if x is 20 percent greater than 98 , then x =
Options: a ) 68 , b ) 70.4 , c ) 86 , d ) 105.6 , e ) 117.6
Rationale: "x = 98 * 1.2 = 117.6 so the answer is e ."
Answer: e
Python program:
a = 20 / 100
b = a * 98
c = 98 + b
Problem: 30 pens and 75 pencils were purchased for 450 . if the average price of a pencil was 2.00 , find the average price of a pen .
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: since average price of a pencil = 2 ∴ price of 75 pencils = 150 ∴ price of 30 pens = ( 450 – 150 ) = 300 ∴ average price of a pen = 360 ⁄ 60 = 10 answer a
Answer: a
Python program:
a = 75 * 2
b = 450 - a
c = b / 30
Problem: a person is traveling at 100 km / hr and reached his destiny in 5 then find the distance ?
Options: a ) 250 km , b ) 300 km , c ) 500 km , d ) 450 km , e ) 350 km
Rationale: "t = 5 hr s = 100 km / hr d = t * s = 100 * 5 = 500 km answer is c"
Answer: c
Python program:
a = 100 * 5
Problem: if jake loses 29 pounds , he will weigh twice as much as his sister . together they now weigh 99 pounds . what is jake ' s present weight , in pounds ?
Options: a ) 69 , b ) 135 , c ) 139 , d ) 147 , e ) 188
Rationale: "j = jake ’ s current weight , in pounds s = sister ’ s current weight , in pounds we are told that “ if jake loses 8 pounds , he will weigh twice as much as his sister . we put this into an equation : j – 29 = 2 s j = 2 s + 29 ( equation 1 ) next , we are told that “ together they now weigh 89 pounds . ” we can also put this into an equation . j + s = 89 ( equation 2 ) to solve this equation , we can substitute 2 s + 8 from equation 1 for the variable j in equation 2 : 2 s + 29 = 89 - s 3 s = 60 s = 20 j + 20 = 89 j = 69 answer : a"
Answer: a
Python program:
a = 99 - 29
b = a / 3
c = b * 2
d = c + 29
Problem: a man can row downstream at the rate of 18 kmph and upstream at 6 kmph . find the man ’ s rate in still water and rate of current ?
Options: a ) 8.5 , b ) 6.0 , c ) 9.5 , d ) 9.0 , e ) 8.25
Rationale: "rate of still water = 1 / 2 ( down stream + upstream ) = 1 / 2 ( 18 + 6 ) = 12 kmph rate of current = 1 / 2 ( down stream - upstream ) = 1 / 2 ( 18 - 6 ) = 1 / 2 ( 12 ) = 6 kmph answer is b ."
Answer: b
Python program:
a = 18 - 6
b = a / 2
Problem: the average ( arithmetic mean ) of the even integers from 0 to 40 inclusive is how much greater than the average ( arithmetic mean ) of the even integers from 0 to 20 inclusive ?
Options: a ) 5 , b ) 8 , c ) 10 , d ) 15 , e ) 20
Rationale: "the sum of even numbers from 0 to n is 2 + 4 + . . . + n = 2 ( 1 + 2 + . . . + n / 2 ) = 2 ( n / 2 ) ( n / 2 + 1 ) / 2 = ( n / 2 ) ( n / 2 + 1 ) the average is ( n / 2 ) ( n / 2 + 1 ) / ( n / 2 + 1 ) = n / 2 the average of the even numbers from 0 to 40 is 40 / 2 = 20 the average of the even numbers from 0 to 20 is 20 / 2 = 10 the answer is c ."
Answer: c
Python program:
a = 20 + 0 
b = a / 2
c = 40 + 0 
d = c / 2
e = b - d
Problem: what is the smallest number h which when increased by 5 is completely divisible by 8 , 11 and 24 ?
Options: a ) 264 , b ) 259 , c ) 269 , d ) 270 , e ) 282
Rationale: this question includes a number of great number property shortcuts that you can take advantage of : 1 ) the question asks for the smallest number that , when increased by 5 is divisible by 8 , 11 and 24 . since the answers are numbers , we can test the answers . 2 ) any number that is divisible by 24 is also divisible by 8 , so we really just need to consider the 11 and the 24 . 3 ) to be divisible by 24 , the end number must be even . since we ' re adding 5 to get to that end number , the starting number must be odd . the last shortcut allows us to eliminate answers a , d and e . between answers b and c , testing b first will prove that , when increased by 5 , the end sum is divisible by both 11 and 24 . final answer : b
Answer: b
Python program:
a = math.lcm(8, 11)
b = math.lcm(a, 24)
c = b - 5
Problem: the cost price of a radio is rs . 1500 and it was sold for rs . 1290 , find the loss % ?
Options: a ) 14 % , b ) 16 % , c ) 17 % , d ) 78 % , e ) 28 %
Rationale: "1500 - - - - 210 100 - - - - ? = > 14 % answer : a"
Answer: a
Python program:
a = 1500 - 1290
b = a / 1500
c = b * 100
Problem: in an election a candidate who gets 60 % of the votes is elected by a majority of 900 votes . what is the total number of votes polled ?
Options: a ) a ) 4500 , b ) b ) 5200 , c ) c ) 6900 , d ) d ) 7520 , e ) e ) 6000
Rationale: "let the total number of votes polled be x then , votes polled by other candidate = ( 100 - 60 ) % of x = 40 % of x 60 % of x - 40 % of x = 900 20 x / 100 = 900 x = 900 * 100 / 20 = 4500 answer is a"
Answer: a
Python program:
a = 100 - 60
b = 60 - a
c = b / 100
d = 900 / c
Problem: ( 17 ) 3.75 x ( 17 ) ? = 178
Options: a ) 2.29 , b ) 2.75 , c ) 4.25 , d ) 4.5 , e ) none of these
Rationale: "solution let ( 17 ) 3.75 * ( 17 ) x = 178 . then , ( 17 ) 3.5 + x = ( 17 ) 8 . ∴ 3.75 + x = 8 ⇔ x = ( 8 - 3.75 ) ⇔ x = 4.25 answer c"
Answer: c
Python program:
a = 17 * 17
Problem: the speed of a boat in still water in 15 km / hr and the rate of current is 3 km / hr . the distance travelled downstream in 12 minutes is :
Options: a ) 1.2 km , b ) 2.4 km , c ) 3.2 km , d ) 3.6 km , e ) 4.6 km
Rationale: "speed downstream = ( 15 + 3 ) kmph = 18 kmph . distance travelled = 18 x 12 / 60 km = 3.6 km . answer : d"
Answer: d
Python program:
a = 15 + 3 
b = 12 / const_60
c = a * b
Problem: if 1000 microns = 1 decimeter , and 1 , 000,000 angstroms = 1 decimeter , how many angstroms equal 1 micron ?
Options: a ) 10 , b ) 1000 , c ) 100 , d ) 0.01 , e ) 0.0001
Rationale: "1000 microns = 1 decimeter , and 1 , 000,000 angstroms = 1 decimeter 1000 microns = 1 , 000,000 angstroms 1 micron = 1 , 000,000 / 1,000 = 1,000 answer : b"
Answer: b
Python program:
a = 100 * 100
b = 1 / a
c = 100 * 100
d = b * c
Problem: 10 men , working 7 hours a day can complete a work in 18 days . how many hours a day must 15 men work to complete the same work in 12 days ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: the number of hours required to complete the work is 10 * 7 * 18 = 1260 15 × 12 × ( x ) = 1260 x = 7 the answer is b .
Answer: b
Python program:
a = 10 * 7
b = a * 18
c = 15 * 12
d = b / c
Problem: calculate the value of n from the below equation : y ^ 4 â ˆ ’ 20 y + 1 = 22
Options: a ) 5 , b ) 3 , c ) 6 , d ) 2 , e ) 1
Rationale: use elimination method to find the correct option . you find that of all the options 3 is the correct value for y answer : b
Answer: b
Python program:
a = 22 - 1
b = 20 + 1 
c = a / b
d = 4 - c
Problem: the average of first five prime numbers greater than 37 is ?
Options: a ) 32.2 , b ) 32.98 , c ) 42.3 , d ) 48.6 , e ) 32.4
Rationale: "41 + 43 + 47 + 53 + 59 = 243 / 5 = 48.6 answer : d"
Answer: d
Python program:
a = 37 + 1
Problem: a bag contains 6 black and 6 white balls . one ball is drawn at random . what is the probability that the ball drawn is white ?
Options: a ) 3 / 4 , b ) 1 / 2 , c ) 1 / 7 , d ) 1 / 8 , e ) 4 / 3
Rationale: "let number of balls = ( 6 + 6 ) = 12 . number of white balls = 6 . p ( drawing a white ball ) = 6 / 12 = 1 / 2 . option b ."
Answer: b
Python program:
a = math.factorial(6)
b = 6 - 2
c = math.factorial(b)
d = a / c
e = math.factorial(2)
f = d / e
g = math.factorial(6)
h = 6 - 2
i = math.factorial(h)
j = g / i
k = math.factorial(2)
l = j / k
m = f + l 
n = 6 + 6 
o = math.factorial(n)
p = 6 + 6 
q = p - 2
r = math.factorial(q)
s = o / r
t = math.factorial(2)
u = s / t
v = m / u
Problem: the list price of an article is rs . 67 . a customer pays rs . 56.16 for it . he was given two successive discounts , one of them being 10 % . the other discount is ?
Options: a ) 3.86 % , b ) 4.86 % , c ) 5.86 % , d ) 6.86 % , e ) 7.86 %
Rationale: 67 * ( 90 / 100 ) * ( ( 100 - x ) / 100 ) = 56.16 x = 6.86 % answer : d
Answer: d
Python program:
a = 10 / 100
b = 67 * a
c = 67 - b
d = c - 56
e = 10 / 100
f = 67 * e
g = 67 - f
h = d / g
i = h * 100
Problem: karen places a bet with tom that she will beat tom in a car race by 4 miles even if karen starts 4 minutes late . assuming that karen drives at an average speed of 60 mph and tom drives at an average speed of 45 mph , how many w miles will tom drive before karen wins the bet ?
Options: a ) 15 , b ) 18 , c ) 21 , d ) 24 , e ) 27
Rationale: "let k and t be the speeds of karen and tom respectively . t be the time that karen will travel - - - - > t + 4 / 60 will be the total time tom will travel by the time the distance between karen and tom is 4 miles . thus , per the question , k ( t ) - t ( t + 4 / 60 ) = 4 - - - > t = 7 / 15 hours thus the distance traveled by tom when karen is 4 miles ahead of him w : t * ( t + 4 / 60 ) = 45 ( 7 / 15 + 4 / 60 ) = 24 miles . d is the correct answer ."
Answer: d
Python program:
a = 45 / 60
b = a * 4
c = b + 4 
d = 60 / 60
e = 45 / 60
f = d - e
g = c / f
h = g - 4
Problem: rectangle a has sides a and b , and rectangle b has sides c and d . if a / c = b / d = 2 / 3 , what is the ratio of rectangle a ’ s area to rectangle b ’ s area ?
Options: a ) 4 / 9 , b ) 2 / 3 , c ) 3 / 2 , d ) 9 / 2 , e ) 9 / 4
Rationale: "the area of rectangle a is ab . c = 3 a / 2 and d = 3 b / 2 . the area of rectangle b is cd = 9 ab / 4 . the ratio of rectangle a ' s area to rectangle b ' s area is ab / ( 9 ab / 4 ) = 4 / 9 . the answer is a ."
Answer: a
Python program:
a = 2 ** 2
b = 3 ** 2
c = a / b
Problem: the probability that event a occurs is 0.4 , and the probability that events a and b both occur is 0.25 . if the probability that either event a or event b occurs is 0.8 , what is the probability that event b will occur ?
Options: a ) 0.05 , b ) 0.15 , c ) 0.45 , d ) 0.5 , e ) 0.65
Rationale: "p ( a or b ) = p ( a ) + p ( b ) - p ( a n b ) 0.8 = 0.4 + p ( b ) - 0.25 p ( b ) = 0.65 ans : e"
Answer: e
Python program:
a = 0 + 8 
b = a - 0
Problem: a lemonade stand sold only small and large cups of lemonade on tuesday . 1 / 5 of the cups sold were small and the rest were large . if the large cups were sold for 7 / 6 as much as the small cups , what fraction of tuesday ' s total revenue was from the sale of large cups ?
Options: a ) 7 / 16 , b ) 7 / 15 , c ) 10 / 21 , d ) 14 / 17 , e ) 1 / 2
Rationale: let the total # of cups be 10 . # of small cups sold 1 / 5 * 10 = 2 ; # of large cups sold 10 - 2 = 8 ; let the price of small cup be $ 6 , then the price of larges cup would be 7 / 6 * 6 = $ 7 ; revenue from small cups : 2 * $ 6 = $ 12 ; revenue from large cups cups : 8 * $ 7 = $ 56 ; fraction of total revenue from large cups : 56 / ( 56 + 12 ) = 14 / 17 . answer : d .
Answer: d
Python program:
a = 1 / 5
b = a * 10
c = 10 - b
d = 7 / 6
e = 1 / 5
f = e * 10
g = d * f
h = c * g
i = 1 / 5
j = i * 10
k = 1 / 5
l = k * 10
m = j * l
n = 1 / 5
o = n * 10
p = 10 - o
q = 7 / 6
r = 1 / 5
s = r * 10
t = q * s
u = p * t
v = m + u 
w = h / v
Problem: if money is invested at r percent interest , compounded annually , the amount of the investment will double in approximately 50 / r years . if luke ' s parents invested $ 14,500 in a long term bond that pays 12 percent interest compounded annually , what will be the approximate total amount of the investment 12 years later , when luke is ready for college ?
Options: a ) 62,000 , b ) 85,500 , c ) 95,500 , d ) 120,500 , e ) 100,000
Rationale: answer equals d in 48 years . i thought by 50 th year it would reach 120,500 . options should have been separated more widely for clarity .
Answer: d
Python program:
a = 2 + 3 
b = a * 1000
c = b * 12
d = c / 2
Problem: 12 is 4 % of a , and 4 is 12 % of b . c equals b / a . what is the value of c ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 6 , d ) 1 / 9 , e ) 1 / 12
Rationale: "4 a / 100 = 12 a = 300 12 b / 100 = 4 b = 100 / 3 c = b / a = 100 / ( 3 * 300 ) = 1 / 9 the answer is d ."
Answer: d
Python program:
a = 4 / 12
b = a * 100
c = 12 / 4
d = c * 100
e = b / d
Problem: a contractor undertook to make 15 km of roadway in 40 weeks . in 10 weeks , 3 km was complete by 180 men working 8 hours a day . the men then agreed to work 1 hour a day overtime , and some boys were engaged to assist them , the work was finished in the stipulated time ( 40 weeks ) . how many boys were employed , if the work of 3 boys is equal to that of 2 men ?
Options: a ) 48 , b ) 50 , c ) 22 , d ) 27 , e ) 221
Rationale: explanation : let the capacity of man = 3 units , and boy = 2 units per hour . now total work = 3 × 180 × 8 × 7 × 10 = 3 km . - - - - - - - ( 1 ) let k boys were recruited . now total work = ( 3 × 180 + 2 × k ) × 9 × 7 × 30 = 12 km . - - - - - - ( 2 ) by dividing 2 nd equation by 1 st , ⇒ ( 540 + 2 k ) × 9 × 7 × 303 × 180 × 8 × 7 × 10 = 4 ( 540 + 2 k ) × 9 × 7 × 303 × 180 × 8 × 7 × 10 = 4 ⇒ k = 50 answer : b
Answer: b
Python program:
a = 3 / 10
b = a / 180
c = b / 8
d = 8 + 1 
e = c * d
f = 40 - 10
g = e * f
h = 180 * g
i = 3 + h 
j = 15 - i
k = 40 - 10
l = 2 / 3
m = 3 / 10
n = m / 180
o = n / 8
p = 8 + 1 
q = o * p
r = l * q
s = k * r
t = j / s
Problem: a man can row 7 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and black . how far is the place ?
Options: a ) 3.3 , b ) 3.4 , c ) 3.5 , d ) 3.6 , e ) 3.7
Rationale: "m = 7 s = 1.2 ds = 7 + 1.2 = 8.2 us = 7 - 1.2 = 5.8 x / 8.2 + x / 5.8 = 1 x = 3.40 . answer : b"
Answer: b
Python program:
a = 7 + 1 
b = 7 - 1
c = a * b
d = 7 + 1 
e = 7 - 1
f = d + e 
g = c / f
h = g * 2
Problem: find the least number of complete years in which a sum of money put out at 33.3 % compound interest will be more than double of itself ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "3 years answer : a"
Answer: a
Python program:
a = math.log(2)
b = 33 / 3
c = 1 + b 
d = math.log(c)
e = a / d
f = e + 1 
g = math.floor(f)
Problem: the sum of the squares of three numbers is 138 , while the sum of their products taken two at a time is 131 . their sum is
Options: a ) 15 , b ) 20 , c ) 25 , d ) 35 , e ) 45
Rationale: "explanation : let the numbers be a , b and c . then , a 2 + b 2 + c 2 = 138 and ( ab + bc + ca ) = 131 ( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 138 + 2 x 131 = 400 = > ( a + b + c ) = 400 − − − √ = 20 . option b"
Answer: b
Python program:
a = 138 - 131
b = a / 2
c = math.sqrt(b)
d = c * 100
e = 138 - 131
f = e / 2
g = 138 - f
h = math.sqrt(g)
i = d + h