DisciplinedPrep wrote:
1 unit of x% alcohol is mixed with 3 units of y% alcohol to give 60% alcohol. If x > y, how many integer values can x take?
A. 10
B. 20
C. 35
D. 13
E. 30
1 part x% alcohol + 3 parts y% alcohol -> 60% alcohol
Since x > y, x must be greater than 60% and y must be less than 60% so that they average out to 60.
The maximum value of x can be 100% (the entire solution can be alcohol).
So x can take any integer value from 61 to 100.
But it seems that the intent of the question is that x and y both should be integer values.
y --- 60 --------- x
Since we are mixing 1 part x with 3 parts y, average will be 1 unit away from y and 3 units away from x.
So if y = 59, x = 63
if y = 58, x = 66
and so on...
x will take values from 63% to 99% i.e. (3*21) to (3*33)
This means (33 - 21 = )12 + 1 = 13 multiples of 3
Check this post for the scale method of weighted avgs:
https://www.veritasprep.com/blog/2011/0 ... -averages/
_________________
Karishma
Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >