# CAT Practice : Averages, Ratios, Mixtures

We are always comfortable when solving and arriving at an answer. How does one approach questions that ask for number of possible integer solutions?

## Mixtures - Number Systems

Q.9: 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?
1. 19
2. 20
3. 21
4. 13

Choice D.13

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## Detailed Solution

To start with x > y => x > 60 > y.
(x – 60) = 3(60 – y).
60 – y is an integer => x – 60 has to be a multiple of 3.
x can take values {63, 66, 69 ….. 99}– A total of 13 values.

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