CAT Quantitative Aptitude Questions | CAT Ratios, Mixtures, Alligations and Averages Questions

The question is from CAT Ratio, Mixtures and Averages. Another question on possible values. It combines number theory with ratios. CAT exam is known to test on basics rather than high funda ideas. A range of CAT questions can be asked from Ratios and Proportions, Mixtures, Alligations and Averages. Make sure you master the topics. 2IIMs CAT questions bank provides you with CAT questions that can help you gear for CAT Exam CAT 2023.

Question 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

Video Explanation

Explanatory Answer

Method of solving this CAT Question from Ratio, Mixtures and Averages: We are always comfortable when solving and arriving at an answer. How does one approach questions that ask for number of possible integer solutions?

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.

The question is "how many integer values can x take?"

Hence, the answer is "13".

Choice D is the correct answer.