At a certain fitness center, are more than 1/6 of the members over 30

Solution:

We need to find whether more than \(\frac{1}{6} \) members of the fitness center are 30 years of age or not.

Statement 1:

Exactly \(60 \%\) of the male members are over \(20\) years of age and of these, \(\frac{3}{5}\) are over \(30\) years of age.
Note:- The given percentage, i.e. \(60 \%\) is with respect to the male members and not total members

• With this information, we can only find what percentage of male members are above the age of \(30\).
• However, we can’t say what percentage of total members are above the age of 30

Hence, statement 1 is not sufficient, we can eliminate answer option A and D.

Statement 2:

Exactly \(15\) female members are over \(30\) years of age.
• Using this information we can’t find the number of male members above the age of \(30\) years.
Hence, statement 2 is also not sufficient, we can eliminate answer option B.

Combining both the statements.

From statement 1: We can find the percentage of males above \(30\) years of age.
From statement 2: Female members above the age of \(30\) years = \(15.\)
By combining both the statements
After combining also, we cannot find the answer, since we don't have any information about the percentage of members above \(30\) years or the total number of members or the percentage of female members above \(30\) years or any relationship between men and women. We need more information to solve this question.
Hence, the correct answer is Option E.