Question

A literary club in a particular university consists of at least 150 members. The number of faculty members in this group is 60% of the number of male students, which is 50% of the number of female students in this club. Which of the following could be the number of faculty members in this literary club? Indicate all possible options.

• A. 19
• B. 21
• C. 23
• D. 26
• E. 27
• F. 29

Hint:

When multiple categories are expressed as percentages of one another, always express all in terms of a single base variable and then simplify.

Answer 1

The Correct Option is B

Step 1: Represent relationships.
Let number of female students = \( F \).
Then number of male students = \( 0.5F \).
Number of faculty = \( 0.6 \times (0.5F) = 0.3F \).
Step 2: Total members.
Total = \( F + 0.5F + 0.3F = 1.8F \).
Step 3: Apply condition.
Since total ≥ 150, \[ 1.8F \geq 150 \quad \Rightarrow \quad F \geq \frac{150}{1.8} = 83.\overline{3} \] So \( F \) must be a whole number \(≥ \) 84.
Step 4: Faculty = 0.3F must be an integer.
For this, \( F \) must be divisible by 10.
Step 5: Check options.
- If \( F = 70 \), Faculty = 21 (valid).
- If \( F = 90 \), Faculty = 27 (valid).
Other options don’t satisfy the ratio conditions. Thus, valid answers are 21 and 27.