Question

Henderson is the elder brother of Mark, and their age difference is 3 years. Mark is 9 years younger than Alisa. If Alisa is at least 33 years old, which of the following could be the age of Henderson?

• A. 21
• B. 24
• C. 26
• D. 27
• E. 29
• F. 35

Hint:

Translate all given conditions into equations and inequalities before checking each option—it avoids careless mistakes.

Answer 1

The Correct Option is C

Step 1: Represent relationships.
Let Mark’s age = \( M \). Then Henderson’s age = \( M + 3 \). Alisa’s age = \( M + 9 \). 
Step 2: Use given condition.
Alisa is at least 33: \[ M + 9 \geq 33 \quad \Rightarrow \quad M \geq 24 \] So Henderson = \( M + 3 \geq 27 \). 

Step 3: Check options.
- (1) 21: Too small, not possible. 
- (2) 24: Too small, not possible. 
- (3) 26: Possible if \( M = 23 \), but then Alisa = 32 (<33), so not valid. 
- (4) 27: Possible, \( M = 24 \), Alisa = 33, valid. 
- (5) 29: Possible, \( M = 26 \), Alisa = 35, valid. 
- (6) 35: Possible only if \( M = 32 \), Alisa = 41, valid too. 
So valid answers are 27, 29, and 35.