Question

Let $S$ be a set of integers $n$ with $1000 \leq n \leq 1200$ and all digits odd. How many $n \in S$ are divisible by 3?

• A. 9
• B. 10
• C. 11
• D. 12

Hint:

Use divisibility rule for 3 by summing possible odd digit combinations.

Answer 1

The Correct Option is A

Digits allowed: 1,3,5,7,9. Thousands digit=1 (since $1000 \le n \le 1200$). Remaining three digits odd. Count multiples of 3 by sum of digits divisible by 3. Enumeration yields 9 such numbers. \[ \boxed{9} \]