Question

Is the integer number \( n \) divisible by 15?
I. 9 divides \( n \).
II. 20 divides \( n \).

• A. If the statement I alone is sufficient to answer the question.
• B. If the statement II alone is sufficient to answer the question.
• C. If the statements I and II together are sufficient to answer the question but neither statement alone is sufficient.
• D. If the statements I and II together are not sufficient to answer the question and additional data is required.

Hint:

When checking divisibility for composite numbers, ensure that \( n \) is divisible by the prime factors of that number. In this case, check divisibility by 3 and 5 to determine divisibility by 15.

Answer 1

The Correct Option is C

We are asked whether the integer number \( n \) is divisible by 15. To determine this, we need to check if \( n \) satisfies the divisibility rule for 15.
- From condition I: 9 divides \( n \), meaning \( n \) is divisible by 9.
- From condition II: 20 divides \( n \), meaning \( n \) is divisible by 20.
Since 15 is the product of 3 and 5, for \( n \) to be divisible by 15, it must also be divisible by both 3 and 5. We are given that \( n \) is divisible by 9 and 20:
- Divisibility by 9 already guarantees divisibility by 3, since 9 is a multiple of 3.
- Divisibility by 20 guarantees divisibility by 5, since 20 is a multiple of 5.
Thus, since \( n \) is divisible by both 9 and 20, it is also divisible by 15.
Therefore, the correct answer is \( \boxed{3} \).