Question

A ∈ Z. Is A divisible by 45?
Statement 1: The number is divisible by 15 
Statement 2: The number is divisible by 315
Directions: This question has a problem and two statements numbered (1) and (2) giving certain information. You have to decide if the information given in the statements is sufficient for answering the problem. Indicate your answer :

• A. statement (1) alone is sufficient to answer the question
• B. statement (2) alone is sufficient to answer the question
• C. both the statements together are needed to answer the question
• D. either statement (1) alone or statement (2) alone is sufficient to answer the question
• E. neither statement (1) nor statement (2) suffices to answer the question

Answer 1

The Correct Option is B

To determine if statement (2) alone is sufficient to answer whether \( A \) is divisible by 45, we will evaluate the divisibility conditions based on the given statements.

1. Statement 1: The number is divisible by 15.

To be divisible by 15, a number must be divisible by both 3 and 5. However, for a number to be divisible by 45, it must be divisible by 5 and 9 (since \( 45 = 5 \times 9 \)). Being divisible by 15 does not guarantee divisibility by 9. Thus, statement 1 alone is insufficient.

2. Statement 2: The number is divisible by 315.

To check if a number is divisible by 45, let's analyze the prime factors involved:

\( 315 = 3^2 \times 5 \times 7 \)

This means that any number divisible by 315 is also divisible by \( 3^2 = 9 \) and 5, which means the number is divisible by 45 as well. Therefore, statement 2 alone is sufficient to determine that the number is divisible by 45.

Hence, the correct answer is that statement (2) alone is sufficient to answer the question.