Question:medium

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 :

Updated On: Jan 13, 2026
  • statement (1) alone is sufficient to answer the question
  • statement (2) alone is sufficient to answer the question
  • both the statements together are needed to answer the question
  • either statement (1) alone or statement (2) alone is sufficient to answer the question
  • neither statement (1) nor statement (2) suffices to answer the question
Show Solution

The Correct Option is B

Solution and Explanation

The correct answer is option (B):
statement (2) alone is sufficient to answer the question

Let's analyze the problem. We want to determine if an integer A is divisible by 45. We know that 45 = 9 * 5. This means A must be divisible by both 9 and 5 to be divisible by 45.

Statement 1 says A is divisible by 15. Since 15 = 3 * 5, this only tells us that A is divisible by 3 and 5. However, it does not guarantee divisibility by 9 (which is required for divisibility by 45). For example, 15 is divisible by 15, but not by 45. So, statement 1 alone is insufficient.

Statement 2 says A is divisible by 315. Since 315 = 45 * 7, if A is divisible by 315, then it is automatically divisible by 45. Thus, knowing that A is divisible by 315 is enough to know that A is divisible by 45. So, statement 2 alone is sufficient.
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