Question

a, b and c are three numbers selected from a set containing ten numbers 0 to 9. Is (a + b + c) a multiple of 9?
Statement 1: Three digit number abc is a multiple of 9
Statement 2: (a x b) + c is a multiple of 9

• 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. 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 A

To determine if \(a + b + c\) is a multiple of 9, let's analyze the given statements:

1. Statement 1: Three-digit number \(abc\) is a multiple of 9.
   In this context, \(abc\) represents a three-digit number where \(a\), \(b\), and \(c\) are the digits of this number. The property of a number being a multiple of 9 is that the sum of its digits is also a multiple of 9. Thus, if the number \(abc\) is divisible by 9, then \(a + b + c\) must be a multiple of 9. Hence, statement 1 alone is sufficient to determine that \(a + b + c\) is a multiple of 9.
2. Statement 2: \((a \times b) + c\) is a multiple of 9.
   This statement provides a relationship involving multiplication and addition, not directly the sum of the digits. Knowing \((a \times b) + c\) is a multiple of 9 does not necessarily give us information about \(a + b + c\), as there is no simple algebraic manipulation or number theory rule that connects these two expressions directly. Therefore, statement 2 alone is insufficient to determine whether \(a + b + c\) is a multiple of 9.

By evaluating both statements, it becomes clear that statement 1 alone gives a direct answer to the question. Thus, the correct answer is: statement (1) alone is sufficient to answer the question.