The correct answer is option (A):
statement (1) alone is sufficient to answer the question
Let's analyze the question and the statements. The question asks if the sum of three distinct numbers (a, b, and c) selected from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} is a multiple of 9.
Statement 1: The three-digit number 'abc' is a multiple of 9.
A number is divisible by 9 if and only if the sum of its digits is divisible by 9. In this case, the three-digit number 'abc' means 100a + 10b + c. Since we are told abc is a multiple of 9, then the sum of the digits (a + b + c) must also be a multiple of 9. This directly answers the question. Therefore, statement 1 alone is sufficient.
Statement 2: (a * b) + c is a multiple of 9.
This statement tells us that the expression (a times b) plus c results in a multiple of 9. However, this doesn't tell us anything about whether the sum a + b + c is a multiple of 9. For example, if a = 3, b = 0, and c = 9, then (3 * 0) + 9 = 9, which is a multiple of 9. And a + b + c = 3 + 0 + 9 = 12, which is not a multiple of 9. Alternatively, if a = 3, b = 3 and c = 0, then (3*3) + 0 = 9 which is a multiple of 9. and a + b + c = 3 + 3 + 0 = 6, which is not a multiple of 9. Thus, statement 2 alone is insufficient.
Since Statement 1 alone provides enough information to determine if a + b + c is a multiple of 9, the correct answer is: statement (1) alone is sufficient to answer the question.