Consider a 3-digit number.
Question: What is the number?
Statement-1: The sum of the digits of the number is equal to the product of the digits.
Statement-2: The number is divisible by the sum of the digits of the number.

Which one of the following is correct in respect of the above Question and the Statements?

Correct Answer: (D) The Question cannot be answered even by using both the Statements together.

From Statement 1, the sum of three single digits equals their product ($a + b + c = abc$). The only set of three positive single-digit numbers satisfying this condition is $\{1, 2, 3\}$ ($1+2+3 = 1$$\times$ 2 $\times$ 3 = 6), which permits six possible 3-digit permutations (123, 132, 213, 231, 312, 321). From Statement 2, the number is divisible by its digit sum (6). Among the permutations, any number ending with the even digit 2 is divisible by 6. This leaves two valid numbers: 132 ($132 / 6 = 22$) and 312 ($312 / 6 = 52$). Because both 132 and 312 satisfy both statements simultaneously, a unique number cannot be determined.