2022 · Q27
Consider the question and two statements given below : A 2-digit number is added to the number formed by reversing the digits of the 2-digit number. Question : What is the 2-digit number?
Statement 1The sum is divisible by 9.
Statement 2The sum is divisible by 2.
Which one of the following is correct in respect of the question and the statements?
Elementary MathematicsNumber System
- AStatement-1 alone is sufficient to answer the question
- BStatement-2 alone is sufficient to answer the question
- CBoth Statement-1 and Statement-2 are sufficient to answer the question
- DBoth Statement-1 and Statement-2 are not sufficient to answer the question
Explanation
The sum is 11(a+b). Statement 1: 9 | 11(a+b) forces a+b ∈ {9,18} — not unique. Statement 2: 2 | 11(a+b) forces a+b even — not unique. Together a+b = 18, which with single digits forces a = b = 9, uniquely determining 99. Both statements together are sufficient. The keyed option is C.