Consider the question and two statements given below:<br><br>A 2-digit number is added to the number formed by reversing the digits of the 2-digit number.<br><br>Question: What is the 2-digit number?<br>Statement-1: The sum is divisible by 9.<br>Statement-2: The sum is divisible by 2.<br><br>Which one of the following is <strong>CORRECT</strong> in respect of the question and the statements?
- A. Statement-1 alone is sufficient to answer the question
- B. Statement-2 alone is sufficient to answer the question
- C. Both Statement-1 and Statement-2 are sufficient to answer the question ✓
- D. Both Statement-1 and Statement-2 are not sufficient to answer the question
Correct Answer: C. Both Statement-1 and Statement-2 are sufficient to answer the question
Explanation
The sum of a 2-digit number 10x+y and its reverse 10y+x is 11(x+y). For 11(x+y) to be divisible by both 9 and 2, x+y must be a multiple of 18. Since digits x, y \le 9, the only possibility is x+y=18 \implies x=9, y=9. Both statements are required to find the unique number 99.
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