Question

What is the two-digit number whose first digit is a and the second digit is b? The number is greater than 9. 
Statement I - The number is a multiple of 51. 
Statement II - The sum of the digits a and b is 6.

• A. If the question can be answered with the help of statement I alone.
• B. If the question can be answered with the help of statement II alone.
• C. If both, statement I and statement II are needed to answer the question.
• D. If the question cannot be answered even with the help of both the statements.

Hint:

When solving number-related problems, combine constraints such as divisibility and digit sums to narrow down the possibilities.

Answer 1

The Correct Option is C

From Statement I:
The number is a multiple of 51, so the number can be one of the multiples of 51: 51, 102, 153, 204, etc.
This gives us some possibilities, but we still don't know which specific number it is.
From Statement II:
The sum of the digits \(a\) and \(b\) is 6. This means \(a + b = 6\).
This narrows down the possibilities to numbers whose digits sum up to 6, such as 15, 24, 33, 42, 51, etc.
Combining both statements:
We now know that the number is a multiple of 51 and the sum of the digits is 6.
The only number that satisfies both conditions is 51.
Thus, both statements are needed to answer the question.