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Solution

 

Steps 1 & 2: Understand Question and Draw Inferences

In this question, we are given that

• The numbers r and s are positive integers.

We need to determine

• Whether r + s is an even number or not.

As both r and s are integers, we can say that r + s will be even, when

• Both r and s are individually even
• Or, both r and s are individually odd

With this understanding, let us now analyze the individual statements.

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Step 3: Analyse Statement 1

As per the information given in statement 1, r is even.

• However, from this statement, we cannot determine the even-odd nature of s.
  • If s is even, then r + s = even + even = even
  • If s is odd, then r + s = even + odd = odd

As we cannot determine the even-odd nature of r + s, statement 1 is not sufficient to answer the question.

 

Step 4: Analyse Statement 2

As per the information given in statement 2, s is even.

• However, from this statement, we cannot determine the even-odd nature of r.
  • If r is even, then r + s = even + even = even
  • If r is odd, then r + s = odd + even = odd

As we cannot determine the even-odd nature of r + s, statement 2 is not sufficient to answer the question.

 

Step 5: Combine Both Statements Together (If Needed)

From statements 1 and 2, we can say that

• r is even
• And, s is even

Therefore, r + s = even + even = even.

On combining the statements, we can determine the even-odd nature of r + s.

• Hence, we can say both statements together are sufficient to answer the question.

Thus, the correct answer choice is option C.

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