## OG 2020: Question No. 288

If r and s are positive integers, is r + s even?

- r is even.
- s is even.

Source | OG 2020 |

Type | Data Sufficiency |

Topic | Number Properties |

Sub-Topic | Even – Odd |

Difficulty | Easy |

### Solution

__Steps 1 & 2: Understand Question and Draw Inferences__

__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.

Here is the solution to GMAT OG question #289. For more solutions of GMAT OG 2020 register for a free trial.

__Step 3: Analyse Statement 1__

__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__

__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)__

__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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