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 | EvenĀ āĀ Odd |
Difficulty | Easy |
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.
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
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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