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If r and s are positive integers...

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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Sun Apr 28, 2019 7:06 am

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

1) r is even.
2) s is even.
Given: r and s are positive integers

Target question: Is r + s even?

Statement 1: r is even.
Since we have no information about s, we cannot determine whether r + s is even
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: s is even
Since we have no information about r, we cannot determine whether r + s is even
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that r is EVEN
Statement 2 tells us that s is EVEN
Since EVEN + EVEN = EVEN, we know that r + s is EVEN
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

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by [email protected] » Sun Apr 28, 2019 11:22 am

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Hi All,

We're told that R and S are POSITIVE INTEGERS. We're asked if R+S is EVEN. This is a YES/NO question and can be solved with Number Properties and/or by TESTing VALUES. To start, you might find it helpful to write down a few Number Property rules:

(Even) + (Even) = Even
(Even) + (Odd) = Odd
(Odd) + (Odd) = Even

Since R and S are both INTEGERS, to end up with a sum that is EVEN, then BOTH numbers must either be EVEN or ODD. Otherwise, the sum will be ODD.

1) R is EVEN.

IF...
S = EVEN, then R+S will be EVEN.
S = ODD, then R+S will be ODD.
Fact 1 is INSUFFICIENT

2) S is EVEN.

IF...
R = EVEN, then R+S will be EVEN.
R = ODD, then R+S will be ODD.
Fact 2 is INSUFFICIENT

Combined, we know...
R is EVEN.
S is EVEN.
Thus, R+S must be EVEN and the answer to the question is ALWAYS YES.
Combined, SUFFICIENT

Final Answer: C

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by SampathKp » Wed Dec 18, 2019 4:03 am

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

1) r is even.
2) s is even.

C

Source: Official Guide 2020
Sum of two positive integers is even if both integers are even or both integeres are odd.

From (1) we only know r is even and s can be even or odd and the value of r+s depends on value of s. SO this is clearly NOT Sufficient to answer if r+s is even or NOT
From (2) we know s is even and r can be odd or even and value of r+s depends of value of r SO this is clearly NOT Sufficient to answer is r+s is even ir NOT

Combining (1) and (2), we know that r is even and s is even. So sum of two positive even integers is always even . We have enough information to answer if r+s is even .

Answer is C, i.e both statement together are sufficient to answer the question and neither alone is sufficient to answer the question.
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