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

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:

GMAT assassins aren't born, they're made,
Rich

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

Cheers,
Brent

r and s are positive integers.

(1) r is even.

s could be even or odd.

Insufficient

(2) s is even.

r could be even or odd.

Insufficient

Combine 1 & 2

r and s are positive EVEN integers. So r + s = even

Sufficient

Answer: C

We need to determine whether r + s is even. We may recall that either odd + odd = even or even + even = even.

Statement One Alone:

r is even

Statement one alone is not sufficient. If s is even, then r + s is even; however, if s is odd, then r + s is odd.

Statement Two Alone:

s is even

Statement two alone is not sufficient. If r is even, then r + s is even; however, if r is odd, then r + s is odd.

Statements One and Two Together

Since we know that both r and s are even, so r + s is even.

Answer: C

O+O=E and E+E=E, Whereas O+E=O. To find whether the sum of two numbers is even or not, we need to know E/O property of both the numbers. Since 1) and 2) gives E/O property of one number each, they are individually insufficient to answer the question. However, combining 1) and 2), we know the E/O property of both the numbers, therefore sufficient. Ans is C.

Answer: Option C

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The key is to be able to work out what combinations would satisfy the question stem. Pick up any simple combinations to test out and shouldn't take more than a couple of seconds.
5+3= 8= even? (combination of 2 odds)
2+2=4= even? (combination of 2 evens)
3+4=7=even? no. (Even+odd=odd)

With that logic, A and B individually don't tell us much, but C resolves the question at hand.

Final answer: C

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