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Math Expert V
Joined: 02 Sep 2009
Posts: 60553
If r and s are positive integers, is r + s even?  [#permalink]

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Difficulty:   5% (low)

Question Stats: 94% (00:26) correct 6% (00:24) wrong based on 321 sessions

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

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

DS76502.01
OG2020 NEW QUESTION

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examPAL Representative P
Joined: 07 Dec 2017
Posts: 1155
Re: If r and s are positive integers, is r + s even?  [#permalink]

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

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

DS76502.01
OG2020 NEW QUESTION

Questions dealing with even/odd properties can usually be solved Logically, with very little calculation.
In particular, if (1) r is even, then if s is even then r+s = even + even = even but if s is odd then r+s=even+odd = odd. Insufficient.
If (2) s is even, then we can use the exact same considerations as above to show this is insufficient.
If both are even, their sum is even.
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Re: If r and s are positive integers, is r + s even?  [#permalink]

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

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

DS76502.01
OG2020 NEW QUESTION

e=e+e
e=o+o
#1
r is even , s not know insufficeint
#2
s = even , r not know
from 1 & 2
r,s even so r+s = even
IMO C
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4219
Re: If r and s are positive integers, is r + s even?  [#permalink]

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Top Contributor
Bunuel 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

Cheers,
Brent
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Re: If r and s are positive integers, is r + s even?  [#permalink]

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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

GMAT assassins aren't born, they're made,
Rich
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Re: If r and s are positive integers, is r + s even?  [#permalink]

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

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

DS76502.01
OG2020 NEW QUESTION

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

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Re: If r and s are positive integers, is r + s even?  [#permalink]

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

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

DS76502.01
OG2020 NEW QUESTION

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.

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Re: If r and s are positive integers, is r + s even?  [#permalink]

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

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

DS76502.01
OG2020 NEW QUESTION

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. Re: If r and s are positive integers, is r + s even?   [#permalink] 09 May 2019, 02:18
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