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

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.
(C) is our answer.

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

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

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

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

Video solution by GMATinsight



Get TOPICWISE: Concept Videos | Practice Qns 100+ | Official Qns 50+ | 100% Video solution CLICK HERE.
Two MUST join YouTube channels : GMATinsight (1000+ FREE Videos) and GMATclub

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

Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1