Brent@GMATPrepNow wrote:

Brent@GMATPrepNow wrote:If x and y are integers, and N = (x² - y + 3x)(2y + x), is N odd?

1) x + y is even
2) 3xy is odd

Target question: Is N odd?

Given: N = (x² - y + 3x)(2y + x)
Before we examine the statements, it might be useful SYSTEMATICALLY examine all of the possible cases we need to consider:
case a: x is even, and y is even
case b: x is even, and y is odd
case c: x is odd, and y is even
case d: x is odd, and y is odd

There are two ways to analyze each case.
- We can take each case and apply the rules for evens and odd (e.g., even + odd = odd, even x even = even, etc)
- We can take each case and plug in even and odd numbers for x and y. The easiest values are 1 for odd numbers and 0 for even numbers.

When we do apply either of these strategies we get:
case a: x is even, and y is even. N is EVEN
case b: x is even, and y is odd. N is EVEN
case c: x is odd, and y is even. N is EVEN
case d: x is odd, and y is odd. N is ODD

The target question ask whether N is odd. Since N is odd only when x is odd and y is odd, we can rephrase our target question...
REPHRASED target question: Are x and y BOTH odd?

Okay, now onto the statements!!!

Statement 1: x+y is even
If x+y is even, then there are two possible cases:
- x and y are both odd, in which case, x and y ARE both odd
- x and y are both even, in which case, x and y are NOT both odd
Since we can answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 3xy is odd
If 3xy is odd, then xy is odd, which means x and y ARE both odd
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent

Brent@GMATPrepNow wrote:

hoppycat wrote: Brent

seems way too long to do in under 2 minutes.