even/odd question: If x and y are integers, and N = . . .

This topic has expert replies

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770
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

Answer: B

Source: www.gmatprepnow.com
Difficulty level: 600
Brent Hanneson - Creator of GMATPrepNow.com
Image

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Thu Apr 27, 2017 6:03 am
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 Hanneson - Creator of GMATPrepNow.com
Image

GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pm
Location: East Bay all the way
Thanked: 625 times
Followed by:119 members
GMAT Score:780

by Matt@VeritasPrep » Fri Apr 28, 2017 12:56 am
N = (x² - y + 3x)(2y + x)

N = (x * (x - 3) - y) * (x + 2y)

x and (x - 3) must be different parities (if x is even, x - 3 is odd, and vice versa), so x * (x - 3) = odd * even = even. We can also say that 2y is even, since it's 2 * some integer.

From here, replacing those terms with evens, we've got

N = (even - y) * (x + even)

N = x * even + even² - y * even - xy

or

N = even + even - even - xy

So the question is reduced to "is xy odd?"

From there, the statements are a cinch! :)

Senior | Next Rank: 100 Posts
Posts: 36
Joined: Sun May 21, 2017 5:41 am

by hoppycat » Sun May 21, 2017 5:55 am
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
seems way too long to do in under 2 minutes.

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Sun May 21, 2017 6:50 am
hoppycat wrote: Brent
seems way too long to do in under 2 minutes.[/quote]

If you try applying the same strategy to other questions, you'll find you can do so in under 30 seconds, at which point it will take very little time to analyze the statements.

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image

Senior | Next Rank: 100 Posts
Posts: 36
Joined: Sun May 21, 2017 5:41 am

by hoppycat » Fri Jun 23, 2017 9:53 am
Brent@GMATPrepNow wrote:
hoppycat wrote: Brent
seems way too long to do in under 2 minutes.
If you try applying the same strategy to other questions, you'll find you can do so in under 30 seconds, at which point it will take very little time to analyze the statements.

Cheers,
Brent[/quote]
Okay thanks

We'll see!