It is currently 13 Dec 2018, 17:12
My Tests

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

If x and y are integers, and w = x^2y + x + 3y, which

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Senior Manager
Senior Manager
Joined: 20 May 2014
Posts: 282
Followers: 15

Kudos [?]: 49 [0], given: 220

CAT Tests
If x and y are integers, and w = x^2y + x + 3y, which [#permalink] New post 20 Nov 2017, 10:47
00:00

Question Stats:

33% (01:48) correct 66% (00:46) wrong based on 6 sessions
If x and y are integers, and \(w = x^2y + x + 3y\), which of the following statements must be true?

Indicate all such statements.

A. If w is even, then x must be even.
B. If x is odd, then w must be odd.
C. If y is odd, then w must be odd.
D. If w is odd, then y must be odd.


Kudos for correct solution.

[Reveal] Spoiler: OA
A, B, and C
[Reveal] Spoiler: OA
1 KUDOS received
Manager
Manager
User avatar
Joined: 15 Jan 2018
Posts: 147
GMAT 1: Q V
Followers: 3

Kudos [?]: 174 [1] , given: 0

Re: If x and y are integers, and w = x^2y + x + 3y, which [#permalink] New post 21 Feb 2018, 10:56
1
This post received
KUDOS
A good technique for problems asking what must be true is to try and make them not true. If you can't, it must be true. Also, a good technique for odd/even questions is to just test using your own odd and even numbers. Since every odd number will behave the same as every other in regards to oddness or evenness, it doesn't matter what number you choose. I like to use 0 and 1 for even and odd, respectively, since they tend to make the math very simple.

Also, it seems like a good idea to factor the equation since they probably didn't give it to us in the easiest format. One way to factor it is

y(3 + x^2) + x

A: I'll try to find a way to make w even when x is odd. Plugging in 1 for x gets me 4y + 1. It doesn't matter what y is; what we've got here is an even number plus 1, which must be odd. So there's no way to make an even number if x is odd. Thus A is in.

B: Well we just tried making x odd and found that w must be odd if x is, so B is in.

C: Let's see what happens if we substitute y for 1: We'll get 1(3 + x^2) + x or just x^2 + x + 3. We'll need to check what happens when x is odd and when x is even:
If x is 0, we get 0 + 0 + 3, which is odd.
If x is 1, we get 1 + 1 + 3, which is odd.
So it looks like C is in as well.

D: Let's try making y even and see whether we can get w to be odd:
If we make y = 0, we'll have 0(3 + x^2) + x, which is just x. So if we pick x to be odd, then w would be odd. And since we got an odd w with an even y, D is out.
_________________

-
-
-
-
-

Need help with GRE math? Check out our ground-breaking books and app.

Re: If x and y are integers, and w = x^2y + x + 3y, which   [#permalink] 21 Feb 2018, 10:56
Display posts from previous: Sort by

If x and y are integers, and w = x^2y + x + 3y, which

  Question banks Downloads My Bookmarks Reviews Important topics  


cron

GRE Prep Club Forum Home| About| Terms and Conditions and Privacy Policy| GRE Prep Club Rules| Contact

Powered by phpBB © phpBB Group

Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.