GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 24 Apr 2019, 05:08

### 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

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

# If x and y are integers, is y an even integer?

Author Message
TAGS:

### Hide Tags

Intern
Joined: 26 Sep 2012
Posts: 23
If x and y are integers, is y an even integer?  [#permalink]

### Show Tags

Updated on: 05 Jul 2014, 05:11
8
00:00

Difficulty:

85% (hard)

Question Stats:

43% (02:26) correct 57% (02:35) wrong based on 123 sessions

### HideShow timer Statistics

If x and y are integers, is y an even integer?

(1) 4y^2+3x^2=x^4+y^4

(2) y=4−x^2

The official answer is A, and the logic is clear to me.

But, is it possible in the first equations also to have x = y = o? Shouldn't the answer be E in such case?
It is not explicitly stated in the wording that x and y are different non-zero integers?

Most probably I just missed smth, so would be grateful for your explanations

M27-02

Originally posted by Maksym on 05 Jul 2014, 03:05.
Last edited by Bunuel on 05 Jul 2014, 05:11, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 54493
Re: If x and y are integers, is y an even integer?  [#permalink]

### Show Tags

05 Jul 2014, 05:14
1
5
Maksym wrote:
If x and y are integers, is y an even integer?

(1) 4y^2+3x^2=x^4+y^4

(2) y=4−x^2

The official answer is A, and the logic is clear to me.

But, is it possible in the first equations also to have x = y = o? Shouldn't the answer be E in such case?
It is not explicitly stated in the wording that x and y are different non-zero integers?

Most probably I just missed smth, so would be grateful for your explanations

M27-02

If x and y are integers, is y an even integer?

(1) 4y^2+3x^2=x^4+y^4 --> rearrange: $$3x^2-x^4=y^4-4y^2$$ --> $$x^2(3-x^2)=y^2(y^2-4)$$. Notice that LHS is even for any value of $$x$$: if $$x$$ is odd then $$3-x^2=odd-odd=even$$ and if $$x$$ is even then the product is naturally even. So, $$y^2(y^2-4)$$ is also even, but in order it to be even $$y$$ must be even, since if $$y$$ is odd then $$y^2(y^2-4)=odd*(odd-even)=odd*odd=odd$$. Sufficient.

(2) y=4-x^2 --> if $$x=odd$$ then $$y=even-odd=odd$$ but if $$x=even$$ then $$y=even-even=even$$. Not sufficient.

As for your doubt: 0 is an even integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even.

Check more tips on zero and number properties here: tips-and-hints-for-specific-quant-topics-with-examples-172096.html#p1371030

This week's PS question
This week's DS Question

Theory on Number Properties: math-number-theory-88376.html

DS Number Properties Problems to practice: search.php?search_id=tag&tag_id=38
PS Number Properties Problems to practice: search.php?search_id=tag&tag_id=59

Hope it helps.
_________________
##### General Discussion
Intern
Joined: 11 Apr 2013
Posts: 1
Re: If x and y are integers, is y an even integer?  [#permalink]

### Show Tags

05 Jul 2014, 03:40
Maksym,

Even if x= y= 0, then too Y will remain an even integer because 0 is an even integer. and as this is a question of data interpretation in which we need to look for UNIQUE SOLUTION and in both the cases i.e.

1)when y is not equal to zero
2) WHEN X=Y=0

we are getting unique answer in both the cases i.e. YES Y is an even integer.
Senior Manager
Joined: 17 Sep 2013
Posts: 330
Concentration: Strategy, General Management
GMAT 1: 730 Q51 V38
WE: Analyst (Consulting)
Re: If x and y are integers, is y an even integer?  [#permalink]

### Show Tags

05 Jul 2014, 04:11
As some one has rightly pointed out..0 is an even integer..So A still stands firm
_________________
Appreciate the efforts...KUDOS for all
Don't let an extra chromosome get you down..
Intern
Joined: 26 Sep 2012
Posts: 23
Re: If x and y are integers, is y an even integer?  [#permalink]

### Show Tags

05 Jul 2014, 05:27
Bunuel wrote:
Maksym wrote:
If x and y are integers, is y an even integer?

(1) 4y^2+3x^2=x^4+y^4

(2) y=4−x^2

The official answer is A, and the logic is clear to me.

But, is it possible in the first equations also to have x = y = o? Shouldn't the answer be E in such case?
It is not explicitly stated in the wording that x and y are different non-zero integers?

Most probably I just missed smth, so would be grateful for your explanations

M27-02

If x and y are integers, is y an even integer?

(1) 4y^2+3x^2=x^4+y^4 --> rearrange: $$3x^2-x^4=y^4-4y^2$$ --> $$x^2(3-x^2)=y^2(y^2-4)$$. Notice that LHS is even for any value of $$x$$: if $$x$$ is odd then $$3-x^2=odd-odd=even$$ and if $$x$$ is even then the product is naturally even. So, $$y^2(y^2-4)$$ is also even, but in order it to be even $$y$$ must be even, since if $$y$$ is odd then $$y^2(y^2-4)=odd*(odd-even)=odd*odd=odd$$. Sufficient.

(2) y=4-x^2 --> if $$x=odd$$ then $$y=even-odd=odd$$ but if $$x=even$$ then $$y=even-even=even$$. Not sufficient.

As for your doubt: 0 is an even integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even.

Check more tips on zero and number properties here: tips-and-hints-for-specific-quant-topics-with-examples-172096.html#p1371030

This week's PS question
This week's DS Question

Theory on Number Properties: math-number-theory-88376.html

DS Number Properties Problems to practice: search.php?search_id=tag&tag_id=38
PS Number Properties Problems to practice: search.php?search_id=tag&tag_id=59

Hope it helps.

Bunueal, thanks for explanation and the link!
Non-Human User
Joined: 09 Sep 2013
Posts: 10619
Re: If x and y are integers, is y an even integer?  [#permalink]

### Show Tags

22 Aug 2017, 00:50
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: If x and y are integers, is y an even integer?   [#permalink] 22 Aug 2017, 00:50
Display posts from previous: Sort by