It is currently 24 Feb 2018, 07:56

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

When x and y are integers, is x+y an even?

Author Message
TAGS:

Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4908
GPA: 3.82
When x and y are integers, is x+y an even? [#permalink]

Show Tags

22 May 2016, 16:55
1
KUDOS
Expert's post
2
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

78% (01:09) correct 22% (01:10) wrong based on 111 sessions

HideShow timer Statistics

When x and y are integers, is x+y an even?
1) x^2+y^2 is an even
2) (x+1)^2+(y+1)^2 is an even

*An answer will be posted in 2 days.
[Reveal] Spoiler: OA

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself

Math Expert
Joined: 02 Aug 2009
Posts: 5660
Re: When x and y are integers, is x+y an even? [#permalink]

Show Tags

22 May 2016, 19:09
MathRevolution wrote:
When x and y are integers, is x+y an even?
1) x^2+y^2 is an even
2) (x+1)^2+(y+1)^2 is an even

*An answer will be posted in 2 days.

X and Y are integers and we have to find if x+y is integers...
If BOTH x and y are same type of numbers that is both odd or both even , ans is YES, otherwise No..

lets test the statements-
1) x^2+y^2 is an even
clearly x and y are either both odd or both even..
ans is YES..
Suff

2) (x+1)^2+(y+1)^2 is an even
clearly x and y are either both odd or both even..
ans is YES..
Suff

D
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

BANGALORE/-

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4908
GPA: 3.82
Re: When x and y are integers, is x+y an even? [#permalink]

Show Tags

25 May 2016, 02:41
X and y in the conditions 1) and 2) can end up being both odd or both even.
The answer to both conditions are ‘yes’, which make the conditions sufficient.
The correct answer, hence, is D.
- Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself

Retired Moderator
Joined: 12 Aug 2015
Posts: 2428
GRE 1: 323 Q169 V154
When x and y are integers, is x+y an even? [#permalink]

Show Tags

20 Nov 2016, 06:55
2
KUDOS
This is a great Question which is testing our fundamental knowledge of evens and odds.
There is one very important property that we must know when we are dealing with even and odd numbers on the GMAT.

POWER/EXPONENTS Do not affect the even/odd nature of any integer.

Now in this question we are told that both x and y are integers(Very important info)
We need to get if x+y is even or not
For x+y to be even => both x and y must have the same even odd nature.

Lets look at statement
Statement 1
x^2+y^2 = even
hmm
as power doesn't not affect the even/odd nature
x+y must be even too

Hence Sufficient
Statement 2
(x+1)^2 +(y+1)^2 is even
Okay
again we can say that
x+1+y+1 is even
hence x+y+2 is even
so x+y must be even too
hence Sufficient

Hence D
_________________

Getting into HOLLYWOOD with an MBA

Stone Cold's Mock Tests for GMAT-Quant(700+)

Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3326
Location: India
GPA: 3.5
Re: When x and y are integers, is x+y an even? [#permalink]

Show Tags

20 Nov 2016, 07:07
MathRevolution wrote:
When x and y are integers, is x+y an even?
1) x^2+y^2 is an even
2) (x+1)^2+(y+1)^2 is an even

*An answer will be posted in 2 days.

FROM STATEMENT - I ( SUFFICIENT )

$$x^2+y^2 = Even$$

Either x = y = Even
Or, x = y = Even

In either case x + y will be even

FROM STATEMENT - II ( SUFFICIENT )

$$(x+1)^2+(y+1)^2 = Even$$

$$x = y = Odd$$

Thus , $$x + y = Even$$

PS : Really love stonecold's explanation, wonderfully explained, Kudos is the least I can add..

_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Intern
Joined: 22 Jun 2016
Posts: 1
Re: When x and y are integers, is x+y an even? [#permalink]

Show Tags

25 Feb 2017, 05:17
As the question does not mention that x and y are positive integers,shouldn't we include the cases where both are negative as well?
Manhattan Prep Instructor
Joined: 04 Dec 2015
Posts: 473
GMAT 1: 790 Q51 V49
GRE 1: 340 Q170 V170
Re: When x and y are integers, is x+y an even? [#permalink]

Show Tags

25 Feb 2017, 11:15
Environo0792 wrote:
As the question does not mention that x and y are positive integers,shouldn't we include the cases where both are negative as well?

Yes, you should, but it doesn't change the solution or the answer. The rules for odds and evens are the same for negative numbers as they are for positive numbers. For instance, -2 and -4 are both even, and their sum is even; -3 and -7 are both odd and their sum is also even.
_________________

Chelsey Cooley | Manhattan Prep Instructor | Seattle and Online

My upcoming GMAT trial classes | GMAT blog archive

Re: When x and y are integers, is x+y an even?   [#permalink] 25 Feb 2017, 11:15
Display posts from previous: Sort by