GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 27 May 2020, 15:30 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If x any y are positive integers,is x even? (1) x^2 + y^2=98 (2) x = y

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 64174
If x any y are positive integers,is x even? (1) x^2 + y^2=98 (2) x = y  [#permalink]

### Show Tags 00:00

Difficulty:   45% (medium)

Question Stats: 64% (01:43) correct 36% (01:32) wrong based on 73 sessions

### HideShow timer Statistics

If $$x$$ and $$y$$ are positive integers, is $$x$$ even ?

(1) $$x^{2} + y^{2} = 98$$

(2) $$x = y$$

Project DS Butler Data Sufficiency (DS3)

Are You Up For the Challenge: 700 Level Questions

_________________
CEO  V
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 3992
Location: India
GMAT: QUANT EXPERT
Schools: IIM (A)
GMAT 1: 750 Q51 V41
WE: Education (Education)
Re: If x any y are positive integers,is x even? (1) x^2 + y^2=98 (2) x = y  [#permalink]

### Show Tags

1
1
Bunuel wrote:
If $$x$$ and $$y$$ are positive integers, is $$x$$ even ?

(1) $$x^{2} + y^{2} = 98$$

(2) $$x = y$$

Project DS Butler Data Sufficiency (DS3)

Are You Up For the Challenge: 700 Level Questions

Given: x and y are positive and Integers

Question: Is x even?

statement 1: $$x^{2} + y^{2} = 98$$

Perfect square $$x^2$$. and $$y^2$$ have to be one of {1, 4, 9, 16, 25, 36, 49, 64, 81}

i.e. $$x^2 = y^2 = 49$$

i.e. x = y = 7 i.e. answer to the question is NO

SUFFICIENT

Statement 2: x = y

Both x and y may be 2 (even) or both may be 7 (odd) hence

NOT SUFFICIENT

_________________
Prosper!!!
GMATinsight .............(Bhoopendra Singh and Dr.Sushma Jha)
e-mail: info@GMATinsight.com l Call : +91-9999687183 / 9891333772
Online One-on-One Skype based classes l Classroom Coaching l On-demand Quant course
Check website for most affordable Quant on-Demand course 2000+ Qns (with Video explanations)
Our SUCCESS STORIES: From 620 to 760 l Q-42 to Q-49 in 40 days l 590 to 710 + Wharton l
ACCESS FREE GMAT TESTS HERE:22 FREE (FULL LENGTH) GMAT CATs LINK COLLECTION
SVP  V
Joined: 20 Jul 2017
Posts: 1506
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: If x any y are positive integers,is x even? (1) x^2 + y^2=98 (2) x = y  [#permalink]

### Show Tags

1
Bunuel wrote:
If $$x$$ and $$y$$ are positive integers, is $$x$$ even ?

(1) $$x^{2} + y^{2} = 98$$
(2) $$x = y$$

(1) $$x^{2} + y^{2} = 98$$
--> Only Possible value of ($$x$$, $$y$$) = ($$7$$, $$7$$)
--> '$$x$$' is definitely not even --> Sufficient

(2) $$x = y$$
--> '$$x$$' can take infinite values (Even or Odd) --> Insufficient

Option A
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8996
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If x any y are positive integers,is x even? (1) x^2 + y^2=98 (2) x = y  [#permalink]

### Show Tags

1
Bunuel wrote:
If $$x$$ and $$y$$ are positive integers, is $$x$$ even ?

(1) $$x^{2} + y^{2} = 98$$

(2) $$x = y$$

Project DS Butler Data Sufficiency (DS3)

Are You Up For the Challenge: 700 Level Questions

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

If x is an even integer, then we have $$x = 2k$$ for an integer $$k$$.
We have $$y^2 = 98 - x^2 = 98 - 4k^2 = 4(24-k^2) + 2$$ from condition 1).
A square of an integer $$y^2$$ can't have a remainder $$2$$ when it is divided by $$4$$ for the following reasoning.
Thus, $$x$$ can not be even.

If $$y$$ is an odd integer, $$y = 2a + 1$$, then $$y^2 = (2a+1)^2 = 4a^2 + 4a + 1 = 4(a^2+a) + 1$$ and $$y^2$$ has a remainder $$1$$.
If $$y$$ is an even integer, $$y = 2a$$, then $$y^2 = (2a)^2 = 4a^2 = 4a^2 + 0$$ and $$y^2$$ has a remainder $$0$$.

Condition 1) yields a unique answer 'no'.

Since 'no' is also a unique answer by CMT (Common Mistake Type) 1, condition 1) is sufficient.

Condition 2)

Since condition 2) does not yield a unique solution obviously, it is not sufficient.

_________________ Re: If x any y are positive integers,is x even? (1) x^2 + y^2=98 (2) x = y   [#permalink] 01 Apr 2020, 09:06

# If x any y are positive integers,is x even? (1) x^2 + y^2=98 (2) x = y  