It is currently 23 Jan 2018, 12:10

### 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

# Is z an even integer?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Aug 2009
Posts: 5545
Is z an even integer? [#permalink]

### Show Tags

29 Apr 2017, 08:09
Expert's post
1
This post was
BOOKMARKED
00:00

Difficulty:

75% (hard)

Question Stats:

33% (01:14) correct 67% (00:41) wrong based on 63 sessions

### HideShow timer Statistics

Is z an even integer?

(1) $$z^2$$ is an even integer.

(2) y*z is an even integer, where z and y are integers.
[Reveal] Spoiler: OA

_________________

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/-

Last edited by Bunuel on 30 Apr 2017, 02:37, edited 1 time in total.
Renamed the topic and edited the question.
Intern
Joined: 02 Mar 2017
Posts: 9
Re: Is z an even integer? [#permalink]

### Show Tags

29 Apr 2017, 08:13
Statement 1 alone is sufficient and statement 2 is not sufficient.

Sent from my iPhone using GMAT Club Forum
Math Expert
Joined: 02 Aug 2009
Posts: 5545
Re: Is z an even integer? [#permalink]

### Show Tags

29 Apr 2017, 08:27
1
KUDOS
Expert's post
Munch wrote:
Statement 1 alone is sufficient and statement 2 is not sufficient.

Sent from my iPhone using GMAT Club Forum

Hi,
What if z is √2...
$$z^2=2$$ and thus an even integer but z is not an even integer.
_________________

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/-

Retired Moderator
Joined: 05 Jul 2006
Posts: 1748
Re: Is z an even integer? [#permalink]

### Show Tags

29 Apr 2017, 14:03
chetan2u wrote:
Is z an even integer?
1) $$z^2$$ is an even integer.
2) y*z is an even integer, where z and y are integers.

from 1

z could be a radical ... insuff

from 2

if y is even integer and no idea about z... insuff

both

z is an integer and z^2 is even thus z is even...C
Intern
Joined: 25 Dec 2016
Posts: 19
Re: Is z an even integer? [#permalink]

### Show Tags

29 Apr 2017, 21:37
Statement 1: Z can be sqrt2 insufficient
Statement 2 : Not Unique answer.

Both we can derive unique answer that Z is an integer and even
Retired Moderator
Joined: 12 Aug 2015
Posts: 2345
GRE 1: 323 Q169 V154
Re: Is z an even integer? [#permalink]

### Show Tags

29 Apr 2017, 22:09
Even/Odd Questions are one of my favourite.
So much to learn.

Here is what i did on this one ->

Firstly => The most important step in any even/odd question before we move to the individual statements is check whether the involved numbers are integers or not.

We are not told that z is an integer.

Lets roll-->

Statement 1 =>
z^2 is even

If z is an integer => z would be even.
But what if z=$$√12$$ ?
z^2 is even
But $$√12$$ isnt even.

Not sufficient.

Statement 2 =>
So y and z are integers.

yz= even
So at-least one out of y or z must be even.
So if y is even => z can be even or odd.

Not sufficient.

Combing the two statements => As z is an integer and z^2 is even => z must be even.
Property in action =>Positive exponent does not affect the even/odd nature of any integer.

Hence C is sufficient.

SMASH THAT C.

_________________

Give me a hell yeah ...!!!!!

Senior CR Moderator
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1318
Location: Viet Nam
Re: Is z an even integer? [#permalink]

### Show Tags

30 Apr 2017, 03:12
chetan2u wrote:
Is z an even integer?

(1) $$z^2$$ is an even integer.

(2) y*z is an even integer, where z and y are integers.

(1) $$z^2$$ is an even integer.

$$z^2=2 \implies z=\sqrt{2}$$ is not an even integer.
$$z^2=4 \implies z=2$$ is an even integer.

Hence (1) is insufficient.

(2) $$y$$ and $$z$$ are both integers.

Since $$y \times z$$ is even, $$y$$ or $$z$$ or both must be even.

If $$y$$ is odd, then $$z$$ must be even.
If $$y$$ is even, then $$z$$ could be odd.

Hence, insufficient.

Cobine (1) and (2), we have $$z$$ is an integer and $$z^2$$ is even. Hence $$z$$ must be even. Sufficient.

_________________
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 10747
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: Is z an even integer? [#permalink]

### Show Tags

10 Dec 2017, 14:17
1
KUDOS
Expert's post
Hi All,

We're asked if Z is an EVEN INTEGER. This is a YES/NO question. We can solve it by TESTing VALUES.

1) Z^2 is an EVEN integer.

IF...
Z^2 = 2, then Z = (root2) and the answer to the question is NO.
Z^2 = 4, then Z = 2 and the answer to the question is YES.
Fact 1 is INSUFFICIENT

2) (Y)(Z) is an EVEN integer and Z and Y are INTEGERS

IF...
Y = 1 and Z = 2, then the answer to the question is YES.
Y = 2 and Z = 1, then the answer to the question is NO.
Fact 2 is INSUFFICIENT

Combined, we know...
Y and Z are INTEGERS
Z^2 is an EVEN integer

The ONLY way to square an INTEGER and end up with an EVEN integer is if you started with an EVEN integer. Fact 2 tells us that Z MUST be an integer, so Z MUST be even and the answer to the question is ALWAYS YES.
Combined, SUFFICIENT

[Reveal] Spoiler:
C

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save \$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Re: Is z an even integer?   [#permalink] 10 Dec 2017, 14:17
Display posts from previous: Sort by