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

 It is currently 16 Jul 2018, 21:09

### 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

# If x and z are positive integers, is x^2 - z^2 odd?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Verbal Forum Moderator
Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
Posts: 2076
Location: India
Concentration: General Management, Strategy
Schools: Kelley '20, ISB '19
GPA: 3.2
WE: Information Technology (Consulting)
If x and z are positive integers, is x^2 - z^2 odd? [#permalink]

### Show Tags

15 Aug 2017, 13:04
1
2
00:00

Difficulty:

15% (low)

Question Stats:

68% (00:57) correct 32% (00:25) wrong based on 71 sessions

### HideShow timer Statistics

If x and z are positive integers, is $$x^2-z^2$$ odd?

(1) x + z is odd
(2) x - z is odd

_________________

When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford
The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long
+1 Kudos if you find this post helpful

CEO
Joined: 12 Sep 2015
Posts: 2630
Location: Canada
If x and z are positive integers, is x^2 - z^2 odd? [#permalink]

### Show Tags

Updated on: 20 Apr 2018, 13:50
Top Contributor
Skywalker18 wrote:
If x and z are positive integers, is $$x^2-z^2$$ odd?

(1) x + z is odd
(2) x - z is odd

Great question!!

Target question: Is x² - z² odd?

Given: x and z are positive integers

IMPORTANT RULES;
Rule #1) (ODD)² = ODD
Rule #2) (EVEN)² = EVEN
Rule #3) ODD + EVEN = ODD
Rule #4) EVEN + ODD = ODD
Rule #5) ODD - EVEN = ODD
Rule #6) EVEN - ODD = ODD

Statement 1: x + z is odd
By Rule #3 or Rule #4, we can conclude that one number (x or z) is ODD and the other number is EVEN.
So, there are two possible cases:
case a: x is ODD and z is EVEN
case b) x is EVEN and z is ODD

Let's examine each case.
Case a: if x is ODD and z is EVEN, then x² is ODD and z² is EVEN. In this case, x² - z² = ODD - EVEN = ODD
Case b: if x is EVEN and z is ODD, then x² is EVEN and z² is ODD . In this case, x² - z² = EVEN - ODD = ODD
In either case, x² - z² is ODD
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x - z is odd
By Rule #5 or Rule #6, we can conclude that one number (x or z) is ODD and the other number is EVEN.
So, there are two possible cases:
case a: x is ODD and z is EVEN
case b) x is EVEN and z is ODD

Let's examine each case.
Case a: if x is ODD and z is EVEN, then x² is ODD and z² is EVEN. In this case, x² - z² = ODD - EVEN = ODD
Case b: if x is EVEN and z is ODD, then x² is EVEN and z² is ODD . In this case, x² - z² = EVEN - ODD = ODD
In either case, x² - z² is ODD
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

RELATED VIDEO

_________________

Brent Hanneson – Founder of gmatprepnow.com

Originally posted by GMATPrepNow on 15 Aug 2017, 13:22.
Last edited by GMATPrepNow on 20 Apr 2018, 13:50, edited 1 time in total.
Senior Manager
Joined: 06 Jul 2016
Posts: 417
Location: Singapore
Concentration: Strategy, Finance
Re: If x and z are positive integers, is x^2 - z^2 odd? [#permalink]

### Show Tags

15 Aug 2017, 13:25
Skywalker18 wrote:
If x and z are positive integers, is $$x^2-z^2$$ odd?

$$x^2$$ - $$z^2$$ can only be odd, if x and z are opposites i.e. if x is odd, z is even and if x is even, z is odd.

Quote:
(1) x + z is odd
(2) x - z is odd

1) x + z is odd
=> one of them is odd, and one of them is even.
Sufficient.

2) x - z is odd
=> one of them is odd, and one of them is even.
Sufficient.

D is the answer.
_________________

Put in the work, and that dream score is yours!

BSchool Forum Moderator
Joined: 28 Mar 2017
Posts: 1040
Location: India
Concentration: Finance, Technology
GMAT 1: 730 Q49 V41
GPA: 4
Re: If x and z are positive integers, is x^2 - z^2 odd? [#permalink]

### Show Tags

15 Aug 2017, 13:25
Skywalker18 wrote:
If x and z are positive integers, is $$x^2-z^2$$ odd?

(1) x + z is odd
(2) x - z is odd

My Answer - D

$$x^2-z^2$$ will be odd if either x or z will be add and other one will be even.

1. sum of an odd and an even number is add; rest all the times its even. Thus either of x or z is odd and the other is even. SUFFICIENT
2. subtraction of an odd and an even number is add; rest all the times its even. Thus either of x or z is odd and the other is even. SUFFICIENT
_________________

Kudos if my post helps!

Long And A Fruitful Journey - V21 to V41; If I can, So Can You!!

Preparing for RC my way

My study resources:
1. Useful Formulae, Concepts and Tricks-Quant
2. e-GMAT's ALL SC Compilation
3. LSAT RC compilation
4. Actual LSAT CR collection by Broal
5. QOTD RC (Carcass)
6. Challange OG RC
7. GMAT Prep Challenge RC

GMAT Tutor
Joined: 24 Jun 2008
Posts: 1345
Re: If x and z are positive integers, is x^2 - z^2 odd? [#permalink]

### Show Tags

15 Aug 2017, 13:34
This is identical to a question in one of my books, so I'm curious where you found it. It's not a very original or unique setup, so I wouldn't be surprised if someone else designed it independently.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Re: If x and z are positive integers, is x^2 - z^2 odd?   [#permalink] 15 Aug 2017, 13:34
Display posts from previous: Sort by

# If x and z are positive integers, is x^2 - z^2 odd?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.