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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Official Answer and Stats are available only to registered users. Register/Login.

_________________

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

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

Show Tags

Updated on: 20 Apr 2018, 12:50

Top Contributor

1

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

_________________

Test confidently with gmatprepnow.com

Originally posted by GMATPrepNow on 15 Aug 2017, 12:22.
Last edited by GMATPrepNow on 20 Apr 2018, 12:50, edited 1 time in total.

Re: If x and z are positive integers, is x^2 - z^2 odd?
[#permalink]

Show Tags

15 Aug 2017, 12:25

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
_________________

Re: If x and z are positive integers, is x^2 - z^2 odd?
[#permalink]

Show Tags

15 Aug 2017, 12:34

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]

Show Tags

19 Jan 2019, 00:33

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.
_________________