It is currently 21 Mar 2018, 21:35

### 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

# If a and b are positive integers (a > b), is a^2 - b^2

Author Message
Senior Manager
Joined: 05 Oct 2008
Posts: 263
If a and b are positive integers (a > b), is a^2 - b^2 [#permalink]

### Show Tags

06 Nov 2008, 04:44
If a and b are positive integers (a > b), is $$a^2 - b^2$$ divisible by 4?

1. a = b + 2
2. a and b are odd

S_1: $$a^2 - b^2 = (b + 2)^2 - b^2 = 4b + 4$$ , which is divisible by 4. S_2: $$a^2 - b^2 = (2n + 1)^2 - (2k + 1)^2 = 4n^2 + 4n - 4k^2 + 4k$$ , which is divisible by 4.

Can someone pls explain how the solution in the explanation is derived? Thanks

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Director
Joined: 14 Aug 2007
Posts: 704

### Show Tags

06 Nov 2008, 05:36
study wrote:
If a and b are positive integers (a > b), is $$a^2 - b^2$$ divisible by 4?

1. a = b + 2
2. a and b are odd

S_1: $$a^2 - b^2 = (b + 2)^2 - b^2 = 4b + 4$$ , which is divisible by 4. S_2: $$a^2 - b^2 = (2n + 1)^2 - (2k + 1)^2 = 4n^2 + 4n - 4k^2 + 4k$$ , which is divisible by 4.

Can someone pls explain how the solution in the explanation is derived? Thanks

S_1 is pretty obvious.

in S_2 , as any odd number can be expressed as 2*n + 1 (n>=0), it is substituted for 2 different odd numbers (by taking n and k variables)

You can try with substituting numbers as other way to solve this problem.

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Re: No. Properties   [#permalink] 06 Nov 2008, 05:36
Display posts from previous: Sort by

# If a and b are positive integers (a > b), is a^2 - b^2

Moderator: chetan2u

 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®.