It is currently 19 Sep 2017, 05:00

### 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

# Contrapositive

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

### Hide Tags

Intern
Joined: 12 Mar 2012
Posts: 1

Kudos [?]: [0], given: 0

### Show Tags

12 Mar 2012, 09:36
1
This post was
BOOKMARKED
Can anyone help, I have the following Contrapositive but not sure how to prove it

If n is not even then n^2 is not divisible by 6

thanks
hazzy

Kudos [?]: [0], given: 0

Math Expert
Joined: 02 Sep 2009
Posts: 41597

Kudos [?]: 123964 [0], given: 12070

### Show Tags

12 Mar 2012, 09:46
hazzy wrote:
Can anyone help, I have the following Contrapositive but not sure how to prove it

If n is not even then n^2 is not divisible by 6

thanks
hazzy

That's not correct: consider $$n=\sqrt{6}\neq{even}$$ but $$n^2=6$$, which IS divisible by 6.

If we are told that n is an integer then it's correct: if n is not even then it's odd, odd^2=odd which can not be divisible by any number which has 2 as a factor, or simply n^2=odd so it's not divisible by 2, hence it can not be divisible by 6=2*3.

Hope it's clear.
_________________

Kudos [?]: 123964 [0], given: 12070

Manager
Joined: 02 Jan 2011
Posts: 193

Kudos [?]: 62 [0], given: 22

### Show Tags

12 Mar 2012, 09:56
In order for a number to be divisible by 6, the number should be divisible by 2 and 3.
Now coming to the problem, it is stated that n is not even which makes it Odd.

Then n^2 is odd
Since 2 is not factor of any odd integer, hence 6 is not factor of n^2.

This holds true when n is an integer.

Hope it helps.

Kudos [?]: 62 [0], given: 22

Re: Contrapositive   [#permalink] 12 Mar 2012, 09:56
Display posts from previous: Sort by

# Contrapositive

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

 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®.