It is currently 22 Jun 2017, 19:06

### 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 y is an integer, is y^3 divisible by 8?

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

### Hide Tags

Intern
Joined: 07 Sep 2012
Posts: 39
GMAT 1: 680 Q50 V32
GMAT 2: 700 Q49 V36
If y is an integer, is y^3 divisible by 8? [#permalink]

### Show Tags

16 Sep 2012, 09:45
2
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

73% (01:45) correct 27% (00:48) wrong based on 116 sessions

### HideShow timer Statistics

If y is an integer, is y^3 divisible by 8?

(1) y is even.
(2) y^3 - y is even.

[Reveal] Spoiler:
Shouldn't the answer be E because y could be 0 which is an even integer?
[Reveal] Spoiler: OA
Senior Manager
Joined: 28 Jun 2009
Posts: 445
Location: United States (MA)
Re: If y is an integer, is y(cube) divisible by 8? [#permalink]

### Show Tags

16 Sep 2012, 09:57
1
This post was
BOOKMARKED
I chose A.

(1) y^3 will always be divisible by 2^3 if y is even. Ex. y =2, 4, etc
(2) Gives two opposite answers.

Lets say y = 0 -> even integer
-> y^3 = 0
-> y^3/2^3 = 0/8
-> 0/8 = 0 [ 0/N = 0 for any N from -infinity to +infinity, except 0.]
Director
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)
Re: If y is an integer, is y(cube) divisible by 8? [#permalink]

### Show Tags

16 Sep 2012, 10:08
2
KUDOS
crackmba2012 wrote:
If y is an integer, is y(cube) divisible by 8?
(1) y is even.
(2) y(cube)- y is even.

Shouldn't the answer be E because y could be 0 which is an even integer?

0 is even and it is divisible by 8. 0 is divisible by any non-zero integer.

(1) $$y=2k,$$ for some integer $$k,$$ then $$y^3=8k^3,$$ obviously divisible by 8.
Sufficient.

(2) Check for example for $$y=1$$ and $$y = 2.$$ You obtain 0 and 6. Both are even, but 6 is not divisible by 8.
Not sufficient.

Remark: $$y^3-y=y(y^2-1)=(y-1)y(y+1)$$ is the product of three consecutive integers, therefore it is always even.
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Senior Manager
Joined: 28 Jun 2009
Posts: 445
Location: United States (MA)
Re: If y is an integer, is y(cube) divisible by 8? [#permalink]

### Show Tags

16 Sep 2012, 10:11
EvaJager wrote:

Remark: $$y^3-y=y(y^2-1)=(y-1)y(y+1)$$ is the product of three consecutive integers, therefore it is always even.

Awesome! I used a very long way to get here. Should have spotted this.
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15917
Re: If y is an integer, is y^3 divisible by 8? [#permalink]

### Show Tags

24 Oct 2015, 12:49
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.
_________________
Re: If y is an integer, is y^3 divisible by 8?   [#permalink] 24 Oct 2015, 12:49
Similar topics Replies Last post
Similar
Topics:
3 Is (x + y)^3 an even integer? 6 21 Nov 2016, 11:34
6 If x and y are positive integers and x + y = 3^x, is y divisible by 6? 7 08 Mar 2017, 23:23
13 If y is an integer, is y^3 divisible by 9 ? 9 23 Jan 2017, 11:29
4 If y is an integer is y^3 divisible by 9 10 22 Nov 2016, 07:09
1 If y is an integer, is y^3 divisible by 9? 9 20 Aug 2013, 06:31
Display posts from previous: Sort by

# If y is an integer, is y^3 divisible by 8?

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

 Powered by phpBB © phpBB Group and phpBB SEO 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®.