If y is a positive integer, is y^2 - y divisible by 4 ? : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 21 Jan 2017, 22:52

### 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 a positive integer, is y^2 - y divisible by 4 ?

Author Message
TAGS:

### Hide Tags

Director
Joined: 07 Jun 2004
Posts: 612
Location: PA
Followers: 5

Kudos [?]: 708 [2] , given: 22

If y is a positive integer, is y^2 - y divisible by 4 ? [#permalink]

### Show Tags

18 Feb 2012, 05:08
2
KUDOS
2
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

36% (03:39) correct 64% (01:44) wrong based on 69 sessions

### HideShow timer Statistics

If y is a positive integer, is y^2 - y divisible by 4 ?

(1) y^2 + y is not divisible by 4

(2) y^3 - y is divisible by 4
[Reveal] Spoiler: OA

_________________

If the Q jogged your mind do Kudos me : )

Manager
Status: Employed
Joined: 17 Nov 2011
Posts: 100
Location: Pakistan
GMAT 1: 720 Q49 V40
GPA: 3.2
WE: Business Development (Internet and New Media)
Followers: 7

Kudos [?]: 135 [8] , given: 10

Re: If y is a positive integer [#permalink]

### Show Tags

18 Feb 2012, 06:27
8
KUDOS
Interesting question. Kudos to you. Very simple explanation though

Question: If $$y$$ is a positive integer , is $$y^2 - y$$ divisible by $$4$$?

Lets factor $$y^2 - y$$:
$$y^2-y=y*(y-1)$$

So we know that these are two consecutive integers, so one of them has to be odd and one of them is even. Which means only one of them can be a multiple of $$4$$. So we need to establish that either $$y$$ is a multiple of $$4$$ or $$(y-1)$$ is a multiple of $$4$$.

Statement A: $$y^2 + y$$ is not divisible by $$4$$

Lets factor this one out : $$y^2+y=y*(y+1)$$

These again are consecutive integers and the statement says that niether of them is a factor of $$4$$. Remember our original conditions. either $$y$$ is a multiple of $$4$$ or $$(y-1)$$ is a multiple of $$4$$. This statement tells us that $$y$$ is not a multiple of $$4$$ but it does not tell us whether $$(y-1)$$ is a multiple of $$4$$ or not. Also note that this again does not tell us whether $$y$$ is even or $$(y-1)$$ is even.So Insufficient.

Statement B: $$y^3-y$$ is divisible by $$4$$

Lets factor this one out : $$y^3-y=y*(y-1)*(y+1)$$ and again these are $$3$$ consecutive integers. The only thing we have found out (from the statement) is that one of them is definitely a multiple of $$4$$ but we do not know which one it is. Also note that we are not sure that one of them is even or two of them are even. And if it is one even, it could be $$2$$ so it is still not sufficient. We need at-least $$2$$ multiples of $$2$$ in there. If there were $$2$$ even numbers, we would be sure that it is divisible by $$4$$. So Insufficient

Combined:

We know that $$y$$ and $$(y+1)$$ are not multiples of $$4$$ from the first statement so from our second statement combined we have found out that $$(y-1)$$ is then, logically speaking, a multiple of $$4$$ and since $$(y-1)$$ is one of our original factors from the question stem, the answer is YES. $$y^2-1$$ whose factors are $$y*(y-1)$$ is divisible by $$4$$ because of the presence of $$(y-1)$$ as a factor. A Kudos won't hurt here!

_________________

"Nowadays, people know the price of everything, and the value of nothing." Oscar Wilde

Manager
Joined: 03 Oct 2009
Posts: 62
Followers: 0

Kudos [?]: 100 [0], given: 8

Re: If y is a positive integer [#permalink]

### Show Tags

18 Feb 2012, 13:04
If y is a positive integer , is y^2 - y divisible by 4

y > 0

is y (y - 1) divisible by 4 ?

1. y^2 + y is not divisible by 4
y (y+1) is not divisible by 4

Not sufficient.

2. y^3 - y is divisible by 4

y (y-1) (y+1) is divisible by 4

Not sufficient.

1 + 2

(y - 1) is divisible by 4.

Hence, y (y - 1) is divisible by 4. Sufficient.
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13492
Followers: 576

Kudos [?]: 163 [0], given: 0

Re: If y is a positive integer [#permalink]

### Show Tags

11 Dec 2013, 14:02
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.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13492
Followers: 576

Kudos [?]: 163 [0], given: 0

Re: If y is a positive integer, is y^2 - y divisible by 4 ? [#permalink]

### Show Tags

22 Nov 2016, 10:11
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 a positive integer, is y^2 - y divisible by 4 ?   [#permalink] 22 Nov 2016, 10:11
Similar topics Replies Last post
Similar
Topics:
If x and y are positive integers, is y – 2x positive? (1) The sum of 5 05 Dec 2016, 08:12
6 If x and y are positive integers and (x + y)^2 is an odd integer, is x 2 11 Apr 2016, 03:01
4 If y is an integer, is y^2 divisible by 4? 4 06 Oct 2015, 05:02
2 If y is an integer, is y^2 divisible by 15? 2 29 Jul 2015, 00:15
If y is an integer, is y^2 divisible by 4? 2 07 Feb 2012, 19:41
Display posts from previous: Sort by