If x and y are nonzero integers, is 18 a factor of xy^2? : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 17 Jan 2017, 18:42

### 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 x and y are nonzero integers, is 18 a factor of xy^2?

Author Message
TAGS:

### Hide Tags

Director
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 651
Followers: 42

Kudos [?]: 860 [0], given: 39

If x and y are nonzero integers, is 18 a factor of xy^2? [#permalink]

### Show Tags

13 Jan 2012, 08:49
4
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

59% (01:57) correct 41% (00:56) wrong based on 281 sessions

### HideShow timer Statistics

If x and y are nonzero integers, is 18 a factor of xy^2?

(1) x is a multiple of 54.
(2) y is a multiple of 6.

[Reveal] Spoiler:
I did A.
In case of option 2 y is a multiple of 6.
So y = 6, 12, 18 .......if y = 6, then the factors of 6 could is 2 & 3 but factors of 18 are 2, 3 & 3. Thus 18 Could be not a factor of xy^2.

What is the wrong with me?
[Reveal] Spoiler: OA

_________________

Collections:-
PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html
DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html
100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html
Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html
Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html

Math Expert
Joined: 02 Sep 2009
Posts: 36540
Followers: 7072

Kudos [?]: 93041 [2] , given: 10541

Re: If x and y are nonzero integers [#permalink]

### Show Tags

13 Jan 2012, 09:20
2
KUDOS
Expert's post
Baten80 wrote:
If x and y are nonzero integers, is 18 a factor of xy^2?
(1) x is a multiple of 54.
(2) y is a multiple of 6.

I did A.
In case of option 2 y is a multiple of 6.
So y = 6, 12, 18 .......if y = 6, then the factors of 6 could is 2 & 3 but factors of 18 are 2, 3 & 3. Thus 18 Could be not a factor of xy^2.

What is the wrong with me?

If x and y are nonzero integers, is 18 a factor of xy^2?

(1) x is a multiple of 54 --> x is a multiple of 18 as well (54=18*3) --> xy^2 is also a multiple of 18. Sufficient.

(2) y is a multiple of 6 --> y^2 is a multiple of 6^2=36 --> y^2 is a multiple of 18 as well (36=18*2) --> the same here: as y^2 is a multiple of 18 then xy^2 is also a multiple of 18. Sufficient.

_________________
Director
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 651
Followers: 42

Kudos [?]: 860 [0], given: 39

Re: If x and y are nonzero integers [#permalink]

### Show Tags

13 Jan 2012, 10:04
Manager
Joined: 29 Jul 2011
Posts: 107
Location: United States
Followers: 5

Kudos [?]: 58 [0], given: 6

Re: If x and y are nonzero integers [#permalink]

### Show Tags

13 Jan 2012, 10:56
1. x=54 = 18 x 3. So, 18 is a factor of x -> 18 is a factor of xy^2. Suff
2. y=6 -> y^2 = 36 = 18x2 -> 18 is a factor of y^2 -> 18 is a factor of xy^2. Suff

D
_________________

I am the master of my fate. I am the captain of my soul.
Please consider giving +1 Kudos if deserved!

DS - If negative answer only, still sufficient. No need to find exact solution.
PS - Always look at the answers first
CR - Read the question stem first, hunt for conclusion
SC - Meaning first, Grammar second
RC - Mentally connect paragraphs as you proceed. Short = 2min, Long = 3-4 min

Math Expert
Joined: 02 Sep 2009
Posts: 36540
Followers: 7072

Kudos [?]: 93041 [0], given: 10541

Re: If x and y are nonzero integers, is 18 a factor of xy^2? [#permalink]

### Show Tags

22 May 2013, 02:39
Bumping for review and further discussion.
_________________
Manager
Joined: 24 Apr 2013
Posts: 54
Schools: Duke '16
Followers: 0

Kudos [?]: 10 [0], given: 76

Re: If x and y are nonzero integers, is 18 a factor of xy^2? [#permalink]

### Show Tags

22 May 2013, 13:40
I was actually thinking C cause they both can be used but wasnt sure if they could be used alone
Manager
Joined: 26 Feb 2013
Posts: 184
Followers: 0

Kudos [?]: 40 [0], given: 25

Re: If x and y are nonzero integers, is 18 a factor of xy^2? [#permalink]

### Show Tags

14 Nov 2013, 09:58
Baten80 wrote:
If x and y are nonzero integers, is 18 a factor of xy^2?

(1) x is a multiple of 54.
(2) y is a multiple of 6.

[Reveal] Spoiler:
I did A.
In case of option 2 y is a multiple of 6.
So y = 6, 12, 18 .......if y = 6, then the factors of 6 could is 2 & 3 but factors of 18 are 2, 3 & 3. Thus 18 Could be not a factor of xy^2.

What is the wrong with me?

Is it safe to rephrase as:
Does any of x or y^2 divide 18 ?
Math Expert
Joined: 02 Sep 2009
Posts: 36540
Followers: 7072

Kudos [?]: 93041 [0], given: 10541

Re: If x and y are nonzero integers, is 18 a factor of xy^2? [#permalink]

### Show Tags

14 Nov 2013, 11:46
Skag55 wrote:
Baten80 wrote:
If x and y are nonzero integers, is 18 a factor of xy^2?

(1) x is a multiple of 54.
(2) y is a multiple of 6.

[Reveal] Spoiler:
I did A.
In case of option 2 y is a multiple of 6.
So y = 6, 12, 18 .......if y = 6, then the factors of 6 could is 2 & 3 but factors of 18 are 2, 3 & 3. Thus 18 Could be not a factor of xy^2.

What is the wrong with me?

Is it safe to rephrase as:
Does any of x or y^2 divide 18 ?

No, xy^2 can be a multiple of 18 even if neither x nor y is a multiple of 18. For example: x=2 and y=3 --> xy^2=18.

Hope it's clear.
_________________
Manager
Joined: 26 Feb 2013
Posts: 184
Followers: 0

Kudos [?]: 40 [0], given: 25

Re: If x and y are nonzero integers, is 18 a factor of xy^2? [#permalink]

### Show Tags

14 Nov 2013, 11:57
Bunuel wrote:
Skag55 wrote:
Baten80 wrote:
If x and y are nonzero integers, is 18 a factor of xy^2?

(1) x is a multiple of 54.
(2) y is a multiple of 6.

[Reveal] Spoiler:
I did A.
In case of option 2 y is a multiple of 6.
So y = 6, 12, 18 .......if y = 6, then the factors of 6 could is 2 & 3 but factors of 18 are 2, 3 & 3. Thus 18 Could be not a factor of xy^2.

What is the wrong with me?

Is it safe to rephrase as:
Does any of x or y^2 divide 18 ?

No, xy^2 can be a multiple of 18 even when neither x nor y is a multiple of 18. For example: x=2 and y=3 --> xy^2=18.

Hope it's clear.

Yes, you're right. Thanks.
Manager
Joined: 06 Dec 2014
Posts: 67
GMAT 1: 670 Q48 V34
Followers: 0

Kudos [?]: 1 [0], given: 4

Re: If x and y are nonzero integers, is 18 a factor of xy^2? [#permalink]

### Show Tags

19 Feb 2015, 14:42
Q) Is 18 a factor of x*y^2??

1) x is a multiple of 54... Means x=54q.
(54q)*y^2/18... =(3q)*y^2 = Integer... So, 18 is a factor. Sufficient.

2) y is a multiple of 6... Means y=6q.
x*(6q)^2/18 = (36x)*q^2/18 = (2x)*q^2 = Integer... So, 18 is a factor. Sufficient.

(D)
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13432
Followers: 575

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

Re: If x and y are nonzero integers, is 18 a factor of xy^2? [#permalink]

### Show Tags

14 May 2016, 07:56
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.
_________________
BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 1889
Followers: 47

Kudos [?]: 357 [0], given: 449

Re: If x and y are nonzero integers, is 18 a factor of xy^2? [#permalink]

### Show Tags

24 Aug 2016, 01:41
Ecelelnt Question
Here is what i did
We need to check whether XY^2/18 =integer or not
Statement 1 => X=54*I for some integer I
Hence XY^2=54*I*Y^2=> 18*x where x=3*I*Y^2
hence Suff
Statement 2 =>
Y=6*I
Y^2=36*I
hence XY^2=X*36*I^2=> 18*x for x=X*2*I^2
hence Suff
SMASH THAT D
_________________

Mock Test -1 (Integer Properties Basic Quiz) ---> http://gmatclub.com/forum/stonecold-s-mock-test-217160.html#p1676182

Mock Test -2 (Integer Properties Advanced Quiz) --->http://gmatclub.com/forum/stonecold-s-mock-test-217160.html#p1765951

Give me a hell yeah ...!!!!!

Re: If x and y are nonzero integers, is 18 a factor of xy^2?   [#permalink] 24 Aug 2016, 01:41
Similar topics Replies Last post
Similar
Topics:
1 If x and y are positive integers, xy-2=? 7 23 Dec 2016, 01:31
1 (x-y)^2-(x+y)^2=? 5 24 Jul 2016, 02:06
12 If (x-y)^2=x^2-y^2, what is the value of nonzero integer xy? 18 31 Jul 2014, 06:03
Are the two nonzero integers x and y 1 24 Aug 2013, 22:36
5 If x and y are nonzero integers, is x/y an integer? 8 03 Apr 2012, 00:41
Display posts from previous: Sort by