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

Question

(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?

Bunuel · Answer

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.

Answer: D.

MHIKER · Answer

I considered y rather y^2
Thank u bunnuel

shinbhu · Answer

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

madzstar · Answer

I was actually thinking C cause they both can be used but wasnt sure if they could be used alone

Skag55 · Answer

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

Bunuel · Answer

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.

Skag55 · Answer

Yes, you're right. Thanks.

gmathopeful90 · Answer

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)

stonecold · Answer

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

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards