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## Is the integer z divisible by 3?

tagged by: rolandprowess

### Top Member

lheiannie07 Legendary Member
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#### Is the integer z divisible by 3?

Mon Oct 30, 2017 6:23 am
Is the integer z divisible by 3?

(1) The LCM of z and 12 is 12
(2) The LCM of z and 15 is 45.

What's the best way to determine whether statement 1 is sufficient?

OA B

### GMAT/MBA Expert

Scott@TargetTestPrep GMAT Instructor
Joined
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Tue Dec 05, 2017 6:34 pm
lheiannie07 wrote:
Is the integer z divisible by 3?

(1) The LCM of z and 12 is 12
(2) The LCM of z and 15 is 45.
We need to determine whether z/3 = integer

Statement One Alone:

The LCM of z and 12 is 12.

Using the information in statement one, we see that z could equal 1, 2, 3, 4, 6, or 12 since the LCM of any of these numbers and 12 is 12. Furthermore, we cannot determine whether z/3 is an integer. For instance, if z = 1, then z/3 is not an integer, but if z = 3, then z/3 is an integer. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

The LCM of z and 15 is 45.

Using the information in statement two, we see that z could only equal 9 or 45 since these two numbers are the only numbers that produce an LCM of 45 when paired with 15. If z = 9, then z/3 is an integer. If z = 45, then z/3 is an integer as well. Statement two alone is sufficient to answer the question.

_________________
Scott Woodbury-Stewart Founder and CEO

### Top Member

lheiannie07 Legendary Member
Joined
07 Sep 2017
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637 messages
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2 members
Wed Jan 17, 2018 9:14 pm
Scott@TargetTestPrep wrote:
lheiannie07 wrote:
Is the integer z divisible by 3?

(1) The LCM of z and 12 is 12
(2) The LCM of z and 15 is 45.
We need to determine whether z/3 = integer

Statement One Alone:

The LCM of z and 12 is 12.

Using the information in statement one, we see that z could equal 1, 2, 3, 4, 6, or 12 since the LCM of any of these numbers and 12 is 12. Furthermore, we cannot determine whether z/3 is an integer. For instance, if z = 1, then z/3 is not an integer, but if z = 3, then z/3 is an integer. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

The LCM of z and 15 is 45.

Using the information in statement two, we see that z could only equal 9 or 45 since these two numbers are the only numbers that produce an LCM of 45 when paired with 15. If z = 9, then z/3 is an integer. If z = 45, then z/3 is an integer as well. Statement two alone is sufficient to answer the question.

Thanks a lot!

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