GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 24 Jan 2020, 04:50 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If x is an integer, is 72/x an integer?

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 60644
If x is an integer, is 72/x an integer?  [#permalink]

### Show Tags 00:00

Difficulty:   25% (medium)

Question Stats: 69% (01:16) correct 31% (01:29) wrong based on 127 sessions

### HideShow timer Statistics

If x is an integer, is 72/x an integer?

(1) 18 < x < 54
(2) x is a multiple of 18

_________________
Retired Moderator G
Joined: 26 Nov 2012
Posts: 554
Re: If x is an integer, is 72/x an integer?  [#permalink]

### Show Tags

Bunuel wrote:
If x is an integer, is 72/x an integer?

(1) 18 < x < 54
(2) x is a multiple of 18

Given to find 72/x an integer ?

Stat 1: 18 < x < 54 ...here x can 19,20,....54... we choose any value, we might get a integer or not..Insufficient..

Stat 2: X is a multiple of 18, then x can 18,36,54,72...etc... Insufficient...only for few values we get integers..Insufficient..

Stat 1 + 2: 36 is the number...we get integer when 72/36.

IMO option C is correct answer...

OA please...will correct if I missed anything..
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4225
Re: If x is an integer, is 72/x an integer?  [#permalink]

### Show Tags

1
Top Contributor
Bunuel wrote:
If x is an integer, is 72/x an integer?

(1) 18 < x < 54
(2) x is a multiple of 18

Target question: Is 72/x an integer?
Important: 72/x will be an integer IF x is a divisor of 72.
In other words, 72/x will be an integer IF x equals one of the following values: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, or 72

Statement 1: 18 < x < 54
Since 24 and 36 are among the possible x-values between 18 and 54, it is possible that 72/x IS an integer.
However, x could also equal a number like 20, in which case 72/x is NOT an integer
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x is a multiple of 18
There are several values of x satisfy statement 2. Here are two:
Case a: x = 18, in which case 72/x = 72/18 = 4. So, in this case, 72/x IS an integer
Case b: x = 90, in which case 72/x = 72/90. So, in this case, 72/x is NOT an integer
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that 18 < x < 54
Statement 2 tells us that x is a multiple of 18 (18, 36, 54, 72, 90, ...)
Since 36 is the ONLY multiple of 18 that's BETWEEN 18 and 54, we can be certain that x = 36
So, 72/x = 72/36 = 2
So, 72/x IS an integer
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Cheers,
Brent
_________________
Non-Human User Joined: 09 Sep 2013
Posts: 14002
Re: If x is an integer, is 72/x an integer?  [#permalink]

### Show Tags

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 x is an integer, is 72/x an integer?   [#permalink] 07 Nov 2019, 01:43
Display posts from previous: Sort by

# If x is an integer, is 72/x an integer?  