GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 20 Jun 2018, 00:33

Close

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
Your Progress

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If 100 < x^2 < 225, what is the greatest possible number of unique fac

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46191
If 100 < x^2 < 225, what is the greatest possible number of unique fac [#permalink]

Show Tags

New post 13 Feb 2017, 03:32
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

54% (01:09) correct 46% (00:53) wrong based on 103 sessions

HideShow timer Statistics

Director
Director
avatar
S
Joined: 21 Mar 2016
Posts: 540
Reviews Badge
Re: If 100 < x^2 < 225, what is the greatest possible number of unique fac [#permalink]

Show Tags

New post 13 Feb 2017, 04:07
since x is an integet,,,x^2 is a perfect square,, i.e x^2 = 121 or 144 or 169 or 196.
implies x is 11 or 12 or 13 or 14

calculating the number of factors for each,, 12 has highes number of factors i.e 6
anc C
Board of Directors
User avatar
G
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3509
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User Premium Member
Re: If 100 < x^2 < 225, what is the greatest possible number of unique fac [#permalink]

Show Tags

New post 13 Feb 2017, 09:43
Bunuel wrote:
If 100 < x^2 < 225, what is the greatest possible number of unique factors of integer x?

A. 3
B. 4
C. 6
D. 12
E. 15


\(100 < x^2 < 225\)

Or, + \(10\) \(< x <\) + \(15\)

So, value of x = \(+11 , -11 , +12 , -12 , + 13 , -13\)

Thus, there will be 6 possible unique values, answer will be (C) 6
_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

1 KUDOS received
Senior SC Moderator
User avatar
V
Joined: 14 Nov 2016
Posts: 1287
Location: Malaysia
GMAT ToolKit User Premium Member CAT Tests
Re: If 100 < x^2 < 225, what is the greatest possible number of unique fac [#permalink]

Show Tags

New post 22 Feb 2017, 20:59
1
Bunuel wrote:
If \(100 < x^2 < 225\), what is the greatest possible number of unique factors of integer x?

A. 3
B. 4
C. 6
D. 12
E. 15


Official solution from Veritas Prep.

Since x is defined as an integer, you can quickly identify your possible values of x by looking at all the perfect squares between 100 and 225. Since 100 is 10-squared and 225 is 15-squared, your only options for x are 11, 12, 13, and 14.

From that list, you should recognize 11 and 13 as primes, meaning that they'll each have exactly two factors ("itself" and 1.) So you can eliminate 11 and 13 as options. From there you can factor the other two options.

14 has as factors 1 and 14, and 2 and 7 (remember with factors that it's helpful to think of them in pairs).

And 12 has as factors 1 and 12; 2 and 6; and 3 and 4. So the maximum number of unique factors of x is 6.
_________________

"Be challenged at EVERY MOMENT."

“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”

"Each stage of the journey is crucial to attaining new heights of knowledge."

Rules for posting in verbal forum | Please DO NOT post short answer in your post!

Re: If 100 < x^2 < 225, what is the greatest possible number of unique fac   [#permalink] 22 Feb 2017, 20:59
Display posts from previous: Sort by

If 100 < x^2 < 225, what is the greatest possible number of unique fac

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.