Find all School-related info fast with the new School-Specific MBA Forum

It is currently 30 Sep 2014, 01:50

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If 144/x is an integer and 108/x is an integer, which of the

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
User avatar
Joined: 23 Aug 2009
Posts: 17
Followers: 0

Kudos [?]: 5 [0], given: 8

If 144/x is an integer and 108/x is an integer, which of the [#permalink] New post 26 Feb 2010, 05:55
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

45% (02:07) correct 55% (00:51) wrong based on 76 sessions
If 144/x is an integer and 108/x is an integer, which of the following must be true?

I. 9/x is an integer
II. 12/x is an integer
III. 36/x is an integer

A. I only
B. III only
C. I and II only
D. II and III only
E. I, II and III

[Reveal] Spoiler:
In a post in november last year this question was solved with option B as the answer.

Here we come to know that the maximum value of x =36.
But the minimum values for x can be 2 or 3.

hence 12/x and 36/x can be an integer. hence the answer can be option D and not option B.

I choose that 12/x can be an integer as x can be 2 or 3.
Am i missing something here pls explain.


OPEN DISCUSSION OF THIS QUESTION IS HERE: if-144-x-is-an-integer-and-108-x-is-an-integer-which-of-the-128415.html
[Reveal] Spoiler: OA

_________________

Peace


Last edited by Bunuel on 12 Nov 2013, 09:17, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
Kaplan Promo CodeKnewton GMAT Discount CodesManhattan GMAT Discount Codes
Senior Manager
Senior Manager
avatar
Joined: 01 Feb 2010
Posts: 268
Followers: 1

Kudos [?]: 35 [0], given: 2

Re: Which of the following must be true? [#permalink] New post 26 Feb 2010, 06:55
ro86 wrote:
If 144/x is an integer and 108/x is an integer, which of the following must be true?

I. 9/xis an integer.
II. 12/x is an integer.
III. 36/x is an integer.

A) I only
B) III only
C) I and II only
D) II and III only
E) I, II, and III

In a post in november last year this question was solved with option B as the answer.
Here we come to know that the maximum value of x =36.
But the minimum values for x can be 2 or 3.
hence 12/x and 36/x can be an integer. hence the answer can be option D and not option B.
I choose that 12/x can be an integer as x can be 2 or 3.
Am i missing something here pls explain.


Factors of 144 = {2,2,3,3,2,2}
Factors of 108 = {2,2,3,3,3}
Common factors = {2,2,3,3} = 36
whats the OA.
Bunuel please suggest?
Manager
Manager
avatar
Joined: 26 May 2005
Posts: 210
Followers: 2

Kudos [?]: 69 [0], given: 1

Re: Which of the following must be true? [#permalink] New post 26 Feb 2010, 07:42
ro86 wrote:
If 144/x is an integer and 108/x is an integer, which of the following must be true?

I. 9/xis an integer.

II. 12/x is an integer.

III. 36/x is an integer.

144 = 2^4 * 3^2
108 = 2^2 * 3^2
common factors = 2 * 2 * 3 * 3
so the values of x could be in total 9 (1, 2, 3, 4, 6, 9, 12, 18, 36)
For must be true we need to find out if the given expressions in I, II, III are intergers for ALL values of x.
and only 36/x will be an integer for all values of x.
I .. 9/x -- this is not an integer if x is 2,4,6,12,18,36
II .. 12/x -- this is not an integer if x is 9, 18,36
III .. 36/x -- this is an integer for all values of x

B
Senior Manager
Senior Manager
User avatar
Joined: 19 Nov 2007
Posts: 477
Followers: 3

Kudos [?]: 51 [0], given: 4

GMAT ToolKit User
Re: Which of the following must be true? [#permalink] New post 26 Feb 2010, 09:31
ro86 wrote:
If 144/x is an integer and 108/x is an integer, which of the following must be true?

I. 9/xis an integer.

II. 12/x is an integer.

III. 36/x is an integer.

A) I only
B) III only
C) I and II only
D) II and III only
E) I, II, and III

In a post in november last year this question was solved with option B as the answer.

Here we come to know that the maximum value of x =36.
But the minimum values for x can be 2 or 3.

hence 12/x and 36/x can be an integer. hence the answer can be option D and not option B.

I choose that 12/x can be an integer as x can be 2 or 3.


Am i missing something here pls explain.


You have to consider all values of 'x', not just 2 or 3.
Only B satisfies this.

_________________

-Underline your question. It takes only a few seconds!
-Search before you post.

Manager
Manager
avatar
Joined: 29 Oct 2009
Posts: 203
Concentration: General Management, Sustainability
WE: Consulting (Computer Software)
Followers: 2

Kudos [?]: 56 [0], given: 12

Re: Which of the following must be true? [#permalink] New post 26 Feb 2010, 09:35
I think, here we should use the greatest common factor.
The greatest common factor for 144 and 108 is 36.
So 36/x is an integer.
For the rest of the answers, if x is 36 then 9/x and 12/x leads to fractions.

Ans is B.
Intern
Intern
avatar
Joined: 04 Mar 2010
Posts: 2
Followers: 0

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

Re: Which of the following must be true? [#permalink] New post 05 Mar 2010, 12:20
ro86 wrote:
If 144/x is an integer and 108/x is an integer, which of the following must be true?

I. 9/xis an integer.

II. 12/x is an integer.

III. 36/x is an integer.

A) I only
B) III only
C) I and II only
D) II and III only
E) I, II, and III

In a post in november last year this question was solved with option B as the answer.

Here we come to know that the maximum value of x =36.
But the minimum values for x can be 2 or 3.

hence 12/x and 36/x can be an integer. hence the answer can be option D and not option B.

I choose that 12/x can be an integer as x can be 2 or 3.
Am i missing something here pls explain.


The question says, which of the following must be true? Why can it not be assumed that x = 12 or 9 or 36; All 3 of these numbers are divisible by both 144 and 108

Any insight?? For these type of questions do we always take the Largest common factor?
Senior Manager
Senior Manager
User avatar
Joined: 19 Nov 2007
Posts: 477
Followers: 3

Kudos [?]: 51 [0], given: 4

GMAT ToolKit User
Re: Which of the following must be true? [#permalink] New post 05 Mar 2010, 16:22
aisha14 wrote:
ro86 wrote:
If 144/x is an integer and 108/x is an integer, which of the following must be true?

I. 9/xis an integer.

II. 12/x is an integer.

III. 36/x is an integer.

A) I only
B) III only
C) I and II only
D) II and III only
E) I, II, and III

In a post in november last year this question was solved with option B as the answer.

Here we come to know that the maximum value of x =36.
But the minimum values for x can be 2 or 3.

hence 12/x and 36/x can be an integer. hence the answer can be option D and not option B.

I choose that 12/x can be an integer as x can be 2 or 3.
Am i missing something here pls explain.


The question says, which of the following must be true? Why can it not be assumed that x = 12 or 9 or 36; All 3 of these numbers are divisible by both 144 and 108

Any insight?? For these type of questions do we always take the Largest common factor?

You can very well assume that x = 1 or 9 or 36. That's why the ans is 36/x.
_________________

-Underline your question. It takes only a few seconds!
-Search before you post.

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23055
Followers: 3535

Kudos [?]: 27190 [0], given: 2725

Re: If 144/x is an integer and 108/x is an integer, which of the [#permalink] New post 12 Nov 2013, 09:19
Expert's post
ro86 wrote:
If 144/x is an integer and 108/x is an integer, which of the following must be true?

I. 9/x is an integer
II. 12/x is an integer
III. 36/x is an integer

A. I only
B. III only
C. I and II only
D. II and III only
E. I, II and III


The question asks which of the following MUST be true, not COULD be true. The largest possible value of x is 36, GCD of 144 and 108, and if x=36 then ONLY III is true.

Answer: B.

Check more Must or Could be True Questions to practice: search.php?search_id=tag&tag_id=193

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-144-x-is-an-integer-and-108-x-is-an-integer-which-of-the-128415.html
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Re: If 144/x is an integer and 108/x is an integer, which of the   [#permalink] 12 Nov 2013, 09:19
    Similar topics Author Replies Last post
Similar
Topics:
3 Experts publish their posts in the topic If 144/x is an integer and 108/x is an integer, which of the BN1989 6 01 Mar 2012, 09:08
2 Experts publish their posts in the topic X is divisible by 144. If X^1/3 is an integer, then which of lylymenko 3 30 Mar 2010, 16:48
5 Experts publish their posts in the topic If 144/x is an integer and 108/x is an integer, which of Navigator 9 03 Nov 2009, 22:08
Which of the following integers is a divisor of alimad 1 18 May 2008, 04:47
If s and t are distinct positive integers, which of the MA 3 24 Jan 2005, 16:57
Display posts from previous: Sort by

If 144/x is an integer and 108/x is an integer, which of the

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.