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

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If 144/x is an integer and 108/x is an integer, which of the [#permalink]  01 Mar 2012, 09:08
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Question Stats:

53% (02:18) correct 47% (01:04) wrong based on 139 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: OA

Last edited by Bunuel on 15 Mar 2012, 02:39, edited 1 time in total.
Edited the question
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Kudos [?]: 338 [1] , given: 108

Re: If 144/x is an integer and 108/x is an integer, which... [#permalink]  01 Mar 2012, 09:36
1
KUDOS
36 is the greatest common factor for 144 and 108, so the greatest possible value of X = 36

so, only III is true for all values X

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Re: If 144/x is an integer and 108/x is an integer, which... [#permalink]  15 Mar 2012, 02:28
Hi,

I didnt get this one. The q askes for which one of the following is an integer. So i plugged in nos. to see, and found that each option is has divisors. On what basis is the answer 36 as d qustn askes for "is an integer" and not greatest factor?

Pls explain,
Thnx
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Kudos [?]: 42146 [1] , given: 5957

Re: If 144/x is an integer and 108/x is an integer, which... [#permalink]  15 Mar 2012, 02:38
1
KUDOS
Expert's post
priyalr wrote:
Hi,

I didnt get this one. The q askes for which one of the following is an integer. So i plugged in nos. to see, and found that each option is has divisors. On what basis is the answer 36 as d qustn askes for "is an integer" and not greatest factor?

Pls explain,
Thnx

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.

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

Hope it helps.
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Kudos [?]: 124 [0], given: 91

If 144/x is an integer and 108/x is an integer, which of the [#permalink]  03 Feb 2013, 11:24
If $$\frac{144}{x}$$ is an integer, and $$\frac{108}{x}$$ is an integer, which of the following must be true?

I. $$\frac{9}{x}$$ is an integer
II. $$\frac{12}{x}$$ is an integer
III. $$\frac{36}{x}$$ is an integer

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

Source: Gmat Hacks 1800 set.

This is a repost, but the previous postings are still confusing. So the way I read this is "If $$\frac{144}{2}$$ is an integer and $$\frac{108}{2}$$ is an integer .." but that reasoning seems to be wrong, can someone explain why?

Edit - I get it now. It's the "MUST BE TRUE" part that I forgot to factor into. Anyway, if you get that part, this is pretty easy question.
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Kudos [?]: 1 [0], given: 28

Re: If 144/x is an integer and 108/x is an integer, which of the [#permalink]  26 May 2014, 03:32
the way i see is x can be 1 or 2 or 3

how do we decide whether 9/x , 12/x or 36/x is an integer if i chose x as 1 still {144}/{x} is an integer, and {108}/{x} is also an integer...same happens when i chose 2 but x as 1 and x as 2 given me differnt answer choices
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Kudos [?]: 42146 [0], given: 5957

Re: If 144/x is an integer and 108/x is an integer, which of the [#permalink]  26 May 2014, 05:32
Expert's post
tyagigar wrote:
the way i see is x can be 1 or 2 or 3

how do we decide whether 9/x , 12/x or 36/x is an integer if i chose x as 1 still {144}/{x} is an integer, and {108}/{x} is also an integer...same happens when i chose 2 but x as 1 and x as 2 given me differnt answer choices

x could be 1, 2, 3, 4, 6, 9, 12, 18 or 36 (these are common factors of 144 and 108). The question asks which of the options MUST be an integer. Now, only 36/x is an integer for all possible values of x.

Does this make sense?

Similar questions to practice:
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Hope this helps.
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Re: If 144/x is an integer and 108/x is an integer, which of the   [#permalink] 26 May 2014, 05:32
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