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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]

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01 Mar 2012, 09:08
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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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Re: If 144/x is an integer and 108/x is an integer, which... [#permalink]

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01 Mar 2012, 09:36
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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]

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15 Mar 2012, 02:38
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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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Re: If 144/x is an integer and 108/x is an integer, which... [#permalink]

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

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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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Re: If 144/x is an integer and 108/x is an integer, which of the [#permalink]

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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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Re: If 144/x is an integer and 108/x is an integer, which of the [#permalink]

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26 May 2014, 05:32
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?

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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]

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Re: If 144/x is an integer and 108/x is an integer, which of the [#permalink]

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04 Nov 2015, 14:09
I attacked this question in a different way:
prime factorization of 144 = 2*2*2*2*3*3 = so we have four 4's and two of 3's
prime factorization of 108 = 2*2*3*3*3 = we have two of 2's and three of 3's.

I 9/x is an integer. well, if x is 3*3 = then yes, 9/x is an integer.
but if x is 2*2*3*3 = then 9/x is not divisible. since our question asks for must be true -> we know for sure that I is not true.
Eliminate (A) I only, (C) I and II only, and (E) I, II, and III

II 12/x is an integer
well, if x is 2*2*3 = or 2*2 or 2*3 = then yes, 12/x is an integer, but x can be 3*3*2.
since it is a must be true, we can eliminate E, and thus B is the answer.
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Re: If 144/x is an integer and 108/x is an integer, which of the [#permalink]

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16 Mar 2016, 01:16
BN1989 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

highest common factor of 144 and 108 is 36. x can be any of the factors of 36. So if x is 36 then I and II are wrong.
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Re: If 144/x is an integer and 108/x is an integer, which of the [#permalink]

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18 Mar 2016, 14:44
Hi guys, I still can't understand in which case I should use LCM and when GCF... Can you please rephrase the question the way that to solve it I would need to use LCM technique?

Thanks!
Re: If 144/x is an integer and 108/x is an integer, which of the   [#permalink] 18 Mar 2016, 14:44
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