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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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26 Feb 2010, 06:55
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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:
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

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Last edited by Bunuel on 12 Nov 2013, 10:17, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
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Re: Which of the following must be true? [#permalink]

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26 Feb 2010, 07:55
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.
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Re: Which of the following must be true? [#permalink]

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26 Feb 2010, 08:42
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
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Re: Which of the following must be true? [#permalink]

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26 Feb 2010, 10:31
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.

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Re: Which of the following must be true? [#permalink]

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26 Feb 2010, 10:35
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.
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Re: Which of the following must be true? [#permalink]

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05 Mar 2010, 13:20
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?
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Re: Which of the following must be true? [#permalink]

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05 Mar 2010, 17:22
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.
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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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12 Nov 2013, 10:19
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BOOKMARKED
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.

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
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Re: If 144/x is an integer and 108/x is an integer, which of the   [#permalink] 12 Nov 2013, 10:19
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