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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 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: if144xisanintegerand108xisanintegerwhichofthe128415.html
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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. Bunuel please suggest?



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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




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







