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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] New post 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.
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Re: If 144/x is an integer and 108/x is an integer, which... [#permalink] New post 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

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

Answer: B.

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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If 144/x is an integer and 108/x is an integer, which of the [#permalink] New post 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] New post 26 May 2014, 03:32
can admin please help on this one.........
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] New post 26 May 2014, 05:32
Expert's post
tyagigar wrote:
can admin please help on this one.........
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


I think your doubt is addressed here: if-144-x-is-an-integer-and-108-x-is-an-integer-which-of-the-128415.html#p1058688

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:
if-n-is-a-positive-integer-and-n-2-is-divisible-by-96-then-127364.html
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if-5400mn-k-4-where-m-n-and-k-are-positive-integers-109284.html

Hope this helps.
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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.


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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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