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# What is the greatest common divisor of positive integers a

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Manager
Joined: 30 May 2009
Posts: 213
What is the greatest common divisor of positive integers a [#permalink]

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30 Jul 2009, 10:56
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What is the greatest common divisor of positive integers a and b?

(1) a and b share exactly one common factor
(2) a and b are both prime numbers

My Solution

(1) Since all numbers share 1 as the common factor, this statement is sufficient. SUFFICIENT.
(2) If a and b are both prime then they can have one and only one common factor which is 1. Hence SUFFICIENT.

Hence I picked D.

But the solution is given as
[Reveal] Spoiler:
A,
because in statement B what if a=b. Then the greatest common factor will be a (or b since a=b). Hence this statement is insufficient, because

CASE 1 - IF a b are prime and a <> b, then GCF = 1
CASE 2 - IF a b are prime and a = b, then GCF = a

There statement 2 is insufficient.

Now my question is if this were an actual GMAT question, do we have to consider the possibility that a = b? Since the question has used 2 separate alphabets a and b to denote 2 positive integers, why do we have to conider the possibility that a = b?
Senior Manager
Joined: 25 Mar 2009
Posts: 296

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30 Jul 2009, 11:06
I always thought that a would not equal b in a question like this. What is the source? But you have an interesting point here and that's BS if they pull tricks like this.
Director
Joined: 01 Apr 2008
Posts: 847
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014

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30 Jul 2009, 12:36
Awesome trap...
In my opinion, yes..we should also consider the possibility a=b UNLESS it is mentioned that a and b are 'different' integers.
GMAT Tutor
Joined: 24 Jun 2008
Posts: 1346

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30 Jul 2009, 13:35
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Expert's post
It's absolutely possible that a = b, unless the question tells you that a and b are distinct, or something equivalent. They're different letters, but they can certainly represent the same number; this happens all the time in real GMAT questions, just as it does in real mathematics. In the DS section of OG 11, take a look at Statement 2 in Q25 ("i = j"), for example, or Statement 1 in Q27 ("x = y"). These statements would be nonsensical if different letters needed to represent different numbers. You also wouldn't need any statements at all to answer Q99.
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Senior Manager
Joined: 23 Jun 2009
Posts: 355
Location: Turkey
Schools: UPenn, UMich, HKS, UCB, Chicago

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31 Jul 2009, 00:58
Thanks to all of you. There is too much to make attention.
Re: GCF.....trap   [#permalink] 31 Jul 2009, 00:58
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