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Manager  Joined: 21 Jan 2014
Posts: 93
GMAT 1: 500 Q32 V28 GPA: 4
Which of the following could be the greatest common factor of positive  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 55% (01:00) correct 45% (01:02) wrong based on 378 sessions

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Which of the following could be the greatest common factor of positive integers a and b?

I. 1
II. a
III. a-b

A) II only
B) I and II only
C) I and III only
D) II and III only
E) I, II and III
Math Expert V
Joined: 02 Sep 2009
Posts: 59725
Re: Which of the following could be the greatest common factor of positive  [#permalink]

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5
2
pepo wrote:
which of the following could be the greatest common factor of positive integers a and b?

I. 1
II. a
III. a-b

A) II only
B) I and II only
C) I and III only
D) II and III only
E) I, II and III

It could be 1 if a and b are co-prime, for example, 1 and 2, 11 and 13...

It could be a itself if a is a factor of b, for example, 2 and 4, 5 and 15...

It could be a-b, for example, when a=b+1: a=2 and b=1, a=3 and b=2...

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Intern  Joined: 09 Nov 2015
Posts: 1
Re: Which of the following could be the greatest common factor of positive  [#permalink]

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Bunuel wrote:
pepo wrote:
which of the following could be the greatest common factor of positive integers a and b?

I. 1
II. a
III. a-b

A) II only
B) I and II only
C) I and III only
D) II and III only
E) I, II and III

It could be 1 if a and b are co-prime, for example, 1 and 2, 11 and 13...

It could be a itself if a is a factor of b, for example, 2 and 4, 5 and 15...

It could be a-b, for example, when a=b+1: a=2 and b=1, a=3 and b=2...

Since greatest is asked it should be a single number not 3 numbers.
Correct me if I'm wrong
Math Expert V
Joined: 02 Sep 2009
Posts: 59725
Re: Which of the following could be the greatest common factor of positive  [#permalink]

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Raahan wrote:
Bunuel wrote:
pepo wrote:
which of the following could be the greatest common factor of positive integers a and b?

I. 1
II. a
III. a-b

A) II only
B) I and II only
C) I and III only
D) II and III only
E) I, II and III

It could be 1 if a and b are co-prime, for example, 1 and 2, 11 and 13...

It could be a itself if a is a factor of b, for example, 2 and 4, 5 and 15...

It could be a-b, for example, when a=b+1: a=2 and b=1, a=3 and b=2...

Since greatest is asked it should be a single number not 3 numbers.
Correct me if I'm wrong

The question asks which of the following could be the greatest common factor (GCF) of positive integers a and b? All three (for different cases) could be the greatest common factors of a and b. So, the answer is E.
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Re: Which of the following could be the greatest common factor of positive  [#permalink]

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Bunuel

In the third case (a-b), a and b can also be 6 and 4?
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Posts: 59725
Re: Which of the following could be the greatest common factor of positive  [#permalink]

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Shiv2016 wrote:
Bunuel

In the third case (a-b), a and b can also be 6 and 4?

Yes. The greatest common factor of 6 and 4 is 2.
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Re: Which of the following could be the greatest common factor of positive  [#permalink]

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The GCF of 4,10 is 2, which does not fall into any of the 3 categories right?
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Joined: 27 Dec 2016
Posts: 309
Re: Which of the following could be the greatest common factor of positive  [#permalink]

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Hi,

I am confused with the second option. If a and b were 2 and 3, their GCF would have been 1. How is second option still sufficient? Please explain!

Thanks!
Math Expert V
Joined: 02 Sep 2009
Posts: 59725
Which of the following could be the greatest common factor of positive  [#permalink]

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1
sasidharrs wrote:
The GCF of 4,10 is 2, which does not fall into any of the 3 categories right?

csaluja wrote:
Hi,

I am confused with the second option. If a and b were 2 and 3, their GCF would have been 1. How is second option still sufficient? Please explain!

Thanks!

Notice that the question asks "Which of the following COULD be the greatest common factor of positive integers a and b?" NOT "Which of the following MUST be the greatest common factor of positive integers a and b?"
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Re: Which of the following could be the greatest common factor of positive  [#permalink]

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Bunuel wrote:
sasidharrs wrote:
The GCF of 4,10 is 2, which does not fall into any of the 3 categories right?

csaluja wrote:
Hi,

I am confused with the second option. If a and b were 2 and 3, their GCF would have been 1. How is second option still sufficient? Please explain!

Thanks!

Notice that the question asks "Which of the following COULD be the greatest common factor of positive integers a and b?" NOT "Which of the following MUST be the greatest common factor of positive integers a and b?"

I see now, makes a lot of sense! Thanks a lot Bunuel!!
Manager  B
Joined: 17 Jun 2015
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GMAT 1: 540 Q39 V26 GMAT 2: 680 Q46 V37 Re: Which of the following could be the greatest common factor of positive  [#permalink]

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I took the two positive integers to be 0 and 2.

Proves right across all the three cases,

hence E
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Which of the following could be the greatest common factor of positive  [#permalink]

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1
Hi All,

We're told that A and B are positive integers. We're asked which of the Roman Numerals COULD be the Greatest Common Factor of A and B. We can solve the problem by TESTing VALUES.

I. 1

IF A=1 and B=2, then the GCF = 1. Roman Numeral 1 COULD be true.

II. A

IF A=1 and B=2, then the GCF = 1 (so the GCF = A). Roman Numeral 2 COULD be true.

III. A - B

IF A=2 and B=1, then the GCF = 1 (so the GCF = A-B). Roman Numeral 3 COULD be true.

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Re: Which of the following could be the greatest common factor of positive  [#permalink]

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pepo wrote:
Which of the following could be the greatest common factor of positive integers a and b?

I. 1
II. a
III. a-b

A) II only
B) I and II only
C) I and III only
D) II and III only
E) I, II and III

Let’s analyze each Roman numeral.

I. 1

If a = 4 and b = 7, then their greatest common factor is 1. So I is possible.

II. a

If a = 4 and b = 8, then their greatest common factor is 4, which is a. So II is possible.

III. a - b.

If b = 8 and a = 4, then their greatest common factor is 4, which is a - b. So III is possible.

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Which of the following could be the greatest common factor of positive  [#permalink]

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pepo wrote:
Which of the following could be the greatest common factor of positive integers a and b?

I. 1
II. a
III. a-b

A) II only
B) I and II only
C) I and III only
D) II and III only
E) I, II and III

The main thing to notice is COULD

1. Can it be 1? Yes if both the numbers are prime
2 Can it be a? Yes is a=2 and b=4 ..GCF is 2
3. Can it be a-b? Yes, if a=8 and b=4. the GCF is 4. a-b is also equal to 4 Which of the following could be the greatest common factor of positive   [#permalink] 11 Jan 2018, 15:22
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