Which of the following could be the greatest . . .

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pm; Thanked: 6 times; Followed by:5 members

Which of the following could be the greatest . . .

by Vincen » Fri Sep 29, 2017 6:48 pm

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 OA is E.

I don't know how can I solve this PS question. I need some help. Thanks.

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Source: Beat The GMAT — Problem Solving | Fri Sep 29, 2017 6:48 pm

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pm; Location: Palo Alto, CA; Thanked: 2867 times; Followed by:511 members; GMAT Score:800

by [email protected] » Sat Sep 30, 2017 3:58 pm

Hi Vincen,

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.
Eliminate Answers A and D.

II. A

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

III. A - B

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

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8085; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Thu Jan 11, 2018 1:50 pm

Vincen 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.

Answer: E

Scott Woodbury-Stewart
Founder and CEO
[email protected]