Manhattan Question Set # 4

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richachampion: Legendary Member; Posts: 698; Joined: Tue Jul 21, 2015 12:12 amFollowed by: 26 members; Location: Noida, India; Thanked: 32 times; GMAT Score:740

by richachampion » Sun Oct 09, 2016 5:57 pm

What is the greatest common factor of positive integers a and b?

(1) a = b + 4
(2) b/4 is an integer

OA: C

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Source: Beat The GMAT — Problem Solving | Sun Oct 09, 2016 5:57 pm

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by [email protected] » Sun Oct 09, 2016 7:47 pm

Hi richachamption,

To start, this should be in the DS Forum. That having been said, this prompt can be solved rather easily by TESTing VALUES.

We're told that A and B are POSITIVE INTEGERS. We're asked for the greatest common factor (GCF) of A and B.

1) A = B + 4

IF... B=1 and A=5 then the GCF = 1
IF... B=2 and A=6 then the GCF = 2
Fact 1 is INSUFFICIENT

2) B/4 is an integer

This fact tells us that B is a MULTIPLE of 4, but tells us nothing about A.
Fact 2 is INSUFFICIENT

Combined we know...
A = B + 4
B is a multiple of 4

Adding a multiple of 4 to another multiple of 4 will give you a SUM that is a multiple of 4, so the GCF of A and B will always be 4. Here's proof.

IF... B=4 and A=8 then the GCF = 4
IF... B=8 and A=12 then the GCF = 4
IF... B=12 and A=16 then the GCF = 4
IF... B=16 and A=20 then the GCF = 4
Etc.
Combined, SUFFICIENT

Final Answer: C

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Rich

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richachampion: Legendary Member; Posts: 698; Joined: Tue Jul 21, 2015 12:12 amFollowed by: 26 members; Location: Noida, India; Thanked: 32 times; GMAT Score:740

by richachampion » Fri Oct 14, 2016 3:09 am

[email protected] wrote: Final Answer: C

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

Can you guide me from where should I get the theory of GCF?

R I C H A,
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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Fri Oct 14, 2016 6:23 am

richachampion wrote: Can you guide me from where should I get the theory of GCF?

Here are a few videos that will help:
- Divisor Rules: https://www.gmatprepnow.com/module/gmat ... /video/831
- Greatest Common Divisor (GCD): https://www.gmatprepnow.com/module/gmat ... /video/833
- Least Common Multiple (LCM): https://www.gmatprepnow.com/module/gmat ... /video/835
- The GCD-LCM Formula: https://www.gmatprepnow.com/module/gmat ... /video/836

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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by [email protected] » Fri Oct 14, 2016 12:19 pm

Hi richachamption,

From a 'math standpoint', both Great Common Factor (GCF) and Least Common Multiple (LCM) can be solved with prime-factorization - and I'm sure that you could find plenty of online practice materials that would explain both in detail. However, as GMAT subjects, they're relatively rare though - you might only see each just 1-2 times on the Exam. In many cases, TESTing VALUES will get you to the correct answer relatively quickly, so there isn't much of a 'reward' for learning all of the little intricacies of these two concepts.

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

Contact Rich at [email protected]

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Fri Oct 14, 2016 11:07 pm

richachampion wrote:What is the greatest common factor of positive integers a and b?

(1) a = b + 4
(2) b/4 is an integer

OA: C

Question : greatest common factor of positive integers a and b?

Statement 1: a = b + 4

@b=1, a=5 and GCD = 1
@b=2, a=6 and GCD = 2
NOT SUFFICIENT

Statement 2: b/4 is an integer
i.e b must be a multiple of 4 but
There is no information of a so
NOT SUFFICIENT

Combining the two statements
@b=4, a=8 and GCD = 4
@b=8, a=12 and GCD = 4
@b=12, a=16 and GCD = 4
@b=16, a=20 and GCD = 4
Since now a and b are two consecutive multiples of 4 therefore GCD will always be 4
SUFFICIENT

Answer: Option C

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