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Manhattan Question Set # 4

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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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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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by richachampion » Fri Oct 14, 2016 3:09 am
[email protected] wrote: Final Answer: C

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

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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.

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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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