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

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

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

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