What is the greatest common factor of positive integers a and b?
(1) a = b + 4
(2) b/4 is an integer
OA: C
Manhattan Question Set # 4
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- richachampion
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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
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
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Can you guide me from where should I get the theory of GCF?
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Here are a few videos that will help:richachampion wrote: Can you guide me from where should I get the theory of GCF?
- 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
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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
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
- GMATinsight
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Question : greatest common factor of positive integers a and b?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
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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