If a and b are positive integers divisible by 6, is 6 the greatest common divisor of a and b?
(1) a = 2b + 6
(2) a = 3b
OAA
It is given that both a and b are divisible by 6.
1) a = 2b + 6
If I put b=6, then a will be 18, which means 6 is the GCF -- YES
If I put a=6, then b will not be divisible by 6, so that means 6 will not be the GCF -- NO.
So how can A be the answer.
Please explain.
Thanks.
If a and b are positive integers divisible by 6
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Hi rsarashi,
When working through GMAT questions, you have to pay careful attention to the information that you're given. Here, we're told that A and B are POSITIVE INTEGERS divisible by 6.
In your second example, you're thinking about A = 6... but that would give you B = 0... That is NOT allowed here (both variables have to be POSITIVE INTEGERS and 0 is not positive). Working 'up' from your initial example, you could try...
B=6, A=18
B=12, A=30
B=18, A=42
B=24, A=54
Etc.
What is the answer to the question when you consider these possibilities....
GMAT assassins aren't born, they're made,
Rich
When working through GMAT questions, you have to pay careful attention to the information that you're given. Here, we're told that A and B are POSITIVE INTEGERS divisible by 6.
In your second example, you're thinking about A = 6... but that would give you B = 0... That is NOT allowed here (both variables have to be POSITIVE INTEGERS and 0 is not positive). Working 'up' from your initial example, you could try...
B=6, A=18
B=12, A=30
B=18, A=42
B=24, A=54
Etc.
What is the answer to the question when you consider these possibilities....
GMAT assassins aren't born, they're made,
Rich
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When working through GMAT questions, you have to pay careful attention to the information that you're given. Here, we're told that A and B are POSITIVE INTEGERS divisible by 6.
In your second example, you're thinking about A = 6... but that would give you B = 0... That is NOT allowed here (both variables have to be POSITIVE INTEGERS and 0 is not positive). Working 'up' from your initial example, you could try...
B=6, A=18
B=12, A=30
B=18, A=42
B=24, A=54
Etc.
What is the answer to the question when you consider these possibilities....
Thank you so much for your reply. I understood .
Just a quick question, we can not put a=12 because if we put, then b will be 3, and 3 is not divisible by 6. So this case is invalid right?
Please confirm if my understanding is correct.
Thanks.
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Yes, rsarash. That's correct. One must choose examples such that a and b each are divisible by 6, so a = 12 does not work.rsarashi wrote:When working through GMAT questions, you have to pay careful attention to the information that you're given. Here, we're told that A and B are POSITIVE INTEGERS divisible by 6.
In your second example, you're thinking about A = 6... but that would give you B = 0... That is NOT allowed here (both variables have to be POSITIVE INTEGERS and 0 is not positive). Working 'up' from your initial example, you could try...
B=6, A=18
B=12, A=30
B=18, A=42
B=24, A=54
Etc.
What is the answer to the question when you consider these possibilities....
Thank you so much for your reply. I understood .
Just a quick question, we can not put a=12 because if we put, then b will be 3, and 3 is not divisible by 6. So this case is invalid right?
Please confirm if my understanding is correct.
Thanks.
-Jay
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Let's take an Algebraic route to this question.rsarashi wrote:If a and b are positive integers divisible by 6, is 6 the greatest common divisor of a and b?
(1) a = 2b + 6
(2) a = 3b
OAA
It is given that both a and b are divisible by 6.
1) a = 2b + 6
If I put b=6, then a will be 18, which means 6 is the GCF -- YES
If I put a=6, then b will not be divisible by 6, so that means 6 will not be the GCF -- NO.
So how can A be the answer.
Please explain.
Thanks.
We have a and b are positive integers divisible by 6. Say a = 6c and b = 6d, where c and d are integers.
If c and d are co-prime, the answer is yes, the greatest common divisor of a and b is 6. Co-primes do not share a common factor between them except 1.
Statement 1: a = 2b + 6
=> 6c = 12d + 6
=> c = 2d + 1
The numbers d and (2d+1) are co-prime. Thus, the answer is yes, the greatest common divisor of a and b is 6.
You may test few values. Since (2d+1) is an odd number, you must not check with even values of d.
d = EVEN and (2d+1) = ODD are always co-prime.
Say,
1. d = 1, (2d+1) = 3 => 1 and 3 are co-prime
2. d = 3, (2d+1) = 7 => 3 and 7 are co-prime
3. d = 5, (2d+1) = 11 => 5 and 11 are co-prime
Statement 2: a = 3b
Say
1. b = 6 => a = 18. GCD = 6. The answer is yes, the greatest common divisor of a and b is 6.
2. b = 12 => a = 36. GCD = 12. The answer is No, the greatest common divisor of a and b is NOT 6.
The correct answer: A
Hope this helps!
Relevant book: Manhattan Review GMAT Data Sufficiency Guide
-Jay
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Hi rsarashi,rsarashi wrote: Thank you so much for your reply. I understood .
Just a quick question, we can not put a=12 because if we put, then b will be 3, and 3 is not divisible by 6. So this case is invalid right?
Please confirm if my understanding is correct.
Thanks.
That is correct! The prompt explicitly states that both A and B are POSITIVE INTEGERS that are divisible by SIX - so when TESTing VALUES, you have to make sure that you use values that fit those restrictions.
GMAT assassins aren't born, they're made,
Rich