Is z divisible by 6? (1) The greatest common factor between

Question

Is z divisible by 6?
(1) The greatest common factor between 12 and z is 3.
(2) The greatest common factor between 15 and z is 15.

Please explain.

maliyeci · Answer

IMO A

If GCF of z and 12 is 3. That means z can be divided by 3 but can not be divided by 2. Thus z can not be divided by 6. So 1 is sufficient.

if gcf of z and 15 is 15 than z can be divided by 15 and 5 and 3. But this does not guarantee that z can be divided by 6. Because we can not see 2 as a factor. But it can be. Say that z is 30. But may be not. say that z is 45. So 2 is insufficient.

topher · Answer

Can you please explain this sentence: "That means z can be divided by 3 but can not be divided by 2."

How do you know this?

Also sorry but I don't have the OA on me right now. This is actually a problem from the MGMAT Number Prop's book.

maliyeci · Answer

factors of 12 are 2x2x3. If gcf of z and 12 is 3. That means z can not be divided by 2. If z could be divided by 2, than gcf of z and 12 might be minimum 6.

mdfrahim · Answer

Is z divisible by 6?
(1) The greatest common factor between 12 and z is 3.
(2) The greatest common factor between 15 and z is 15.

Stmt 1.
Lets calculate he gcf of 12 and Z.
12 = 2 * 2 * 3
Z = 3 * X * Y * Z *...............(Z can be anything)..............1
-----------------
GCF = 3
See to calculate the GCF betweem two numbers we look at the common facors between the two. 
Since GCF is 3 we know that common factor between 12 and Z is only 3. We don' care about any factors of Z what we care is that any of the factor of Z can no be 2 because in that case gcf would not have been 3.
Since we can not have 2 as any of the factor of z it can not be divible by 6.
Suff.

Stmt 2.
Lets calculate he gcf of 15 and Z.
15 = 3 * 5
Z = 3 * 5 * X * Y* Z.................(Z can be anything)
------------------------------------------
GCF = 15
In this case if we assume X = 1 then GCF = 15 and if we assume X = 2 then also GCF = 15.
However when X = 1 , Z is not divisible by 6.
But when X = 2 , Z is divisible by 6.
Insuff.

bigtreezl · Answer

1)in order for z to be divisible by 6 it must have 2 and 3 in it. We know it has three and we know it doesnt have two, otherwise the GCF would be at least 6. suff

2)we know that z has 3 and 5 in it, but we dont know if it has two in it. insuff

topher · Answer

Thank you all for the responses. I understand now. For some reason I was having a hard time wrapping my head around this concept when I was reading the book. Thanks again.

Is z divisible by 6? (1) The greatest common factor between

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