Data Sufficiency

Is the integer divisible by 6?

1)The GCF of z and 12 is 3.
2)THE GCF of z and 15 is 15.

Can someone help me with this problem? A


when the GCF of z and 12 is 3...it is possible that z is the number 3, which woul make it insufficient.

The answer is A
Statement I alone is sufficient.
When the GCF is 3 for example 12 and 15 or 12 and 9, the number will not be divisible by 6.
When you consider the other numbers like 18, 24 etc the GCF will be 6.

Statement II not sufficient
When the GCF is 15, the numbers can be 15, 30,45, 60 etc which may or may not be divisible by 6

Hence I alone is sufficient

batman73 wrote:Is the integer divisible by 6?

1)The GCF of z and 12 is 3.
2)THE GCF of z and 15 is 15.

Can someone help me with this problem? A


when the GCF of z and 12 is 3...it is possible that z is the number 3, which woul make it insufficient.

restate question: does z have the factos 2 and 3?

statement 1)

GCF of z and 12 is 3 means that z can only be 3.

z in statement does not have both factors 2 and 3. it only has 3. which means z is not divisible by 6. Sufficient. remember this is yes/no questions. If you can definitively answer yes and no with the info given in statement it is sufficient.

Statement 2)

GCF of z and 15 is 15 means z could be 15, 30,.... if z is 30 it is divisible by 6. however if z is 15 it is not divisible by 6. we have conflicting solutions. hence, not sufficient.

A is the winner.