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GCD

by Deepthi Subbu » Fri Dec 10, 2010 4:00 am
Is the integer z divisible by 6?

1. The greatest common factor of z and 12 is 3
2. The greatest common factor of z and 15 is 15 .

OA after some discussion as am unable to agree with the given OA.
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Source: — Data Sufficiency |
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by shovan85 » Fri Dec 10, 2010 4:37 am
Deepthi Subbu wrote:Is the integer z divisible by 6?

1. The greatest common factor of z and 12 is 3
2. The greatest common factor of z and 15 is 15 .

OA after some discussion as am unable to agree with the given OA.

1. The greatest common factor of z and 12 is 3

GCF(z,12) = 3

Possible values of z with GCF(z,12) = 3 are 3,9,15,21,... I mean any prime number (except 2) multplied to 3.

Also, Quite evident that if z were a multiple of 6 then GCF will be at least 6.

Thus z is not div by 6. (Sufficient)

2. The greatest common factor of z and 15 is 15 .

GCF(z,15) = 15

So, z can be at least 15 and possible values of z are all multiples of 15.

Hence, when z = 15 not div by 6 and when z = 30 is a multiple of 6. (Not Sufficient)

IMO A
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by Rahul@gurome » Fri Dec 10, 2010 4:45 am
Deepthi Subbu wrote:Is the integer z divisible by 6?
1. The greatest common factor of z and 12 is 3
2. The greatest common factor of z and 15 is 15
Statement 1: The greatest common factor of z and 12 is 3.
If z is divisible by 6, then GCD of z and 12 is would have been 6 or 12. But as the GCD is 3 (which means z is divisible by 3 but not by 2), z is not divisible by 6.

Sufficient.

Statement 2: The greatest common factor of z and 15 is 15.
In this case we know for sure that z is divisible by 3 and 5. But z may or may not be divisible by 2. Thus z may or may not be divisible by 6.

Not sufficient.

The correct answer is A.
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by Deepthi Subbu » Fri Dec 10, 2010 10:14 am
Thanks Shovan and Rahul . I had missed the nuances , and couldn't figure out the correct answer . I am clear now :)
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