Disagreement with MGMAT Practise question

[bfman]

MGMAT Guide 1. 4th Edition. Number Properties. Page 120.
Here is the question:

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.

Book says answer is A, and z is NOT divisible by 6.

I disagree because considering Statement 1, z could be 6 as well as 12, no? In which case it will be divisible by 6.

What do you guys think?

To me, it seems like answer is E. Neither is sufficient.

[bfman]

ahh nevermind I got it.. if it was 6 or 12 then GCF would be 6 or 12... ahh.. I'm gonna fail this thing

[rahulmehra13]

IMO A.

1st thing z cannot be equal to 6 coz if z = 6 the HCF of 6 & 12 will be 6 and not 3.

(To find the GCF of given numbers, resolve the numbers into their prime factors and then pick the
common term(s) from them and multiply them if more than one.)

6 = 2 * 3
12 = 2 * 2 * 3
GCF = 2*3 = 6

Similarly if z =12 the GCF of 12 & 12 will be 12 and not 3.


to have 3 as GCF of z & 12, z can be = 3,9,15,21 and so on

In any case z wont be divisible by 6.

Note : If z is a multiple of 6 then GCF of z & 12 will always be 6 or 12.

Stmnt 2:

The greatest common factor of z and 15 is 15

In this case z can be 15,30,45..

30 is divisible by 6 but 15 is not.

Insufficient.

[apoorva.srivastva]

The question is a Yes/No type DS.

so "NO" too is an answer....Hence A is sufficient as per the reasoning that rahul has enlisted is simply awesome!!

[bfman]

Well yeah. Rahul has listed the same strategy which MGMAT uses.
I was just having problem bcuz I've been out of practice for way too long

Thank you Rahul.

[rahulmehra13]

You are welcome