Question: Is k Divisible by 18?

Comment on Is k Divisible by 18?

I solved it in this way.
1) 2k is divisible by 9. Lets take 2k = 9 then k = 4.5. but k must be an integer. so take 2k=18, then k = 9 which is not divisible by 18.
when 2k=36, k = 18 which is divisible by 18.
So statement 1 is not sufficient.
2) 9k is divisible by 2 which means 9k is even
so, k must be even which means k can be.
But 2 is not divisible by 18.
Same time 18 is also even, 18 is divisible by 18. So statement 2 is also not sufficient.
Combining we can say, k must be even and divisible by 9. so obviously as it includes 2, 2 x (multipliers of 9) always will be divided by 18. So, Answer is C.
gmat-admin's picture

Perfect!

Can we just say:

1: 2 isn´t divisible by 9, so k has to be.

2: 9 isn´t divisible by 2, so k has to be.

1 & 2: k is divisible by 9 and 2, so it has to be divisible by 2 times 9.

Thanks for your thoughts.
gmat-admin's picture

I agree with "1 & 2: k is divisible by 9 and 2, so it has to be divisible by 2 times 9."

For your first 2 comments, I'm not sure what you mean by "so k has to be"
Has to be what?

I meant to say:

1: 2 isn´t divisible by 9, so k has to be divisible by 2. However, maybe not by 18.

2: 9 isn´t divisible by 2, so k has to be divisible by 9. However, maybe not by 18.

and then combining, k needs to be div. by 2 and 9, thus also 18.

are the assumptions based on 1 and 2 ok that way?
gmat-admin's picture

Yes, that's correct.

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