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.

In first statement K = 3*3*?*?*?*—— it means K may contain 2 or may not contain 2 in the prime factorisation . Is it right ? If we take K=9 , it has only two 3 s’ and if we take K=36 the prime factorisation contains two 3s and 2 s each. Did I comprehend properly.
gmat-admin's picture

Yes, that's a perfect summary of the concepts involved!

Hi Brent, individual is not sufficient. In both Statements combined that I multiply both 2k/9 * 9k/2 = 18k/18 = K therfore C sufficient.
Is this way of calculation correct? Thanks Brent for your great help always and sorry for too many questins from me :)
gmat-admin's picture

I don't follow your solution.
What do the expressions 2k/9 and 9k/2 represent?
And why does "2k/9 * 9k/2 = 18k/18 = k" make the two combined statements sufficient?

My bad Brent.
2k/9 and 9k/2 are from St 1 and 2.
So in combined I multiply them? Is that possible or not the right way?
gmat-admin's picture

I understand that 2k/9 and 9k/2 are from statements 1 and 2, but why are you dividing 2k by 9, and dividing 9k by 2?
Also, why did you multiply these values?
It's hard for me to tell whether your solution is valid if I can't follow the steps you took.
I need you to tell me more about your rationale.

Hi Brent, I divide 2k by 9 according to the statement that 2k is divisible by 9.
In combined both statements, I multiply these values to see if k is divisible by 9 * 2?
My bad if not explain it properly.
gmat-admin's picture

I would stay clear of that strategy. Here's why:

Let's say the question is:
Is integer k divisible by 11?
(1) 2k divisible by 9
(2) 9k divisible by 2
If we apply the same solution you applied, we conclude that the answer is C, BUT the answer is actually E.

Now consider this question:
Is integer k divisible by 3?
(1) 2k divisible by 9
(2) 9k divisible by 2
If we apply the same solution you applied, we conclude that the answer is C, BUT the answer here is A.

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