_I_ | _II_ | _III_ | _IV_ | _V_ | _VI_

The even places can be filled in 3! ways = 6 ways ( 3 Different adds of Company X )
The remaining places can be filled in 3! ways = 6 ways ( 3 Different adds of companies A, B, and C )

Thus, Total No of ways will be 6*6 = 36 ways...

Hence, Correct answer must be (D) 36..
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Take the task of filling the 6 advertisement spots and break it into stages.

Stage 1: Select an ad for the 1st advertisement spot
We have 3 options (ads from companies A, B or C)
So, we can complete stage 1 in 3 ways

Stage 2: Select an ad for the 2nd advertisement spot
This must be one of the 3 ads from company X
So we can complete stage 2 in 3 ways

Stage 3: Select an ad for the 3rd advertisement spot
We now have 2 options remaining, since we already selected one of the ads from companies A, B or C in stage 1.
So we can complete stage 3 in 2 ways

Stage 4: Select an ad for the 4th advertisement spot
This must be one of the 2 remaining ads from company X
So we can complete stage 4 in 2 ways

Stage 5: Select an ad for the 5th advertisement spot
We now have 1 option remaining, since we already selected two of the ads from companies A, B or C.
So we can complete stage 5 in 1 way

Stage 6: Select an ad for the 6th advertisement spot
This must be the 1 remaining ad from company X
So we can complete stage 6 in 1 way

By the Fundamental Counting Principle (FCP), we can complete all 6 stages (and thus fill all six advertising spots) in (3)(3)(2)(2)(1)(1) ways (= 36 ways)

Answer: D

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.

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