Seven family members are seated around their circular dinner table. If only arrangements that are considered distinct are those where family members are seated in different locations relative to each other, and Michael and Bobby insist on sitting next to one another, then how many distinct arrangements around the table are possible?

A. 120
B. 240
C. 360
D. 480
E. 720

Are you sure you got the right OA on this one ?

As I see it : 7 members, and Michael & Bobby sit together. So treat those two like a single person. Now you have to arrange 6 people around a table. This may be done in 5! or 120 ways

The number of ways to arrange Michael & Bobby is 2 (MB or BM).

So net there are 240 ways or B

I don't think this is a GMAT level question, may be a tad too hard
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If Bobby and Michael must sit next to each other, we treat them as a single entity, and that leaves us with 6 total spots to arrange. Using the circular permutations formula (n - 1)!, we have

(6 - 1)! = 5! = 120 ways to arrange the family members with Bobby and Michael together.

However, we also must include the number of ways to arrange Bobby and Michael, which is 2P2 = 2! = 2.

So, in total, we have:

(6 - 1)! * 2! = 120 x 2 = 240

Answer: B
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