P&C

vipulgoyal wrote:There are x people and y chairs in a room where x and y are positive prime numbers. How many ways can the x people be seated in the y chairs (assuming that each chair can seat exactly one person)?
(1) x + y = 12
(2) There are more chairs than people.
OAlater

I'm not a big fan of this question.

As mevicks pointed out, if x and y are prime AND x + y = 12, it seems that x = 5 and y = 7 is the only reasonable conclusion since the wording of the question seems to suggest that we can't have more people than chairs. In other words, we can't ask "How many ways can 7 people be seated in 5 chairs" since not all 7 people can be seated. So, it SEEMS that the correct answer must be A.

However, statement 2 suggests that we can't assume that the number of people is less than (or equal) to the number of chairs. In which case, the answer would be C

For these reasons, I don't think this is a very good question.

Cheers,
Brent