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P&C

by vipulgoyal » Fri Oct 25, 2013 2:00 am
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.
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by mevicks » Fri Oct 25, 2013 3:31 am
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
Given: x & y are prime numbers.
Q: We need to find out the number of ways in which x people could be assigned to y chairs

St1: x + y = 12
The possible values for x and y are 5 & 7 since x and y are primes

people = 7, seats = 5
No of ways = 7P5 = 7!/(7-5)! = 7*6*5*4*3

people = 5, seats = 7
Use the slot method to find out the no of seats which can be occupied by a person
Chairs -> _7 _6 _5 _4 _3
People -> P1 P2 P3 P4 P5

Both the cases yield the same result, SUFFICIENT

St2: There are more chairs than people
y > x
But several prime numbers fit this criteria, INSUFFICIENT
[spoiler]
Answer : A[/spoiler]
Last edited by mevicks on Fri Oct 25, 2013 4:08 am, edited 1 time in total.
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by Uva@90 » Fri Oct 25, 2013 4:00 am
--Sorry, I have wrongly posted--
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by Brent@GMATPrepNow » Fri Oct 25, 2013 5:43 am
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
Brent Hanneson - Creator of GMATPrepNow.com
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