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Question
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.
(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not.
(B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not.
(C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question.
(E) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question.
(1) x+y = 12. We know x or y cannot be 2, since either one being 2 will result in the other not being a prime number. x or y also cannot be 3. So the (x,y) pair can be (5,7) or (7,5).
If x = 5, y = 7, then the question is to arrange 5 people in 7 chairs. The # of ways to do this is 7P5 = 7!/2!.
If x = 7, y=5, then the question is to arrange 7 people in 5 chairs. Again, the # of ways to do this is 7P5 = 7!/2!.
So no matter which pair we take, we end up with the same number and so we can answer the question. Statement 1 is therefore sufficient.
(2) There are more chairs than people. For this, there are many possible (x,y) pairs and so there is no single answer. Statement 2 is therefore insufficient.
because say x =7 ,y =5 total ways is 7p5 = 7!/2! = 7*6*5*4*3
when x =5 and y =7 take it this way
first one has 7 option to choose from ----7
second has 6 option to choose from -----7*6
third has 5 option to choose from -----7*6*5
fourth has 4 option to choose from ----7*6*5*4
last has 3 option to choose from ----- 7*6*5*4*3
so in both cases we get the same ans ...hence A is the right choice .