SOLUTION WITH EXPLANATION :
This question is simply asking us to come up with the number of permutations that can be formed when x people are seated in y chairs. It would seem that all we require is the values of x and y. Let's keep in mind that the question stem adds that x and y must be prime integers.
(1) SUFFICIENT: If x and y are prime numbers and add up to 12, x and y must be either 7 and 5 or 5 and 7. Would the number of permutations be the same for both sets of values?
Let's start with x = 7, y = 5. The number of ways to seat 7 people in 5 positions (chairs) is 7!/2!. We divide by 2! because 2 of the people are not selected in each seating arrangement and the order among those two people is therefore not significant. An anagram grid for this permutation would look like this:
A B C D E F G
1 2 3 4 5 N N
But what if x = 5 and y = 7? How many ways are there to position five people in 7 chairs? It turns out the number of permutations is the same. One way to think of this is to consider that in addition to the five people (A,B,C,D,E), you are seating two ghosts (X,X). The number of ways to seat A,B,C,D,E,X,X would be 7!/2!. We divide by 2! to eliminate order from the identical X's.
(2) INSUFFICIENT: This statement does not tell us anything about the values of x and y, other than y > x. The temptation in this problem is to think that you need statement 2 in conjunction with statement 1 to distinguish between the x = 5, y= 7 and the x = 7, y = 5 scenarios.
ps : i dont know the source!
The more you suffer before the test, the less you will do so in the test!
