M15#11

Thanks Bunuel for the reply. That make sense now. I did a similar problem on MGMAT CAT. The difference is that on the MGMAT problem there is a constrain of x < y < 0

If x and y are integers such that x < y < 0, what is x – y?

(1) (x + y)(x – y) = 5

(2) xy = 6

Official Explanation:
The problem stem tells you that x and y are both negative integers, and x is less than y. You are asked for the value of x – y. Note that in order to answer this question, you might not need the separate values of x and y; however, if you can find those separate values, then you can solve for x – y or any other “combo.”

(1) SUFFICIENT: This statement is tricky. One approach is to distribute the left side to get the difference of squares:

x2 – y2 = 5

Now, since both x and y are integers, x2 and y2 are integers as well. Let’s look at the sequence of squares, and consider their differences (we can leave out zero, since neither x nor y can be zero):

1 4 9 16 25 36…
Diff = 3 5 7 9 11…

As you can see, the difference between squares grows as the squares themselves get larger. The only difference between two squares that equals 5 is the difference between 4 and 9. Since x and y are both negative, this tells us that x = –3 and y = –2; therefore, x – y = –1.

Alternatively, we could note that both x + y and x – y are themselves integers. Looking at the statement, we have
(x + y)(x – y) = 5
int × int = 5

The only possible integer pairs that give 5 as a product are (5, 1) and (-5, -1), since 5 is prime. Now, because both x and y are negative, the (5, 1) pair won’t work either way (either with x + y = 5 or with x + y = 1). So let’s try (-5, -1):

x + y = –5
x – y = –1

Adding these two equations, we get 2x = -6, or x = -3. Substituting back into x + y = –5, we get y = –2. (If we had assigned x + y = –1 and x – y = –5, we would have gotten y = 2, which doesn’t fit the problem constraints.)

(2) INSUFFICIENT: There are two pairs of integers that fit the constraint x < y < 0 and the statement xy = 6: (-3)(-2) = 6 AND (-6)(-1) = 6.

The correct answer is A.