gmattesttaker2 wrote:Hello,
Can you please assist with this:
If x > y > 0, what is the value of x - y ?
(1) sq. root (x) - sq. root (y) = 1
(2) sq. root (x - y) = sq. root (11)
OA: B
Hi Sri!
We know that both x and y are positive and that x is greater than y. We need to find an exact value for (x-y).
1) tells us that root(x) - root(y) = 1
If we square both sides, we get:
(rootx - rooty)^2 = 1
x - 2root(xy) - y = 1
well, since have no clue what x and y are, there's no unique solution that will provide us with x-y.
The trap in (1) is squaring the left side and forgetting that it's a quadratic, not simply (x-y).
We could also just pick numbers to see that (1) is insufficient alone.
If rootx = 9 and rooty = 8, then the statement holds true.
So, x=81 and y=64... x-y = 17
However, we could also pick rootx=8 and rooty=7, also making the statement true.
Now, x=64 and y=49... x-y = 15
Since we get different results, (1) is insufficient.
(2) root(x-y) = root(11)
This time when we square both sides, we get:
(x-y) = 11
Since we're asked to solve for (x-y), we have exactly what we need!
(2) is sufficient, (1) isn't: choose B!
Stuart
