Data Sufficiency

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

Thanks a lot,
Sri

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

Stuart Kovinsky wrote:

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

Hello Stuart,

Thank you very much for your explanation. It is clear now. I just had a question here. Here we have:

(rootx - rooty)^2 = 1
x - 2root(xy) - y = 1


Can (rootx - rooty)^2 also be written as x - 2root(xy) + y ?

Thanks again for your help.

Best Regards,
Sri