LGmat wrote:If x and y are positive integers, what is the value of √x + √y (radical of x + radical of y)
(1) x + y = 15
(2) √xy = 6 (radical of (x times y)) = 6
GMAT quant is not really a math test but rather a test of hacking skills and vision.
With that in mind, here's one way to get to the answer to that question.
For Statement 1 I would plug in some numbers to confirm what immediately seems to be the case, that there are multiple possibilities.
11 + 4 = 15 So √x + √y = approximately 3.xx + 2 = 5.xx (something greater than 5)
1 + 14 = 15 So √x + √y = approximately 1 + 3.xx = 4.xx (something less than 5)
So, yes, there are multiple possible answers and Statement 1 is insufficient.
For Statement 2 we could do something similar.
We could use x = 1 and y = 36. So √x + √y = 1 + 6 = 7
Or we could use x = 4 and y = 9. So √x + √y = 2 + 3 = 5
So Statement 2 is insufficient.
Now comes the key part. We have to determine whether we can find the answer by combining the statements, and to do that you have to see something specific. What you need to see is the following.
(√x + √y)² = x + 2√xy + y
That's the same as (x + y) + (2√xy).
We know from Statement 1 that x + y = 15, and from Statement 2 that √xy = 6.
So (x + y) + (2√xy) = 15 + 12 = 27, and we have our answer. Since (√x + √y)² = 27, √x + √y = √27.
You actually don't need to calculate all the way to √27, by the way. Once you notice that (√x + √y)² = x + 2√xy + y, and realize that the two statements give you the values of x + y and 2√xy, you are done.
So combined the statements provide sufficient information and the correct answer is
C.
That explanation may seem long, but it's full of explanatory stuff, and actually, getting the answer takes just quickly plugging in some numbers or otherwise determining that neither statement is sufficient alone and then seeing that (√x + √y)² = x + 2√xy + y.
