The question asks us to figure out the PERIMETER of rectangle Q. For that, we'll need the length (L) and width (W) of the rectangle.
1) Each diagonal of rectangle Q has length 10.
From this Fact, we can create one equation:
L^2 + W^2 = 10^2
Unfortunately, there are lots of different values for L and W here (and most of them are non-integers), so there are lots of possible perimeters. Here are two possibilities:
L = 6, W = 8... Perimeter = 28
L = 1, W = (Root99)... Perimeters = 2 + 2(Root99)
Fact 1 is INSUFFICIENT
2) The area of rectangle Q is 48.
From this Fact, we can create one equation:
(L)(W) = 48
Again though, there are lots of different values for L and W here, so there are lots of possible perimeters. Here are two possibilities:
L = 6, W = 8... Perimeter = 28
L = 1, W = 48... Perimeter = 98
Fact 2 is INSUFFICIENT
Combined, we know...
L^2 + W^2 = 10^2
(L)(W) = 48
We have a 'system' of equations here - two variables and two unique equations. Since rectangles cannot have "negative sides", there's just one solution to this system (and it happens to be 6 and 8, although you don't have to do that work).
Combined, SUFFICIENT
Final Answer:
It's certainly important to have strong basic 'math skills', but the Quant section of the GMAT is NOT a 'math test' - it's a critical thinking Test - so you should adjust your 'view' of that section accordingly.
GMAT assassins aren't born, they're made,
Rich