Faster way to solve this?

I'd say write down the list of squares i.e.

1 4 9 16 25 36 49 64

The sum has to be 75. So, try plugging numbers in reverse order
(64, 49, etc.) and get the sum to 75

64 + 11 = 75, can't get 11 as sum using any combination above.
So, ignore.

49 + 25 + 1 = 75, yes. there you have it

You don't have to try numbers less than 36 as you can't get a sum
of 75.

Since GMAT problems will have a unique answer, you can stop at
step 2 above.

Thanks jayhawk.. I used similar method...