GMAT Prep - Factors

my 2 cents:

what is being asked : x^2+y^2+z^2=75, what is x+y+z?

I wrote down the integer numbers :
1,2,3,4,5,6,7,8,9 (because 9 square is 81, it will be excluded!)

Then, I start to take the square of 8 which is 64, subtract it from 75 which is 11, then I try to figure out what other numbers' squares add up to 11? Only 9, 2 leaeves alone...So I start all the process starting from 7 and I got the answer :

7*7 = 49, 75- 49 : 26, 5*5 + 1*1 is 26

so answer is 7+5+1 : 13

hope this helps!

I'd only add one thing, with the disclaimer that it barely saves time on this problem, if indeed it saves any at all... I'm just saying this because it's good practice to get in the habit of thinking about number properties as often as possible

In this problem, we're summing three squares to get an odd number (75). This means there are only two possibilities: either all three of those addends are odd, or two are even and one is odd. Since all integers have the same parity (i.e. even-or-odd-ness) as their squares, we can also conclude that the breakdown among the three integers themselves is the same -- either all odd, or two even and one odd -- and in any case, those integers themselves will also have an odd sum. Of course, that only knocks out two of the answer choices given here, and as I said, I don't think it's really a time-saver on this problem -- just good practice thinking about it. But you can imagine a problem where it might be more helpful -- for instance, if GMAC had wanted to test your number properties facility and so had given some much larger odd number and provided answer choices such that only one was odd:

The number 461 can be written as the sum of squares of three different positive integers. What is the sum of these integers?

a. 30
b. 34
c. 37
d. 40
e. 44

In that case I wouldn't go looking for the integers. I'd just use the number properties trick.