Hey jfrick,
Good question - honestly, there are so few squares in that neighborhood of 1-100 (inclusive, it's ten) that whenever I see questions like this I think it's easiest to just write those squares out and go from there. Here, because you're cut off at 75, you only have:
1
4
9
16
25
36
49
64
From there, I hate to just lean on "trial and error", but there aren't that many combinations that you could use:
1, 4, 9, and 16 are prohibitively small, so you can't use more than one of them without using something one of the larger ones.
36, 49, and 64 can't be used together because a sum of just two of them is too big.
So you can play with combinations of "small, medium, and large" numbers to see what you need, and it should fairly quickly give you something that works: 1 + 49 + 25 = 75, and the sum of the square roots is 1 + 5 + 7 = 13
My "ace in the hole here" is the ace itself. My hunch with these number properties questions is that the author expects you to overlook numbers like 0 and 1 (obviously 0 doesn't count here, but in other questions), so that was the one I started with. By matching 1 with other numbers, I pretty quickly saw that I could get 50 out of 1 + 49, and 25 "clicked" almost immediately after.
For me, this one came down to a little trial-and-error with some "insider" perspective on the GMAT - that it was likely to bank on my overlooking 1, so I'd try that one first.
A few other things that I considered (all within a few seconds)
-I needed at least one odd number to be part of this one (adding only evens wouldn't get me to an odd number like 75)
-64 is so close to 75 that I could ignore it once 1,9; 1,4; 4,9 didn't work, so I could just throw it out and work with fewer numbers.
Keep in mind that, with squares and cubes, if they're looking for combinations of them (I did a problem in a tutoring session this week that dealt with numbers that are both squares and cubes and used the same idea) there aren't that many of them if the range is small, so you can always start by just jotting them down and going from there.
Brian Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep
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