Hi j_shreyans,

What is the source of this question? I ask because it's poorly worded (and the "intent" is vague).

I assume that we're meant to be dealing with perfect squares (greater than 1), so we'd have a finite group of values:

4, 9, 16, 25, 36, 49, 64

From the answer choices, I have to assume that duplicates ARE allowed (but the question doesn't technically state that)

eg 25 + 25 + 25 = 75
et 49 + 9 + 9 + 4 + 4 = 75

There's really only one way to answer this question: LOTS of brute-force math (and the answer choices are not "spaced out" enough to provide you with any type of shortcut or hint). While the concepts (arithmetic, perfect squares, etc.) will show on the GMAT, this "design" isn't common on Test Day.

GMAT assassins aren't born, they're made,
Rich

Hi j_shreyans,

I'd still like to know the source of this question....???

With the perfect squares that I mentioned earlier:

4, 9, 16, 25, 36, 49, 64

We have to come up with all the various ways to sum to 75 (and apparently "duplicates" are allowed). The "key" to solving this prompt faster (and there isn't really a "fast" way) is to realize that the above numbers can be "rewritten" in various forms:

36 = 9 + 9 + 9 + 9
25 = 16 + 9
16 = 4 + 4 + 4 + 4

So, here are all of the possibilities:
49 + 2(9) + 2(4)
36 + 3(9) + 3(4)

3(25)
2(25) + 16 + 9
2(25) + 4(4) + 9
25 + 2(16) + 2(9)
25 + 16 + 2(9) + 4(4)
25 + 2(9) + 8(4)

3(16) + 3(9)
2(16) + 3(9) + 4(4)
16 + 3(9) + 8(4)
7(9) + 3(4)
3(9) + 12(4)

Total Options: 13

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

I'm not a big fan of this question (for many reasons).
The first tip-off is the phrase "positive square integers."
Are we trying to distinguish these squares from negative ones?

Cheers,
Brent