The number 75 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers?

(A) 17
(B) 16
(C) 15
(D) 14
(E) 13

This question is from the free official GMAT practice tests 1 and 2 so avoid if you haven't done those already. This is a number properties puzzle that benefits from doing a bit of organizing. The sum of the squares of the 3 integers sum is 75. So go ahead and list the first bunch of squares starting from 1 up to just below 75. Once you've got that you just need to find the combination that works. To make your job easier use units digits. 75 ends in 5 so your three numbers must create that units digit. The other tip is: start from the bigger integers and work down. To get to 75 you're going to need one of those big guys (64, 49, or 36). Finding a constraint can be very helpful (in this case the units digit and the requirement of 36, 49, or 64). Usually with these GMAT puzzles there are little shortcuts. Generally you don't pull them out of thin air. They are the natural conclusion of good organization. Make sure to take your time with setup so you pave the way for success. Here's another GMAT question that relies on just staying organized and paying attention: For a certain race, 3 teams were allowed to enter 3 members each. A team earned 6 – n points whenever one of its members finished in nth place, where 1 ≤ n ≤ 5. The details are very different but the style is similar and I think it requires the same kind of thinking.

The number 75 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers

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