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by GMATGuruNY » Fri Mar 04, 2016 5:57 am
The number 75 can be written as the sum of the squares of 3 diff positive integers. What is the sum of these 3 integers?
a) 17
b) 16
c) 15
d) 14
e) 13
75 = the sum of three PERFECT SQUARES.
List the perfect squares less than 75.
Ask yourself the following:
Which perfect square will the average test-taker forget to consider?
Answer:
1² = 1.
Don't be an average test-taker.
Be sure to include 1² = 1 in your list:
1² = 1.
2² = 4.
3² = 9.
4² = 16.
5² = 25.
6² = 36.
7² = 49.
8² = 64.

The sum of the 3 values in red is 75:
1²+ 5² + 7² = 1 + 25 + 49 = 75.

Thus, the sum of the 3 integers = 1+5+7 = 13.

The correct answer is E.
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by [email protected] » Fri Mar 04, 2016 9:47 am
Hi eitijan,

A few questions on the GMAT Quant section are going to come down to 'limited options' - there usually not a fancy way to solve these types of questions, there's just "brute force" - pound on this question until you find the answer.

Here, we're told that the sum of the squares of 3 positive integers = 75, so the options are severely limited....

Since 9^2 = 81, we know that all 3 of the integers must be between 1 and 8.

From there, it's just a matter of "working down"....

If one of the numbers was 8^2, then you'd have 64 and the other two squares would have to add up to 11. You won't find this in the possibilities. As Mitch pointed out, it helps to write them down.

Next, try 7^2 = 49, the other two squares have to add up to 26. THAT'S pretty easy...5^2 + 1^2.

Now you've got the 3 integers and can sum them up.

Final Answer: E

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by Matt@VeritasPrep » Fri Mar 04, 2016 3:32 pm
I'd start with the obvious one: 75 = 25 + 25 + 25

Now that I see 25 is part of the equation, I want to look for squares that sum to 50. 49 is really close ... all I need is to add 1! Aha!

So I've got 75 = 1 + 25 + 49, and I'm set.

Don't get stuck looking for a formula here: just play with numbers and get closer to the solution, backtracking or rebooting if anything goes wrong.
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