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Number Properties

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by OptimusPrep » Sun Jun 26, 2016 9:17 pm
750+ wrote:Can someone please provide a solution?

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
75 = a^2 + b^2 + c^2

1^2 = 1
2^2 = 4
3^2 = 9
4^2 = 16
5^2 = 25
6^2 = 36
7^2 = 49
8^2 = 64

We need to put in the values of a,b and c from the above list of values and see which ones satisfy.
71 = 49 + 25 + 1 = 7^2 + 5^2 + 1^2
Hence (a,b,c) = (7,5,1)
a+b+c = 7+5+1 = 13

Correct Option: E
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by 800_or_bust » Mon Jun 27, 2016 8:46 am
750+ wrote:Can someone please provide a solution?
This is a tricky one. A good place to start is to consider all of the perfect squares less than 75, and try to find three that sum to 75. The answer is E. 5^2 + 7^2 + 1^2 = 25 + 49 + 1 = 75.
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by [email protected] » Mon Jun 27, 2016 9:00 am
Hi 750+,

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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Rich
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