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The number 75 can be written as the sum of the squares of 3

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by Jay@ManhattanReview » Tue Nov 26, 2019 8:41 pm
BTGmoderatorDC wrote: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

OA E

Source: GMAT Prep
I think trial and error is the best method for this type of question.

The sum of three different positive integers must be from 1, 4, 9, 16, 25, 36, 49, and 64.

The only combination of three different positive integers works is 1 + 25 + 49 = 75. Or 75 = 1^2 + 5^2 + 7^2.

Thus, sum = 1 + 5 + 7 = 13.

The correct answer: E

Hope this helps!

-Jay
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by Brent@GMATPrepNow » Wed Nov 27, 2019 6:26 am
BTGmoderatorDC wrote: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

OA E

Source: GMAT Prep
We're looking for 3 DIFFERENT squares that add to 75

Here are the only squares we need to consider: 1, 4, 9, 16, 25, 36, 49, 64

Can you find 3 that add to 75?
After some fiddling, we may notice that 1 + 25 + 49
In other words, 1² + 5² + 7² = 75
We want the SUM of 1 + 5 + 7, which is 13

Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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