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

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by BTGmoderatorLU » Mon May 17, 2021 4:55 pm

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Source: GMAT Prep

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

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

by Brent@GMATPrepNow » Tue May 18, 2021 7:19 am
BTGmoderatorLU wrote: ↑
Mon May 17, 2021 4:55 pm
 Source: GMAT Prep

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

The OA E
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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