swerve 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

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

swerve wrote: I guessed this right - but is there an algebraic way to do this PS question? Please, can any expert explain it? I need your help. Thanks.

No, there's no straightforward algebraic solution.

Cheers,
Brent

Hi swerve,

This question can be solved with a bit of 'brute force' arithmetic, but the speed with which you solve it will likely depend on how quickly you can write everything down and how you do the work.

We're asked to find the three positive integers, whose squares add up to 75. To start, we should write down the list of possible squares:

1
4
9
16
25
36
49
64

We're limited to these 8 numbers. To work efficiently, we should work from 'greatest to least'..

If we use 64, then the other two numbers have to add up to 11....but there's NO WAY to make that happen (so 64 is NOT one of the numbers we need).

Next, let's try 49... then the other two numbers have to add up to 26....25 and 1 'fit', so the three numbers are 49, 25 and 1 (7, 5 and 1 --> that sum = 13).

Final Answer: E

GMAT assassins aren't born, they're made,
Rich