Problem Solving

Here's the original question:

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

Hi Apoorva@5,

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

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