Set S consists of all positive integers

Adam Lyons, Magoosh Tutor

Hey John,

13 and 17 are actually included in the 72 numbers that are not equal to the square of an integer. All numbers from 1-80 are included in Set S except for 1, 4, 9, 16, 25, 36, 49, and 64. Those are the only numbers that ARE the square of an integer and hence NOT included. There are 8 of them, so the total number of integers in Set S is 80 - 8 = 72.

Nov 12, 2018 • Reply

David Recine, Magoosh Tutor

"That are not equal to the square of an integer" basically means that the numbers in Set S do not have integers as square roots, and cannot be gotten from squaring other integers.

So for example, Set S would not include the number 4, because the number 4 is 2^2, and has a square root that's an integer: 2. 9 would also be excluded from Set S, since it's the result of 3 squared, 16 would not be in Set S because 16 is 4^2, and so on.

Jun 26, 2018 • Reply

Kevin Rocci, Magoosh Tutor

:)

Apr 25, 2014 • Reply

Kevin Rocci, Magoosh Tutor

True, Yosef!

https://www.youtube.com/watch?v=d5ab8BOu4LE

And for more information on picking numbers, here is a good article to look at:

http://magoosh.com/gre/2011/gre-math-review-quiz-plugging-in/

Apr 18, 2014 • Reply

ANMOL SETH

why is 0 not included?

Sep 14, 2016 • Reply

Cydney Seigerman, Magoosh Tutor

Hi Anmol,

Happy to help! Zero is not included because zero is not a positive integer. Zero is not a negative integer either! In fact, 0 is non-negative and non-positive. It's the only number that's considered "neutral" meaning it's neither negative nor positive. That means if you ever see a problem with the wording referring to "all positive integers", then 0 is absolutely not included :)

Hope this helps! :D

Sep 14, 2016 • Reply