Source: Official Guide Revised GRE 1st Ed. Part 6; Set 3; #6


Set S consists of all positive integers

Set S consists of all positive integers less than 81 that are not equal to the square of an integer. Quantity A : The number of integers in Set S Quantity B : 72 Quantity A is greater., Quantity B is greater., The two quantities are equal., The relationship cannot be determined from the information given.

4 Explanations


Josephine Owusu

I don't understand the problem, mainly the part "...that are not equal to the square of an integer." Could you further explain this please?

Jun 21, 2018 • Comment

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


Yosef Lewis

Thanks Kevin! The video made me laugh :)

Apr 23, 2014 • Comment

Kevin Rocci, Magoosh Tutor


Apr 25, 2014 • Reply


Yosef Lewis

1 is the loneliest number. Don't forget to include 1! :)

Apr 15, 2014 • Comment

Kevin Rocci, Magoosh Tutor

True, Yosef!

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

Apr 18, 2014 • Reply


Gravatar Chris Lele, Magoosh Tutor

Oct 7, 2012 • Comment


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

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