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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.

5 Explanations


John Bohne

Why are numbers like 13 and 17 not included? They are positive numbers less than 81 and do not have a integer number when square rooted. I think the question is worded vaguely and I don't know why numbers greater than or equal to 9 cannot be included.

Nov 10, 2018 • Comment


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


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

"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


Apr 25, 2014 • Reply


Yosef Lewis

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

Apr 15, 2014 • Comment

True, Yosef!

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

Apr 18, 2014 • Reply


Chris Lele

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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