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
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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.
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.
"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.
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 :)
5 Explanations