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Set S consists of all positive integers less than 81 [#permalink]
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Question Stats: 55% (00:49) correct 44% (00:45) wrong based on 78 sessions
Set S consists of all positive integers less than 81 that are not equal to the square of an integer.

 Quantity A Quantity B The number of integers in set S 72

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

Practice Questions
Question: 6
Page: 156
Difficulty: hard
[Reveal] Spoiler: OA

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Re: Set S consists of all positive integers less than 81 [#permalink]
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Expert's post
Here we have a set which is a set of positive integers from 1 to 80. Now we can list the perfect squares which lie in the 1 to 80 interval such as
• $$1^2 = 1$$..
• $$2^2 = 4$$
• ......
• ......
• $$8^2 = 64$$

Hence these 8 numbers exist in 1 -80. Thus there are exactly 72 numbers which are not squares of an integers.

Thus both quantities are equal.
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Re: Set S consists of all positive integers less than 81 [#permalink]
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Expert's post
One quick note here is that there's no need to "build up" from $$1^2$$...instead try a number close to 72 and you will know that all the perfect squares below it work as well.

$$8^2 = 64$$, yep that works
$$9^2 = 81$$, no that's too big

Hence every perfect square less than 8^2 will work as well, making 8 terms total ($$1^2, 2^2, 3^2, 4^2, 5^2, 6^2, 7^2, and 8^2$$). Subtract these 8 terms from the 80 total terms in the list, 80-8=72.

Choice C.
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Re: Set S consists of all positive integers less than 81 [#permalink]
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Set S = {1, 2, 3, 4, 5, 6, 7, 8, ..., 81} - {1, 4, 9, 16, 25, 36, 49, 64, 81}
Set S has 81 - 9 = 72 integers.
A and B are equal.

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Re: Set S consists of all positive integers less than 81 [#permalink]
Set S = {1, 2, 3, 4, 5, 6, 7, 8, ..., 81} - {1, 4, 9, 16, 25, 36, 49, 64, 81}
Set S has 81 - 9 = 72 integers.
A and B are equal.

I think so that , Intern Joined: 05 Nov 2018
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Re: Set S consists of all positive integers less than 81 [#permalink]
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Here we have a set which is a set of positive integers from 1 to 80. Now we can list the perfect squares which lie in the 1 to 80 interval such as
12=112=1..
22=422=4
......
......
82=6482=64

Hence these 8 numbers exist in 1 -80. Thus there are exactly 72 numbers which are not squares of an integers.

Thus both quantities are equal.
_________________
Sandy

WHY YOU SUBTRACT THE 8 TO THE 80 AND NOT TO THE 81? GRE Prep Club Legend  Joined: 07 Jun 2014
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Re: Set S consists of all positive integers less than 81 [#permalink]
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Expert's post
checomartinez11 wrote:

WHY YOU SUBTRACT THE 8 TO THE 80 AND NOT TO THE 81?

There are 80 positive integers less than 81. 81 is not included.

For example positive integer less than 11 is 1, 2, 3, 4,5, 6, 7, 8, 9, 10. So a total of 10 numbers. 11 is not included.
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Re: Set S consists of all positive integers less than 81 [#permalink]
thanks for this! Manager Joined: 22 Feb 2018
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Re: Set S consists of all positive integers less than 81 [#permalink]
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Set S = {1,2,3,4,…,80} - {1^2, 2^2, 3^2, 4^2, 5^2, 6^2, 7^2, 8^2}

A: then number of integers in S is:
|S| = 80 - 8 = 72

B: 72
Answer is C, since Both of them are equal
_________________ Re: Set S consists of all positive integers less than 81   [#permalink] 28 Nov 2018, 12:42
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