Author 
Message 
TAGS:


GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4856
WE: Business Development (Energy and Utilities)
Followers: 102
Kudos [?]:
1742
[1]
, given: 397

Set S consists of all positive integers less than 81 [#permalink]
24 Dec 2015, 07:55
1
This post received KUDOS
Question Stats:
51% (00:55) correct
48% (00:53) wrong based on 49 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
_________________
Sandy If you found this post useful, please let me know by pressing the Kudos Button
Try our free Online GRE Test




GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4856
WE: Business Development (Energy and Utilities)
Followers: 102
Kudos [?]:
1742
[2]
, given: 397

Re: Set S consists of all positive integers less than 81 [#permalink]
24 Dec 2015, 08:14
2
This post received KUDOS
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.
_________________
Sandy If you found this post useful, please let me know by pressing the Kudos Button
Try our free Online GRE Test



Intern
Status: Professional GRE Tutor
Affiliations: AB, cum laude, Harvard University (Class of '02)
Joined: 10 Apr 2016
Posts: 46
Location: United States (CA)
Age: 38
Followers: 8
Kudos [?]:
51
[1]
, given: 2

Re: Set S consists of all positive integers less than 81 [#permalink]
10 Apr 2016, 19:34
1
This post received KUDOS
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, 808=72. Choice C.
_________________
Harvard grad and verified 99% GRE scorer, offering highquality private GRE tutoring and coaching, both inperson (San Diego, CA, USA) and online worldwide, since 2002.
GRE Action Plan and Free EBook  McElroy Tutoring
Personal Best GRE Score: 168/170 Quant (95%), 169/170 Verbal (99%), 5.5 AWA (98%)
GRE Vocab Capacity  Amazon.com
Vince and Brian's GRE PowerPrep Explanations  Amazon.com
My GRE AMA on Reddit
Check Me Out on GMAT Club



Manager
Joined: 22 Feb 2018
Posts: 156
Followers: 2
Kudos [?]:
94
[1]
, given: 21

Re: Set S consists of all positive integers less than 81 [#permalink]
15 Mar 2018, 17:16
1
This post received KUDOS
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.
_________________
Follow your heart



Intern
Joined: 12 Mar 2018
Posts: 5
Followers: 0
Kudos [?]:
1
[0], given: 0

Re: Set S consists of all positive integers less than 81 [#permalink]
15 Mar 2018, 22:24
FatemehAsgarinejad wrote: 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
Posts: 1
Followers: 0
Kudos [?]:
0
[0], given: 1

Re: Set S consists of all positive integers less than 81 [#permalink]
25 Nov 2018, 06:29
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?
THANKS IN ADVANCE



GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4856
WE: Business Development (Energy and Utilities)
Followers: 102
Kudos [?]:
1742
[1]
, given: 397

Re: Set S consists of all positive integers less than 81 [#permalink]
25 Nov 2018, 07:11
1
This post received KUDOS
checomartinez11 wrote: WHY YOU SUBTRACT THE 8 TO THE 80 AND NOT TO THE 81?
THANKS IN ADVANCE
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.
_________________
Sandy If you found this post useful, please let me know by pressing the Kudos Button
Try our free Online GRE Test



Intern
Joined: 25 Nov 2018
Posts: 29
Followers: 0
Kudos [?]:
1
[0], given: 0

Re: Set S consists of all positive integers less than 81 [#permalink]
25 Nov 2018, 10:06
thanks for this!



Manager
Joined: 22 Feb 2018
Posts: 156
Followers: 2
Kudos [?]:
94
[0], given: 21

Re: Set S consists of all positive integers less than 81 [#permalink]
28 Nov 2018, 12:42
Answer: C
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
_________________
Follow your heart




Re: Set S consists of all positive integers less than 81
[#permalink]
28 Nov 2018, 12:42





