It is currently 19 Dec 2018, 05:48
My Tests

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Set S consists of all positive integers less than 81

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4756
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1668 [1] , given: 396

CAT Tests
Set S consists of all positive integers less than 81 [#permalink] New post 24 Dec 2015, 07:55
1
This post received
KUDOS
Expert's post
00:00

Question Stats:

50% (00:52) correct 50% (00:52) wrong based on 42 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

_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

2 KUDOS received
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4756
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1668 [2] , given: 396

CAT Tests
Re: Set S consists of all positive integers less than 81 [#permalink] New post 24 Dec 2015, 08:14
2
This post received
KUDOS
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.
_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

1 KUDOS received
Intern
Intern
User avatar
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
GRE 1: Q168 V169
Followers: 8

Kudos [?]: 51 [1] , given: 2

Re: Set S consists of all positive integers less than 81 [#permalink] New post 10 Apr 2016, 19:34
1
This post received
KUDOS
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.
_________________

Harvard grad and verified 99% GRE scorer, offering high-quality private GRE tutoring and coaching, both in-person (San Diego, CA, USA) and online worldwide, since 2002.

GRE Action Plan and Free E-Book - 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

1 KUDOS received
Manager
Manager
Joined: 22 Feb 2018
Posts: 127
Followers: 2

Kudos [?]: 77 [1] , given: 15

CAT Tests
Re: Set S consists of all positive integers less than 81 [#permalink] New post 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
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] New post 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
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] New post 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
1 KUDOS received
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4756
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1668 [1] , given: 396

CAT Tests
Re: Set S consists of all positive integers less than 81 [#permalink] New post 25 Nov 2018, 07:11
1
This post received
KUDOS
Expert's post
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
Intern
Joined: 25 Nov 2018
Posts: 29
Followers: 0

Kudos [?]: 1 [0], given: 0

CAT Tests
Re: Set S consists of all positive integers less than 81 [#permalink] New post 25 Nov 2018, 10:06
thanks for this!
Manager
Manager
Joined: 22 Feb 2018
Posts: 127
Followers: 2

Kudos [?]: 77 [0], given: 15

CAT Tests
Re: Set S consists of all positive integers less than 81 [#permalink] New post 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
Display posts from previous: Sort by

Set S consists of all positive integers less than 81

  Question banks Downloads My Bookmarks Reviews Important topics  


GRE Prep Club Forum Home| About| Terms and Conditions and Privacy Policy| GRE Prep Club Rules| Contact

Powered by phpBB © phpBB Group

Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.