GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 23 May 2019, 10:19

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.

Close

Request Expert Reply

Confirm Cancel

Is the median of set S even?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

 
Manager
Manager
avatar
Joined: 13 May 2010
Posts: 110
Is the median of set S even?  [#permalink]

Show Tags

New post 07 Feb 2012, 13:59
2
4
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

65% (01:17) correct 35% (01:20) wrong based on 191 sessions

HideShow timer Statistics

Is the median of set S even?

(1) Set S is composed of consecutive odd integers
(2) The mean of set S is even
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 55266
Re: club 13 - q1  [#permalink]

Show Tags

New post 07 Feb 2012, 14:04
2
2
teal wrote:
Is the median of set \(S\) even?

1. Set \(S\) is composed of consecutive odd integers
2. The mean of set \(S\) is even

Can someone please explain the correct approach for this one?


Is the median of set S even?

(1) Set S is composed of consecutive odd integers --> set S is evenly spaced --> for any every evenly spaced set mean=median. But still insufficient.

(2) The mean of set S is even. Insufficient on its own.

(1)+(2) From (1) mean=median and from (2) mean=even --> mean=median=even. Sufficient.

Answer: C.

Hope it helps.
_________________
Manager
Manager
avatar
Joined: 13 May 2010
Posts: 110
Re: Is the median of set S even?  [#permalink]

Show Tags

New post 07 Feb 2012, 14:44
can you please give me an example of a set in which mean is even and median is odd for statement 2?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 55266
Re: Is the median of set S even?  [#permalink]

Show Tags

New post 07 Feb 2012, 14:46
Intern
Intern
avatar
Joined: 10 Jan 2014
Posts: 22
Re: Is the median of set S even?  [#permalink]

Show Tags

New post 11 Feb 2014, 05:47
why isn't the correct answer A?

from statement 1 we know that S is a set containing consecutive odd integers, hence, it is an evenly spaced set. For all evenly spaced sets --> Mean = Median . Also, for all evenly spaced sets, Mean = Sum of first and last Number/ 2. Since we know that all numbers in the set are odd, we know that the first and the last number are odd, too, therefore odd + odd = even. Even/2=even --> the mean, and therefore the median of the set are even. Statement 1 is sufficient. If i did make a mistake, can someone please explain?

Cheers,
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 55266
Re: Is the median of set S even?  [#permalink]

Show Tags

New post 11 Feb 2014, 06:00
1
damamikus wrote:
why isn't the correct answer A?

from statement 1 we know that S is a set containing consecutive odd integers, hence, it is an evenly spaced set. For all evenly spaced sets --> Mean = Median . Also, for all evenly spaced sets, Mean = Sum of first and last Number/ 2. Since we know that all numbers in the set are odd, we know that the first and the last number are odd, too, therefore odd + odd = even. Even/2=even --> the mean, and therefore the median of the set are even. Statement 1 is sufficient. If i did make a mistake, can someone please explain?

Cheers,


Why wouldn't you check your theories with simple examples?

{1, 3} --> median = 2 = even.
{1, 3, 5} --> median = 3 = odd.

Mistake in your reasoning is that even/2 = integer, not necessarily even. For, example, 4/2 = 2 = even, but 6/2 = 3 = odd.

Does this make sense?
_________________
Intern
Intern
avatar
Joined: 10 Jan 2014
Posts: 22
Re: Is the median of set S even?  [#permalink]

Show Tags

New post 11 Feb 2014, 06:08
thanks Bunuel!! you're right, i assumed even/2=even when in fact, as you pointed out, even/2=integer. thanks for the advice, i'll try to double-check my answers next time with some simple examples :)
Senior Manager
Senior Manager
User avatar
D
Joined: 24 Oct 2016
Posts: 412
GMAT 1: 670 Q46 V36
GMAT 2: 690 Q47 V38
Is the median of set S even?  [#permalink]

Show Tags

New post 24 Mar 2019, 10:23
Bunuel wrote:
teal wrote:
Is the median of set \(S\) even?

1. Set \(S\) is composed of consecutive odd integers
2. The mean of set \(S\) is even

Can someone please explain the correct approach for this one?


Is the median of set S even?

(1) Set S is composed of consecutive odd integers --> set S is evenly spaced --> for any every evenly spaced set mean=median. But still insufficient.

(2) The mean of set S is even. Insufficient on its own.

(1)+(2) From (1) mean=median and from (2) mean=even --> mean=median=even. Sufficient.

Answer: C.

Hope it helps.


Bunuel wrote:
teal wrote:
can you please give me an example of a set in which mean is even and median is odd for statement 2?


Sure: {1, 1, 4} --> mean=(1+1+4)/3=2=even and median=1=odd.


If you tested cases for stmt 2 instead of using theory, then you'll need to consider the 3 cases mentioned below:

3 Cases


1) When list just has one item: Mean = Median
2) When list has even # of items:

(x + y)/2 = even
x + y = even

So x & y could be both even or both odd.
In either case, median = even.

3) When list has odd # of items:

(x + y + z)/3 = even
(x + y + z) = even

If x & z are both even or odd, then (x + z) = even and y = even.
If x & z are opposite, then (x + z) = odd and y = odd.
_________________

Most Comprehensive Article on How to Score a 700+ on the GMAT (NEW)
Verb Tenses Simplified



If you found my post useful,

KUDOS

are much appreciated. Giving Kudos is a great way to thank and motivate contributors, without costing you anything.
GMAT Club Bot
Is the median of set S even?   [#permalink] 24 Mar 2019, 10:23
Display posts from previous: Sort by

Is the median of set S even?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.