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

 It is currently 18 Oct 2019, 02:25 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

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.  For a set X containing n integers, is the mean even? (1) n

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

Hide Tags

Manager  Joined: 26 Mar 2007
Posts: 61
Concentration: General Management, Leadership
Schools: Thunderbird '15
For a set X containing n integers, is the mean even? (1) n  [#permalink]

Show Tags

5
13 00:00

Difficulty:   65% (hard)

Question Stats: 54% (01:34) correct 46% (01:26) wrong based on 497 sessions

HideShow timer Statistics

For a set X containing n integers, is the mean even?

(1) n is even.

(2) All of the integers in set X are even.

Best approach Math Expert V
Joined: 02 Sep 2009
Posts: 58439
For a set X containing n integers, is the mean even? (1) n  [#permalink]

Show Tags

7
2
kannn wrote:
For a set X containing n integers, is the mean even?

(1) n is even.

(2) All of the integers in set X are even.

Best approach For a set X containing n integers, is the mean even?

The mean of a set = The sum of the elements / number of elements, so the question is whether mean=sum/n=even.

(1) n is even --> mean=sum/even. Not sufficient.

(2) All of the integers in set X are even --> so the sum of the elements is even --> mean=even/n. Not sufficient.

(1)+(2) The question becomes whether mean=even/even=even, which can not be determined as even/even could be even (for example 4/2=2=even), could be odd (for example 6/2=3=odd) or could be non-integer (for example 6/4=3/2). Not sufficient.

_________________
General Discussion
Director  Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 654
Re: Even Mean  [#permalink]

Show Tags

1
2
This one is tricky.

1. Insufficient
n = 2
X = {0,2} mean = 1. The answer is NO
X = {3,5} mean = 4. The answer is YES

2. Insufficient
X = {0,2} mean = 1. The answer is NO
X = {2,2} mean = 2. The answer is YES

1) + 2)
X = {0,2} mean = 1. The answer is NO
X = {2,2} mean = 2. The answer is YES

Hence E.

kannn wrote:
For a set X containing n integers, is the mean even?

(1) n is even.

(2) All of the integers in set X are even.

Best approach Originally posted by gmat1220 on 09 Mar 2011, 10:31.
Last edited by gmat1220 on 09 Mar 2011, 10:32, edited 1 time in total.
Retired Moderator B
Joined: 16 Nov 2010
Posts: 1253
Location: United States (IN)
Concentration: Strategy, Technology
Re: Even Mean  [#permalink]

Show Tags

From (1), 1,2 mean = 1.5 or 4,8 mean = 6, so (1) is not enough

Again, 2,4 mean = 3 or 4,8 mean = 6, so (2) is not enough

From (1) and (2), there is no definitive conclusion, so answer is E.
_________________
Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings
GMAT Tutor G
Status: Tutor - BrushMyQuant
Joined: 05 Apr 2011
Posts: 622
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31 GPA: 3
WE: Information Technology (Computer Software)
Re: For a set X containing n integers, is the mean even?  [#permalink]

Show Tags

1
For a set X containing n integers, is the mean even?

(1) n is even.

(2) All of the integers in set X are even.

Doesn't both the statements combined give an odd answer? Thus Statement (C) is correct but the MGMAT says that (E) is correct. Can someone explain the answer.

take Set S as {2,4} then you will get the mean as 3 (odd)
take Set S as {4,4,4,4} then you will get the mean as 4 (even)

so answer will be E
_________________
Intern  Joined: 17 Mar 2011
Posts: 6
Schools: INSEAD, Booth, LBS
WE 1: Operations,
WE 2: IT Consulting, Hi Tech Project Management
WE 3: Baby Sitter
Re: For a set X containing n integers, is the mean even?  [#permalink]

Show Tags

1
Trick here is that integers in Set S is NOT UNIQUE EVEN INTEGER. Hence Ans. E. If integers were unique EVEN integers then Ans. would have been C.
_________________
The question isn’t who is going to let me; it’s who is going to stop me.
Senior Manager  Joined: 15 Sep 2011
Posts: 309
Location: United States
WE: Corporate Finance (Manufacturing)
For a set X containing n integers, is the mean even? (1) n  [#permalink]

Show Tags

asif780 wrote:
Trick here is that integers in Set S is NOT UNIQUE EVEN INTEGER. Hence Ans. E. If integers were unique EVEN integers then Ans. would have been C.

Not true, for instance.

If set {2,4}, then Avg. = 3
If set {2,6}, then Avg. = 4

Since both sets are unique even integers, the average can still be odd of even, and therefore whatever is above is not valid.
Intern  B
Joined: 05 Nov 2012
Posts: 45
Re: For a set X containing n integers, is the mean even? (1) n  [#permalink]

Show Tags

Bunuel wrote:
kannn wrote:
For a set X containing n integers, is the mean even?

(1) n is even.

(2) All of the integers in set X are even.

Best approach For a set X containing n integers, is the mean even?

The mean of a set = The sum of the elements / number of elements, so the question is whether mean=sum/n=even.

(1) n is even --> mean=sum/even. Not sufficient.

(2) All of the integers in set X are even --> so the sum of the elements is even --> mean=even/n. Not sufficient.

(1)+(2) The question becomes whether mean=even/even=even, which can not be determined as even/even could be even (for example 4/2=2=even), could be odd (for example 6/2=3=odd) or could be non-integer (for example 6/4=3/2). Not sufficient.

Hi Bunuel,

I still do not understand how to solve these kind of questions methodically because everytime we have to consider cases I forget one or other cases to consider. So instead of trying numbers can you please describe a methodical approach to test this.

For eg when we consider cases how many cases are possible and how to check against them. Such as we know that for the mean to be even the sum mandatorily has to be even however the base could be even or odd and can yield even or odd mean in both the cases i.e when N= even or when n=odd as non integers are also included.
Intern  Joined: 15 Jun 2016
Posts: 45
Location: India
Concentration: Technology, Strategy
GMAT 1: 730 Q50 V39 Re: For a set X containing n integers, is the mean even? (1) n  [#permalink]

Show Tags

One doubt - if the question had mentioned n positive integers, how does the answer varies ? My doubt is - whether the addition of "zero" to the set changes the even\odd nature of the mean ?
Senior Manager  Joined: 02 Mar 2012
Posts: 272
Schools: Schulich '16
Re: For a set X containing n integers, is the mean even? (1) n  [#permalink]

Show Tags

good question

take 2,4,6,8 and 4444 for both statements

and will come out to be E

hope it helps
Director  S
Joined: 12 Nov 2016
Posts: 700
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37 GRE 1: Q157 V158 GPA: 2.66
Re: For a set X containing n integers, is the mean even? (1) n  [#permalink]

Show Tags

kannn wrote:
For a set X containing n integers, is the mean even?

(1) n is even.

(2) All of the integers in set X are even.

Best approach :wink:

This is very tricky because 0 is actually an even number and there not many restriction on the type of integers that are permitted in set X.

0 4 4 4

This conforms to the criteria in statements 1 and 2; however, the result is an odd mean. But if we have

2 2 2 2

Then the mean is even

E
Non-Human User Joined: 09 Sep 2013
Posts: 13241
Re: For a set X containing n integers, is the mean even? (1) n  [#permalink]

Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: For a set X containing n integers, is the mean even? (1) n   [#permalink] 08 Oct 2018, 13:22
Display posts from previous: Sort by

For a set X containing n integers, is the mean even? (1) n

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

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