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

 It is currently 21 Mar 2019, 08:59 ### 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. ### Request Expert Reply # If numbers N and K are added to set X{2,8,10,12}, its mean w

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

### Hide Tags

Senior Manager  Status: Up again.
Joined: 31 Oct 2010
Posts: 489
Concentration: Strategy, Operations
GMAT 1: 710 Q48 V40 GMAT 2: 740 Q49 V42 If numbers N and K are added to set X{2,8,10,12}, its mean w  [#permalink]

### Show Tags

4 00:00

Difficulty:   15% (low)

Question Stats: 80% (02:11) correct 20% (01:51) wrong based on 247 sessions

### HideShow timer Statistics

If numbers N and K are added to set X{2,8,10,12}, its mean will increase by 25%. What is the value of $$N^2+2NK+K^2$$ ?

A. 28
B. 32
C. 64
D. 784
E. 3600

_________________

My GMAT debrief: http://gmatclub.com/forum/from-620-to-710-my-gmat-journey-114437.html

Math Expert V
Joined: 02 Sep 2009
Posts: 53768
Re: Numbers added to a set  [#permalink]

### Show Tags

4
3
gmatpapa wrote:
If numbers N and K are added to set X{2,8,10,12}, its mean will increase by 25%. What is the value of $$N^2+2NK+K^2$$ ?

A. 28
B. 32
C. 64
D. 784
E. 3600

Mean of {2,8,10,12} is $$mean=\frac{2+8+10+12}{4}=\frac{32}{4}=8$$ --> new mean thus should equal to $$8*1.25=10$$, so $$\frac{2+8+10+12+n+k}{6}=10$$ (note that now we have the set of 6 terms not 4) --> $$n+k=60-32=28$$ --> $$n^2+2nk+k^2=(n+k)^2=28^2=784$$.

_________________
##### General Discussion
Intern  Joined: 05 Apr 2013
Posts: 17
GPA: 3.21
Re: If numbers N and K are added to set X{2,8,10,12}, its mean w  [#permalink]

### Show Tags

If numbers N and K are added to set X{2,8,10,12}, its mean will increase by 25%. What is the value of N^2+2NK+K^2 ?

A. 28
B. 32
C. 64
D. 784
E. 3600

Before adding N & K, mean of X = 32/4 = 8.
After adding N & K, the new mean of X = 125/100*8 = 10.
i,e (32 + N+K )/6 = 10 => N+K = 60-32 = 28

The question is find the value of N^2+2NK+K^2 => (N+K)^2 = 28^2 = 784.
Veritas Prep GMAT Instructor D
Joined: 16 Oct 2010
Posts: 8998
Location: Pune, India
Re: If numbers N and K are added to set X{2,8,10,12}, its mean w  [#permalink]

### Show Tags

2
1
gmatpapa wrote:
If numbers N and K are added to set X{2,8,10,12}, its mean will increase by 25%. What is the value of $$N^2+2NK+K^2$$ ?

A. 28
B. 32
C. 64
D. 784
E. 3600

You can also use the conceptual and deviation based methods to solve this.

Mean of set X{2,8,10,12} = 8 (Note that if we assume 8 to be the mean, 2 is 6 less than 8 and 10 and 12 are together 6 more than 8. Hence 8 must be the actual mean - the deviation approach)

When we add two numbers, the mean increases by 25% i.e. by 2. Had the two numbers been both 8, the mean would have stayed 8. But they have 2 extra for each of the 6 numbers so they must be a total of 8 + 8 + 6*2 = 28
(N + K)^2 = 28^2 = 784

For more on these, check:
http://www.veritasprep.com/blog/2012/04 ... etic-mean/
http://www.veritasprep.com/blog/2012/05 ... eviations/
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

Intern  Joined: 10 Aug 2014
Posts: 2
Re: If numbers N and K are added to set X{2,8,10,12}, its mean w  [#permalink]

### Show Tags

Bunuel wrote:
gmatpapa wrote:
If numbers N and K are added to set X{2,8,10,12}, its mean will increase by 25%. What is the value of $$N^2+2NK+K^2$$ ?

A. 28
B. 32
C. 64
D. 784
E. 3600

Mean of {2,8,10,12} is $$mean=\frac{2+8+10+12}{4}=\frac{32}{4}=8$$ --> new mean thus should equal to $$8*1.25=10$$, so $$\frac{2+8+10+12+n+k}{6}=10$$ (note that now we have the set of 6 terms not 4) --> $$n+k=60-32=28$$ --> $$n^2+2nk+k^2=(n+k)^2=28^2=784$$.

Magician!!! Why do my eyes escape these little details like the a+b whole square formula being expanded in the question ://
Non-Human User Joined: 09 Sep 2013
Posts: 10166
Re: If numbers N and K are added to set X{2,8,10,12}, its mean w  [#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: If numbers N and K are added to set X{2,8,10,12}, its mean w   [#permalink] 28 Oct 2018, 22:37
Display posts from previous: Sort by

# If numbers N and K are added to set X{2,8,10,12}, its mean w

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