It is currently 22 Nov 2017, 19:23

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Current Student
Status: Up again.
Joined: 31 Oct 2010
Posts: 526

Kudos [?]: 547 [0], given: 75

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

09 Jan 2011, 10:43
3
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

81% (01:21) correct 19% (01:13) wrong based on 218 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
[Reveal] Spoiler: OA

_________________

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

Kudos [?]: 547 [0], given: 75

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7745

Kudos [?]: 17853 [2], given: 235

Location: Pune, India
Re: If numbers N and K are added to set X{2,8,10,12}, its mean w [#permalink]

### Show Tags

20 Sep 2013, 00:22
2
KUDOS
Expert's post
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
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Kudos [?]: 17853 [2], given: 235

Math Expert
Joined: 02 Sep 2009
Posts: 42305

Kudos [?]: 133076 [1], given: 12403

### Show Tags

09 Jan 2011, 11:19
1
KUDOS
Expert's post
5
This post was
BOOKMARKED
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) --> $$n+k=60-32=28$$ --> $$n^2+2nk+k^2=(n+k)^2=28^2=784$$.

_________________

Kudos [?]: 133076 [1], given: 12403

Intern
Joined: 05 Apr 2013
Posts: 18

Kudos [?]: 16 [1], given: 8

GPA: 3.21
Re: If numbers N and K are added to set X{2,8,10,12}, its mean w [#permalink]

### Show Tags

19 Sep 2013, 22:47
1
KUDOS
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.

Kudos [?]: 16 [1], given: 8

Intern
Joined: 10 Aug 2014
Posts: 3

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

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

### Show Tags

08 Sep 2014, 23:09
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 ://

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

Non-Human User
Joined: 09 Sep 2013
Posts: 15546

Kudos [?]: 283 [0], given: 0

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

### Show Tags

08 Dec 2016, 20:16
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.
_________________

Kudos [?]: 283 [0], given: 0

Re: If numbers N and K are added to set X{2,8,10,12}, its mean w   [#permalink] 08 Dec 2016, 20:16
Display posts from previous: Sort by