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

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If numbers N and K are added to set X{2,8,10,12}, its mean w [#permalink] New post 09 Jan 2011, 09:43
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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

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Re: If numbers N and K are added to set X{2,8,10,12}, its mean w [#permalink] New post 19 Sep 2013, 23:22
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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/
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Re: Numbers added to a set [#permalink] New post 09 Jan 2011, 10:19
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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.

Answer: D.
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Re: If numbers N and K are added to set X{2,8,10,12}, its mean w [#permalink] New post 19 Sep 2013, 21:47
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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.
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If numbers N and K are added to set X [#permalink] New post 19 Sep 2013, 02:50
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
N2 + 2NK + K2 ?

(A) 28 (B) 32 (C) 64 (D) 784 (E) 3600
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Re: If numbers N and K are added to set X [#permalink] New post 19 Sep 2013, 03:49
Expert's post
christykarunya 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
N2 + 2NK + K2 ?

(A) 28 (B) 32 (C) 64 (D) 784 (E) 3600


Merging similar topics. Please refer to the solution above.
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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If numbers N and K are added to set X{2,8,10,12}, its mean w [#permalink] New post 20 Sep 2013, 01:59
Thanks all for helping me on this :-D
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Re: If numbers N and K are added to set X{2,8,10,12}, its mean w [#permalink] New post 08 Sep 2014, 22:09
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.

Answer: D.


Magician!!! Why do my eyes escape these little details like the a+b whole square formula being expanded in the question ://
Re: If numbers N and K are added to set X{2,8,10,12}, its mean w   [#permalink] 08 Sep 2014, 22:09
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