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
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