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Mean 2

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Mean 2

by ranjeet75 » Fri Feb 03, 2012 5:20 am
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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by shankar.ashwin » Fri Feb 03, 2012 6:03 am
Mean of 2,8,10 and 12 = 32/4 = 8

25% increase = 1.25* 8 = 10

Now since 2 numbers are added, the sum of the 6 numbers should be 60

We know sum of given 4 = 32

Therefore, sum of N and K = 60-32 = 28

(N+K)^2 = 784 - D
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by Anurag@Gurome » Fri Feb 03, 2012 6:37 pm
ranjeet75 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
Mean of the set X = (2 + 8 + 10 + 12)/4 = 32/4 = 8
When number N and K are added to the set X, the mean increases by 25% implies new mean = 8 + (0.25 * 8) = 10
This means that the mean of 6 numbers is 60, which implies N + K = 60 - 32 = 28
N² + 2NK + K² = (N + K)² = 28² = 784

The correct answer is D.
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