When 18 is included in a list of natural numbers, the average of these numbers is increased by 2. When 8 is also included in this new list, the average of the new list remains the same. If there are N natural numbers in the original list with average X, find the values of N and X respectively.
A5, 6 ✓ Correct
B6, 8
C8, 6
D6, 5
Correct answer: (A) 5, 6
Explanation
N = 5 and X = 6.
Adding 18 raises the average by 2, so NX + 18 = (N + 1)(X + 2), giving 2N + X = 16.
Adding 8 keeps the new average X + 2, so NX + 26 = (N + 2)(X + 2), giving N + X = 11.
Subtract the second from the first: N = 5.
Then X = 11 - 5 = 6.
So N and X are 5 and 6.
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