48. The average of three numbers p, q and r is k. p is as much more than the average as q is less than the average. What is the value of r?

1. A. k
2. B. k – 1
3. C. k + 1
4. D. k/2

Answer: A

Explanation

Given that the average of p, q, and r is k.
So, (p + q + r) / 3 = k, which implies p + q + r = 3k.

We are also given that p is as much more than the average (k) as q is less than the average (k).
Let this difference be ‘x’.
So, p = k + x
And q = k – x

Now substitute these values of p and q into the sum equation:
(k + x) + (k – x) + r = 3k
2k + r = 3k
Subtract 2k from both sides:
r = 3k – 2k
r = k

Alternatively, if p is ‘x’ more than the average and q is ‘x’ less than the average, then the sum of p and q is (k+x) + (k-x) = 2k. This means the average of p and q is (2k)/2 = k. If the average of p and q is k, and the average of p, q, and r is also k, then r must necessarily be k to maintain the overall average. This question is a straightforward application of the definition of average.