Question

If the mean of 3, 4, 9, 2k, 10, 8, 6 and $(k + 6)$ is 8, and the mode of 2, 2, 3, $2p$, $(2p + 1)$, 4, 4, 5 and 6 (where $p$ is a natural number) is 4, then the value of $k - 2p$ is:

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

The Correct Option is A

The mean of the first set is 8, so $3 + 4 + 9 + 2k + 10 + 8 + 6 + (k + 6) = 64 \Rightarrow 46 + 3k = 64 \Rightarrow k = 6$. For the mode to be 4, $2p = 4$, so $p = 2$. Hence, $k - 2p = 6 - 4 = 0$.