If the mean of 3, 4, 9, 2k, 10, 8, 6… - CUET UG 2024 General Test PYQ

CUET UG 2024 — General Test Arithmetic

2024mcqmedium

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

Official previous-year question

Verified 13 Jul 2026.

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Solution

Mean $= \dfrac{3+4+9+2k+10+8+6+(k+6)}{8}=8$

$\Rightarrow 46+3k = 64$
$\Rightarrow 3k = 18 \rightarrow k = 6$

If $4$ is the mode then $4$ must have the maximum frequency in the given series.

This means that either $2p$ or $2p+1$ must be equal to 4.
Also, the question mentions that $p$ is a natural number so $2p+1$ can't be equal to 4.

$\therefore 2p = 4 \rightarrow p=2$

$(k-2p) = 6-4=2$

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