For the data 2, 9, $x + 6$, $2x + 3$, 5, 10, 5; if the mean is 7, then the value of $x$ is :

Question

Accepted Answer

## Model Answer **Option (D) 3** Mean = $\dfrac{2 + 9 + (x+6) + (2x+3) + 5 + 10 + 5}{7} = 7$ $\Rightarrow 2x + 40 = 49 \Rightarrow 2x = 9$... Recalculating: $2 + 9 + x + 6 + 2x + 3 + 5 + 10 + 5 = 3x + 40$ $\dfrac{3x + 40}{7} = 7 \Rightarrow 3x + 40 = 49 \Rightarrow 3x = 9 \Rightarrow x = 3$ **Answer: D) 3** ## Explanation Sum all terms: $2 + 9 + (x+6) + (2x+3) + 5 + 10 + 5 = 3x + 40$. Set $\frac{3x+40}{7} = 7$, solve to get $x = 3$. Watch out for carefully collecting like terms ($x + 2x = 3x$) — a common slip.

Mathematics — Standard (041) — CBSE Class 10 board question