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Properties of Measures of Central Tendency

If the mean o...

Question

If the mean of x + 2, 2x + 3, 3x + 4 and 4x + 5 is x + 2 then find the value of x

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Solution

The correct option is C $- 1$
Given: The mean of x + 2, 2x + 3, 3x + 4 and 4x + 5 is x + 2
Mean = $\frac{(x + 2) + (2 x + 3) + (3 x + 4) + (4 x + 5)}{4}$
$\Rightarrow x + 2 = \frac{10 x + 14}{4}$
$\Rightarrow 4 x + 8 = 10 x + 14$
$\Rightarrow 6 x = - 6$
$\Rightarrow x = - 1$
$∴$ Option C is correct.

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∣ ∣ ∣ ∣ \begin{matrix} x + 2 & 2 x + 3 & 3 x + 4 2 x + 3 & 3 x + 4 & 4 x + 5 3 x + 5 & 5 x + 8 & 10 x + 17 \end{matrix} ∣ ∣ ∣ ∣ = 0

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\frac{(2 x + 3) (3 x - 4)}{(x - 1) (4 x + 5)} = f (x) - \frac{5}{9 (x - 1)} + \frac{31}{18 (4 x + 5)}

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f (x) = 2 x^{3} - 6 x^{2} + 4 x - 5

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∣ ∣ ∣ ∣ \begin{matrix} 3 x + 4 & x + 2 & 2 x + 3 4 x + 5 & 2 x + 3 & 3 x + 4 10 x + 17 & 3 x + 5 & 5 x + 8 \end{matrix} ∣ ∣ ∣ ∣ = 0

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