Average value of numbers 15,21,32,35, 46 , x, 59,65,72 should be greater than or equal to 43 but les

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The average value of the numbers $15,21,32,35,$ $46$ $, x, 59,65,72$ should be greater than or equal to $43$ but less than or equal to $44 .$ Then the value of $x$ should be

A

$42 \leq x \leq 51$

B

$43 \leq x \leq 50$

C

$42 \leq x \leq 49$

D

$43 \leq x \leq 50$

Solution

$43 \leq$ Average $\leq 44$

$\Rightarrow 43 \leq \frac{345+x}{9} \leq 44$

$\Rightarrow 387 \leq 345+x \leq 396$

$\Rightarrow 387-345 \leq x \leq 396-345$

$\Rightarrow 42 \leq x \leq 51$

Standard 13

Quantitative Aptitude

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