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1. If a number is multiplied by two-third of itself the value so obtained is 864. What is the number ?

A. 34

B. 36

C. 38

D. 44

Solution:

Let the number be x
Then,

\begin{aligned} \Leftrightarrow x \times \frac{2}{3} x = 864 \\ \Leftrightarrow \frac{2}{3} x^{2} = 864 \\ \Leftrightarrow x^{2} = (\frac{864 \times 3}{2}) \\ \Leftrightarrow x^{2} = 1296 \\ \Leftrightarrow x = \sqrt{1296} \\ \Leftrightarrow x = 36 \end{aligned}

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