Quantitative Aptitude Ques 286

Question: If $ {3^{2x-y}}={3^{x+y}}=\sqrt{27}, $ then the value of $ {3^{x-y}} $ will be

Options:

A) $ \frac{1}{\sqrt{27}} $

B) 3

C) $ \sqrt{3} $

D) $ \frac{1}{\sqrt{3}} $

Show Answer

Answer:

Correct Answer: C

Solution:

  • $ {3^{2x-y}}={3^{x+y}}=\sqrt{27} $
    $ \Rightarrow $ $ {3^{2x-y}}={3^{3/2}} $ Now, $ 2x-y=\frac{3}{2} $ … (i) and $ {3^{x+y}}={3^{3/2}} $
    $ \Rightarrow $ $ x+y=\frac{3}{2} $ … (ii) On adding Eqs. (i) and (ii), we get $ 3x=3 $
    $ \Rightarrow $ $ x=1 $ and $ y=\frac{1}{2} $ Hence, $ {3^{x-y}}={3^{1-\frac{1}{2}}}={3^{1/2}}=\sqrt{3} $
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