Quantitative Aptitude Ques 79

Question: Directions: In each of the following questions two equations I and II are given. You have to solve both the equations and find out values of x, y and give answer. [LIC (AAO) 2014]

I. $ \frac{12}{\sqrt{(x)}}+\frac{8}{\sqrt{(x)}}=\sqrt{(x)} $ II. $ y^{4}-\frac{{{(18)}^{9/2}}}{\sqrt{(y)}}=0 $

Options:

A) If $ x>y $

B) If $ x\le y $

C) If $ x<y $

D) If $ x\ge y $

E) If relationship cannot be established

Show Answer

Answer:

Correct Answer: A

Solution:

  • I. $ \frac{12}{\sqrt{x}}+\frac{8}{\sqrt{x}}=\sqrt{x} $
    $ \Rightarrow $ $ \frac{12\times 8}{\sqrt{x}}=\sqrt{x} $

$ \Rightarrow $ $ 12+8=x $
$ \Rightarrow $ $ x=20 $ II. $ y^{4}-\frac{{{(18)}^{9/2}}}{\sqrt{y}}=0 $
$ \Rightarrow $ $ y^{4}=\frac{{{(18)}^{9/2}}}{\sqrt{y}} $

$ \Rightarrow $ $ {{(y)}^{9/2}}={{(18)}^{9/2}} $
$ \Rightarrow $ $ y=18 $ Hence, $ x>y $