Quantitative Aptitude Ques 2489

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

I. $ x^{2}-{{(16)}^{2}}={{(23)}^{2}}-56 $ II. $ {y^{1/3}}-55+376={{(18)}^{2}} $

Options:

A) If $ x>y $

B) If $ x\le y $

C) If $ x<y $

D) If $ x\ge y $

E) If relationship between x and y cannot be determined

Show Answer

Answer:

Correct Answer: B

Solution:

  • I. $ x^{2}-{{(16)}^{2}}={{(23)}^{2}}-56 $

$ \Rightarrow $ $ x^{2}-256=529-56\Rightarrow x^{2}=729 $

$ \therefore $ $ x=\pm ,27 $ II. $ {y^{1/3}}-55+376={{(18)}^{2}} $

$ \Rightarrow $ $ {y^{1/3}}-55+376=324\Rightarrow {y^{1/3}}=3 $

$ \Rightarrow $ $ y=27 $ [taking cube on both sides]

$ \therefore $ $ x\le y $

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