Quantitative Aptitude Ques 659

Question: If the LCM and HCF of two expressions are $ (x^{2}+6x+8)(x+1) $ and $ (x+1) $ respectively and one of the expressions is $ x^{2}+3x+2, $ then find the other expression.

Options:

A) $ x^{2}+5x+4 $

B) $ x^{2}-5x+4 $

C) $ x^{2}+4x+5 $

D) $ x^{2}-4x+5 $

Show Answer

Answer:

Correct Answer: A

Solution:

  • Given, $ LCM=(x^{2}+6x+8)(x+1) $ or $ (x+4)(x+2)(x+1) $ and $ HCF=\text{(}x+1) $ Ist expression $ =x^{2}+3x+2 $ or $ (x+1)(x+2) $ As we know that, Product of two expressions $ LCM\times HCF $

$ \Rightarrow $ $ (x+1)(x+2)\times 2ndexpression $ $ =(x+4)(x+2)(x+1)(x+1) $

$ \therefore $ 2nd expression $ =\frac{(x+4)(x+2)(x+1)(x+1)}{(x+1)(x+2)} $ $ =(x+4)(x+1) $ $ =x^{2}+4x+x+4 $ $ =x^{2}+5x+4 $

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