Quantitative Aptitude Ques 1327

Question: Simplify $ \frac{ \begin{aligned} & 24\times 24\times 24+32\times 32\times 32+45\times 45 \\ & \times 45-3\times 24\times 32\times 45 \\ \end{aligned}}{ \begin{aligned} & 24\times 24\times 32\times 32+45\times 45-24\times 32 \\ & -32\times 45-45\times 24 \\ \end{aligned}} $

Options:

A) 105

B) 101

C) 103

D) 107

Show Answer

Answer:

Correct Answer: B

Solution:

  • Given expression is of the form $ a^{3}+b^{3}+c^{3}-3abc $ $ =(a+b+c)(a^{2}+b^{2}+c^{2}-ab-bc-ca) $

$ \therefore $ $ \frac{a^{3}+b^{3}+c^{3}-3abc}{a^{2}+b^{2}+c^{2}-ab-bc-ca}=a+b+c $

$ \therefore $ $ a+b+c=24+32+45=101 $