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SSC CGL 2021 PYQ — Question 54

SSC CGL - 17 Aug 2021 - Shift 3 • Quantitative Aptitude • Q54

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Simplify the following expression:

108×108×108−92×92×92108×108+92×92+108×92\frac{108×108×108-92×92×92}{108×108+92×92+108×92}

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Correct answer: A

Explanation

The correct answer is Option 1 i.e ​​​​​​ 16.

One knows that , a3 - b3 = (a - b)(a2 + ab + b2)

⇒ 108×108×108−92×92×92108×108+92×92+108×92\frac{108×108×108-92×92×92}{108×108+92×92+108×92} 

⇒ 1083−9231082+922+108×92\frac{108^3 - 92^3}{108^2+92^2+108×92}

⇒ (108 - 92) = 16