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SSC CPO 2023 PYQ — Question 105

SSC CPO - 04 Oct 2023 - Shift 2 • Quantitative Aptitude • Q105

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Simplify the given expression.

(3.254×3.254×3.254)−(0.746×0.746×0.746)(3.254×3.254)+(0.746×0.746)+(3.254×0.746)\frac{(3.254\times3.254\times3.254)-(0.746\times0.746\times0.746)}{(3.254\times3.254)+(0.746\times0.746)+(3.254\times0.746)}

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 2.508.

Given that

(3.254×3.254×3.254)−(0.746×0.746×0.746)(3.254×3.254)+(0.746×0.746)+(3.254×0.746)\frac{(3.254\times3.254\times3.254)-(0.746\times0.746\times0.746)}{(3.254\times3.254)+(0.746\times0.746)+(3.254\times0.746)}

⇒ Formula used

a3 − b3  = (a−b)(a2 + b2 + ab)

⇒ (3.254−0.746)((3.254×3.254)+(0.746×0.746)+(3.254×0.746))(3.254×3.254)+(0.746×0.746)+(3.254×0.746)\frac{(3.254- 0.746)((3.254\times3.254)+(0.746\times0.746)+(3.254\times0.746))}{(3.254\times3.254)+(0.746\times0.746)+(3.254\times0.746)}

⇒ 3.254 - 0.746

⇒ 2.508