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SSC CGL 2024 PYQ — Question 71

SSC CGL - 09 Sep 2024 - Shift 2 • Quantitative Aptitude • Q71

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Simplify: (8.3)3+(9.2)3+(6.1)3−3×8.3×9.2×6.1(8.3)2+(9.2)2+(6.1)2−8.3×9.2−9.2×6.1−6.1×8.3\frac{(8.3)^3+(9.2)^3+(6.1)^3-3\times8.3\times9.2\times6.1}{(8.3)^2+(9.2)^2+(6.1)^2-8.3\times9.2-9.2\times6.1-6.1\times8.3}

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Correct answer: B

Explanation

The correct answer is Option 2 i.e. 23.6.

a3 + b3 + c3 - 3abc = (a + b + c)(a2 + b2 + c2 - ab - bc - ca)

⇒ (8.3)3+(9.2)3+(6.1)3−3×8.3×9.2×6.1(8.3)2+(9.2)2+(6.1)2−8.3×9.2−9.2×6.1−6.1×8.3\frac{(8.3)^3+(9.2)^3+(6.1)^3-3\times8.3\times9.2\times6.1}{(8.3)^2+(9.2)^2+(6.1)^2-8.3\times9.2-9.2\times6.1-6.1\times8.3}

⇒ (8.3+9.2+6.1)((8.3)2+(9.2)2+(6.1)2−8.3×9.2−9.2×6.1−6.1×8.3)((8.3)2+(9.2)2+(6.1)2−8.3×9.2−9.2×6.1−6.1×8.3)\frac{(8.3+9.2+6.1)((8.3)^2+(9.2)^2+(6.1)^2-8.3\times9.2-9.2\times6.1-6.1\times8.3)}{((8.3)^2+(9.2)^2+(6.1)^2-8.3\times9.2-9.2\times6.1-6.1\times8.3)}

⇒ 8.3 + 9.2  + 6.1 = 23.6