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SSC CGL 2024 PYQ — Question 53

SSC CGL - 13 Sep 2024 - Shift 2 • Quantitative Aptitude • Q53

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Simplify 1.5×1.5+2.5×2.5+3.5×3.5+2×1.5×2.5+2×2.5×3.5+2×1.5×3.51.5+2.5+3.51.5 × 1.5 + 2.5 × 2.5 + 3.5 × 3.5 + 2 × 1.5 × 2.5 + 2 × 2.5 × 3.5 + 2 × 1.5 × 3.5\over 1.5 + 2.5 + 3.5

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 7.5.

1.5×1.5+2.5×2.5+3.5×3.5+2×1.5×2.5+2×2.5×3.5+2×1.5×3.51.5+2.5+3.51.5 × 1.5 + 2.5 × 2.5 + 3.5 × 3.5 + 2 × 1.5 × 2.5 + 2 × 2.5 × 3.5 + 2 × 1.5 × 3.5\over 1.5 + 2.5 + 3.5

=1.52+2.52+3.52+(2×1.5×2.5)+(2×2.5×3.5)+(2×1.5×3.5)1.5+2.5+3.5={1.5^2 + 2.5^2 + 3.5^2 + (2 × 1.5 × 2.5) + (2 × 2.5 × 3.5) + (2 × 1.5 × 3.5)\over 1.5 + 2.5 + 3.5}

= (1.5 + 2.5 + 3.5)2/(1.5 + 2.5 + 3.5)   [∵ (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca]

= (1.5 + 2.5 + 3.5)

= 7.5

Therefore, the value of the given expression is 7.5