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Quantitative Aptitude

Polygons(n>3)

The sum of th...

Question

The sum of the squares of three consecutive natural numbers is 2030.What is the middle number?

A

25

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B

26

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C

27

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D

28

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E

24

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Solution

The correct option is B
26

Let the numbers be x and x+1 and x+2

Then, $x^{2} + {(x + 1)}^{2} + {(x + 2)}^{2} = 2030 \Leftrightarrow 3 x^{2} + 6 x - 2025 = 0.$ $\Leftrightarrow x^{2} + 2 x - 675 = 0 \Leftrightarrow (x + 27) (x - 25) = 0 \Leftrightarrow x = 25.$

$∴$ Middle number = $(x + 1) = 26.$

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