SSC CGL Model Paper 14

Question : 51 of 100

Marks: +1, -0

If the square of sum of three positive consecutive natural numbers exceeds the sum of their squares by 292, then what is the largest of the three numbers?

Validate

Solution:

Let the three positive consecutive natural numbers be x, x + 1 and x + 2, respectively.
According to the question,

[x + x + 1 + x + 2 ]^2

- [ x^2 + (x + 1)^2 + (x + 2 )^2]

= 292

⇒ [3x + 3 ]^2 - [ x^ 2 + x ^2 + 1

+ 2 x + x ^2 + 4 + 4 x ] =292

⇒ 9x^2 + 9 + 1 8 x

-3 x ^2 - 6 x - 5=292

⇒ 6 x ^2 + 12x + 4 -2 9 2 = 0

⇒ x^2+2 x - 4 8 = 0

⇒ x ^2 + 8 x - 6 x - 4 8 = 0

⇒ x (x + 8) - 6 (x + 8) = 0

⇒ (x + 8 ) ( x - 6 ) = 0

∴ x =6

The largest of the three numbers

= x + 2 = 6 + 2 = 8

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