SSC CGL 20 Aug 2021 Shift 1 Paper

Question : 65 of 100

Marks: +1, -0

The average of squares of five consecutive odd natural numbers is 233. What is the average of the largest number and the smallest number?

Solution:

Let the 5 consecutive odd natural numbers are

(x-4),(x-2), x,(x+2)

and

(x+4)

(x-4)^{2}+(x-2)^{2}+x^{2}+(x+2)^{2}

+(x+4)^{2}=233 × 5

⇒ x^{2}+16-8 x+x^{2}+4-4 x+x^{2}+x^{2}

+4+4 x+x^{2}+16+8 x=1165

⇒ \;\; 5 x^{2}+40=1165

⇒ \;\; 5 x^{2}=1125

⇒ \;\; x^{2}=225

⇒ \;\; x=15

Now, Largest number

=(x+4)

=15+4=19

Smallest number

=(x-4)

=15-4=11

∴

Average of 2 numbers

=\;{11+19}/{2}

=\;{30}/{2}=15

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