The average of the squares of four consecutive odd natural numbers is 201. The average of 7 times of the largest number and 3 times of the smallest number is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 76
Explanation:
Let x be an odd natural number.
Then 4 consecutive odd numbers = (x - 2), (x + 2), (x + 4)
Acording to the given question,
(x - 2)2 + x2 + (x + 2)2 + (x + 4)2 = (201 × 4)
⇒ x2 - 4x - 4 + x2 + x2 + 4x + 4 + x2 + 8x + 16 = 804
⇒ 4x2 + 8x + 24 = 804
⇒ x2 + 2x + 6 = 201
⇒ x2 + 2x - 195 = 0
⇒ x2 + 15x - 13x - 195 = 0
⇒ x(x + 15) - 13(x + 15) = 0
⇒ (x - 13)(x + 15) = 0
⇒ x = 13; x = -15(not possible)
Now, Largest number = (x + 4) = 13 + 4 = 17
Smallest Number = (x -2 ) = 13 - 2 = 11
So, required value = = = = 76
Hence the required answer is 76.