Question

There are 3 consecutive odd numbers and 3
consecutive even numbers. The smallest even
number is 9 more than largest odd number. If the
square of average of all the 3 given odd number is
507 less than the square of the average of all the 3
given even number, what is the smallest odd
number.
(a) 11 (b) 13 (c) 17
(d) 19 (e) 9

Answer 1

Let the three consecutive odd numbers be: 2x+1, 2x+3, 2x+5.
Let the three consecutive even numbers be: 2x+14, 2x+16, 2x+18.

According to first condition,
2x+14 = (2x+5) + 9 which is true.

According to second condition,
((6x+9)/3))^2 = ((6x+48)/3))^2- 507

By simplifying,
x= 5.
The smallest odd number is 2(5)+1= 11.