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 number , what is the smallest odd number.
A. 11
B. 13
C. 17
D. 19

Answer 1

Correct Answer - A
Let 3 consecutive odd numbers =x-2
x and x+2
and consecutive even numbers =y-2,y,y+2
So, y-2=9+x+2
y-x=13 `" "…`(i)
and
`(x)^(2)+507=(y)^(2)`
`y^(2)-x^(2)=507`
`(x+y)(y-x)=507`
`(x+y)=(507)/(13) implies x+y=39 " "...(ii)`
Solving (i) and (ii) y=26 and x=13
so smallest odd number =x-2
=13-2=11