Question

If 1≤x≤3 and 3≤y≤5. The least possible average of 1/x and 1/y is:

(A) 2/3 (B) 3/5 (C) 4/15 (D) 8/15 (E) 4 /5

Answer 1

(C) 4/15

Explanation:

Given that 1 ≤ x ≤ 3 and we need to find the least value of 1/x. The least value of 1/x is gotten by taking the maximum value of x in the interval, hence the least value of 1/x = 1/5

Given that 3 ≤ y ≤ 5 and we need to find the least value of 1/y. The least value of 1/y is gotten by taking the maximum value of y in the interval, hence the least value of 1/y = 1/3

The least possible average of 1/x and 1/y =
`((1)/(x)+(1)/(y) )/(2) =((1)/(5)+(1)/(3) )/(2)=((8)/(15) )/(2) =(4)/(15)`