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

Answer:

(C) 4/15

Step-by-step 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 = $\frac{\frac{1}{x}+\frac{1}{y} }{2} =\frac{\frac{1}{5}+\frac{1}{3} }{2}=\frac{\frac{8}{15} }{2} =\frac{4}{15}$