Question

If the sum of two distinct positive numbers is 8 and the difference between the arithmetic mean and harmonic mean of the given two numbers is 1, then the value of the largest number is

• A. 4
• B. 8
• C. 6
• D. 7

Answer 1

The correct option is B

8

Let the two distinct positive numbers be a and b .

a + b = 8

$\frac{(a+b)}{2}-\frac{2ab}{(a+b)}=1(a+b{)}^2-4ab=2(a+b\left)\right(a-b{)}^2=16a-b=4$

Solving we get a =6 , b= 2

The largest number among the two is 6