Question

$A , B$ and $C$ are distinct positive integers, less than or equal to 10 . The arithmetic mean of $A$ and $B$ is 9 . The geometric mean of $A$ and $C$ is $6 \sqrt{2}$. The harmonic mean of $B$ and $C$ is

• A. $9 \frac{9}{19}$
• B. $8 \frac{8}{9}$
• C. $2 \frac{7}{19}$
• D. $2 \frac{8}{17}$

Answer 1

Answer: (A)

$A + B = 18$ .....(1)
$AC = 72 $ ....(2)
There are only two possibilities
$A = 10$ and $B = 8$
If $A = 10$ then from (2) C is not an integer.
Hence $A = 8$ and $ B = 10; C = 9$
$\therefore \quad$ H.M. between $B$ and $C=\frac{2 \cdot 10 \cdot 9}{10+9}=\frac{180}{19}=9 \frac{9}{19}$