Question

Two numbers whose arithmetic mean is $34$ and the geometric mean is $16,$ then ratio of numbers is

• A. $5$ or $1/5$
• B. $4$ or $1/4$
• C. $2$ or $1/2$
• D. $16$ or $1/16$

Answer 1

Answer: (D)

Let the two numbers be $a$ and $b$. Then, $AM=34$
$\Rightarrow \frac{a+b}{2}=34$
$\Rightarrow a+b=68$
and $GM=16\Rightarrow \sqrt{ab}=16\Rightarrow ab=256(1)$
$\therefore (a-b{)}^2=(a+b{)}^2-4ab$
$\Rightarrow (a-b{)}^2=(68{)}^2-4\times 256=3600$
$\Rightarrow a-b=60(2)$
On solving (1) and $(2),$ we get $a=64$ and $b=4$
Hence ratio of number is $16$ or $1/16$