Question

If the A.M of two numbers is greater than G.M by $2$. Then the numbers are

• A. $4,1$
• B. $12,3$
• C. $16,4$
• D. None of these

Answer 1

Answer: (C)

$16,4$

Let the two numbers be a and b.

$A.M.=\frac{a+b}{2}$

$G.M.=\sqrt{ab}$

$A.M.=G.M+2$

$\frac{a+b}{2}=\sqrt{ab}+2$

$a+b=2\sqrt{ab}+4$

Now considering each option

(A)

$LHS=5$ and $RHS=8$

(B)

$LHS=15$ and $RHS=16$

(C)

$LHS=20$ and $RHS=20$ so $LHS=RHS$

So the correct answer is (C).