Subject: General Aptitude · Chapter: Average · Exam: 2006 · Marks: · Difficulty:
The average of two numbers is 6.5 and square root of their product is 6. What are the numbers?
(a)11 and 2
(b)8 and 5
(c)9 and 4
(d)10 and 3
Answer
Answer (as printed): C
Explanation
Let the two numbers be $x$ and $y$. Then, $x+y=6.5 \times 2=13$ and $\sqrt{x y}=6$ or $x y=36$. $$\begin{aligned} & (x-y)^{2}=(x+y)^{2}-4 x y=(13)^{2}-4 \times 36=169-144=25 \\ & \Rightarrow(x-y)=5 . \end{aligned}$$ Solving $x+y=13$ and $x-y=5$, we get: $x=9, y=4$.
Explanation as extracted from the printed page; notation may be imperfect.