# Difficult Averages Solved QuestionAptitude Discussion

 Q. In a set of three numbers, the average of first two numbers is 2, the average of the last two numbers is 3, and the average of the first and the last numbers is 4. What is the average of three numbers?
 ✖ A. 2 ✖ B. 2.5 ✔ C. 3 ✖ D. 3.5

Solution:
Option(C) is correct

Let the three numbers be $x, y$, and $z$. We are given that

$\dfrac{x+y}{2}=2$

$\dfrac{y+z}{2}=3$

$\dfrac{x+z}{2}=4$

Summing the three equations yields

$\dfrac{x+y}{2}+\dfrac{y+z}{2}+\dfrac{x+z}{2}=2+3+4$

$x+y+z=9$

The average of the three numbers is

$=\dfrac{x+y+z}{3}$

$=\dfrac{9}{3}=3$

## (1) Comment(s)

SUHAIL AHMED
()

$=\dfrac{3XYZ}{XY}+YZ+ZX$
First two terms $= XY$
Last two terms $= YZ$
First and Last terms $= ZX$
Average of three numbers $= XYZ$