Question

If the average of $x$ and $y$ is $50$, and the average of $y$ and $z$ is $80$, what is the value of $z-x$?

• A. $60$
• B. $70$
• C. $40$
• D. $50$

Answer 1

The correct option is A $60$

The sum of two numbers is twice their average. Therefore:

$x+y=100y+z=160$

$x=100-yz=160-y$

Substitute these expressions for $z$ and $x$:

$z-x=(160-y)-(100-y)=160-y-100+y=160-100=60$

Alternatively, pick smart numbers for x and y. Let $x=50$ and $y=50$ (this is an easy way to make their average equal to $50$). Since the average of y and z must be $80$, you have $z=110$. Therefore, $z-x=110-50=60$.