Question

If $x$ and $y$ are positive integers, $y>x$, and the average (arithmetic mean) of $x$ and $y$ is $100$, then find the greatest possible value of $y$.

• A. $150$
• B. $198$
• C. $199$
• D. $200$
• E. $201$

Answer 1

Answer: (C)

$199$

Given, $x$ and $y$ are positive integers,
Arithmetic mean of $x$ and $y$ is $100$.
$\frac{x+y}{2}=100$
$x+y=200$
Given is $y>x$ and we know $x+y=200$ and both $x$ and $y$ are positive integers,
When $x$ will be smallest $y$ will be greatest, so if $x=1$ then $y$ will be $199$.
$1+y=200$
$y=199$
Greatest possible value of $y$ is $199$.