Question

Let a, b, and c be positive integers($a<b<c$). If the average (arithmetic mean) of a, b, and c is $100$, which of the following is NOT a possible value of any of the integers?

• A. $2$
• B. $100$
• C. $297$
• D. $298$
• E. $299$

Answer 1

Answer: (E)

$299$

Formula for mean is $m=\frac{a+b+c}{3}$.
Substituting the value in the formula for Mean, $m=\frac{a+b+c}{3}=100$

$\Rightarrow a+b+c=300$

$\Rightarrow a<b<c$ lies between $0$ and $299$.

where,

$(a,b,c)\ge 0$ and $(a,b,c)\le 298$

In case $E$

if $c=299$ then $b=1$ and $a=0$. This is not possible since a,b,c are positive integers.