On a recent chemistry test, the average (arithmetic mean) score among 5 students was 83, where the loest and highest possible scores were 0 and 100, respectively. If the teacher decides to increase each student's score bt 2 points, and if none of the students originally scored more than 98, which of the following must be true?
I. After the scores are increased, the average score is 85.
II. When the scores are increased, the difference between the highest and lowest scores increases.
III. After the increase, all 5 scores are greater than or equal to 25.

Question

Uniteasy Admin · Accepted Answer

$$ \dfrac{a+b+c+d+e}{5}  =83 $$
$$ \dfrac{a+b+c+d+e}{5} \cdotp 1.02  = 83	imes 1.02 =84.66\approx 85  $$

So I is right

Let $$ a $$ is the lowest, $$ b $$ the highest
Before scores increased, the difference is
$$ b-a $$
After scores increased, the difference is
$$ 1.02(b-a) $$
So II is also right

Let a,b,c,d are near 100 after increase because none of them is larger than 98.
$$ a+b+c+d<400 $$

 $$ \because  \dfrac{a+b+c+d+e}{5}=85 $$
$$ e=425-(a+b+c+d)>525-400=25 $$
Therefore  III is also right

Multiple Choice Question (MCQ)

Answer