Question

On a recent chemistry test, the average (arithmetic mean) score among $5$ students was $83$, where the lowest and highest possible scores were $0$ and $100$, respectively. If the teacher decides to increase each student's score by $2$ 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 $25$

• A. I only
• B. II only
• C. I and II only
• D. I and III only
• E. None of the above

Answer 1

The correct option is D I and III only

Given the average score among $s$ student was $83$.

Then total score $=$ $83\times 5=415$

If teacher increase $2$ point each student the total score $=$ $415+10=425$

(I)Then average score after increased $=$ $\frac{425}{5}=85$

(II) when the score are increased the difference between the height and lower score not increased because originally scored not more then $98$.

(III)After the increase all $5$ score are greater then or equal to $25$ is write because all score is equal to and grater then $25$.

Then option I and III is write.