# Problem of the Day

Joe took 20 equally weighted quizzes for his biology class and received an average score of 96% on those quizzes. If he received a grade of 96% on exactly of the quizzes, what is ?

(1)

(2)

A. Statement 1 alone is sufficient, but statement 2 alone is insufficient.

See the Solution

### Solution

[latexpage]

Statement 1: If he took 20 quizzes, and $n>18$ then either $n=19$ or $n=20$. However, it is impossible that $n=19$. If he were to score exactly 96% on 19 of the quizzes, then he would also have to score 96% on his 20th quiz to maintain the 96% average. Otherwise, his average would be slightly above or below 96%. SUFFICIENT.

Statement 2: $n\leq20$ doesn’t tell us anything we don’t already know. If he took 20 quizzes than obviously the number that he scored exactly 96% on is less than 20. INSUFFICIENT.