Question

A teacher gave a test to a class in which $10\%$ of the students are juniors and $90\%$ are seniors. The average score on the test was $84.$ The juniors all received the same score, and the average score of the seniors was $83.$ What score did each of the juniors receive on the test?

$85$

$88$

$93$

$94$

$98$

Answer: C

Concepts:mean ratio and proportion

Difficulty rating: 1330

Solution:

Suppose the class has $10$ students: one junior and nine seniors. The total of all scores is $10\cdot 84=840.$

The nine seniors total $9\cdot 83=747,$ so the junior's score is $s=840-747=93.$

Thus, the correct answer is C.

2007 AMC 10B Problem 16

Answer: C

Difficulty rating: 1330

Solution:

Problem 16 in Other Years