2007 AMC 12B Problem 12

Below is the professionally curated solution for Problem 12 of the 2007 AMC 12B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2007 AMC 12B solutions, or check the answer key.

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Concepts:meanpercentage

Difficulty rating: 1330

12.

A teacher gave a test to a class in which 10%10\% of the students are juniors and 90%90\% are seniors. The average score on the test was 84.84. The juniors all received the same score, and the average score of the seniors was 83.83. What score did each of the juniors receive on the test?

8585

8888

9393

9494

9898

Solution:

Take a class of 1010 students, so there is 11 junior and 99 seniors.

The total of all scores is 1084=840,10\cdot84=840, and the seniors contribute 983=747.9\cdot83=747. So the junior scored 840747=93. 840-747=93.

Thus, the correct answer is C.

Problem 12 in Other Years