Maths Olympiad Prep

Library / /45 of 520

Algebra Difficulty 4.7 AIME Find the answer

6、The table below shows the score distribution of 50 students in Ye's class:
\begin{array}{c|c|c|c|c|c|c|c|c} \hline Score & 0 & 1 & 2 & 3 & 4 & \mathbf{5} & 6 & Total \\ \hline \begin{array}{c} Number \\ of \\ Students \end{array} & 4 & 4 & 5\mathbf{5} & AA & 15 & BB & 2\mathbf{2} & 50 \\
\hline
\end{tabular}

The average score in this exam is 3 points.
(1) How many students should be filled in the AA and BB columns?
(2) This exam consists of 3 questions, with the scoring distribution as follows: 1 point for the first question, 2 points for the second question, and 3 points for the third question. How many students answered at least 2 questions correctly?

A number or a short expression. Spacing and $ signs are ignored.

Solution

6. ( 1 ) AA is 18 people, BB is 2 people; (2)19 people or more.

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.