AMC 10 Daily Practice Round 2

Complete problem set with solutions and individual problem pages

Problem 15 Medium

Consider a 20-problem test with multiple choices and fill-in-the-blanks. Each multiple choice worth 4 points and each fill-in-the-blank worth 6 points. The overall correct rate is 53\% (accross the problems). In addition, the correct rate of fill-in-the-blanks is 45\% and the average score is 53.2. Determine the correct rate of multiple choices.

  • A.

    52

  • B.

    55

  • C.

    60

  • D.

    63

  • E.

    65

Answer:E

Average number of problems correct: 20\times53\%=10.6.

Average number of correct fill-in-the-blanks: (53.2-4\times10.6)\div (6-4)=5.4, so average number of correct multiple choices: 10.6-5.4=5.2.

There are 5.4\div45\%=12 multiple choices, so there are 20-12=8 fill-in-the-blanks.

Correct rate on multiple choices: \frac{5.2}{8}\times 100 \% =65\%.

Related Problems
Problem 13 AMC 10 Daily Practice Round 2
Problem 14 AMC 10 Daily Practice Round 2
Problem 16 AMC 10 Daily Practice Round 2
Problem 17 AMC 10 Daily Practice Round 2
Think Academy Powered by ChatGPT