2019 AMC 10 A

Complete problem set with solutions and individual problem pages

Problem 4 Easy

A box contains 28 red balls, 20 green balls, 19 yellow balls, 13 blue balls, 11 white balls, and 9 black balls. What is the minimum number of balls that must be drawn from the box without replacement to guarantee that at least 15 balls of a single color will be drawn? (2019 AMC 10A Problem, Question#4)

  • A.

    75

  • B.

    76

  • C.

    79

  • D.

    84

  • E.

    91

Answer:B

By choosing the maximum number of balls while getting <15 of each color, we could have chosen 14 red balls, 14 green balls, 14 yellow balls, 13 blue balls, 11 white balls, and 9 black balls, for a total of 75 balls. Picking one more ball guarantees that we will get  15 balls of a color -- either red, green, or yellow. Thus the answer is 75+1=76.

Related Problems
Problem 2 2019 AMC 10 A
Problem 3 2019 AMC 10 A
Problem 5 2019 AMC 10 A
Problem 6 2019 AMC 10 A
Think Academy Powered by ChatGPT