2015 AMC 12B Problem 5

Attempt Problem 5 of the 2015 AMC 12B below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2015 AMC 12B solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

The Tigers beat the Sharks

2

out of the first

3

times they played. They then played

N

more times, and the Sharks ended up winning at least

95\%

of all the games played. What is the minimum possible value for

N?

35

37

39

41

43

To minimize

N,

let the Sharks win all

N

additional games

Solve

\dfrac{1 + N}{3 + N} \ge \dfrac{95}{100}

The Sharks won

1

of the first

3

games. To reach

95\%

with the fewest extra games, they should win all

N

additional games, giving a win fraction

\dfrac{1 + N}{3 + N}.

Requiring

\dfrac{1 + N}{3 + N} \ge \dfrac{19}{20}

gives

20 + 20N \ge 57 + 19N,

N \ge 37.

Thus, the correct answer is B.

Problem 5 in other years