2018 AMC 12B Problem 5

Attempt Problem 5 of the 2018 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 2018 AMC 12B solutions, or check the answer key.

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

How many subsets of

\{2, 3, 4, 5, 6, 7, 8, 9\}

contain at least one prime number?

128

192

224

240

256

Count all subsets, then subtract those containing no prime number

The non-primes are

\{4,6,8,9\},

so subsets with no prime number are subsets of that set

The set has

8

elements, giving

2^8=256

subsets. The subsets with no prime use only the four non-primes

\{4,6,8,9\},

and there are

2^4=16

of these.

So the number containing at least one prime is

256-16=240.

Thus, the correct answer is D.

Problem 5 in other years