Difference between revisions of "2018 AMC 10B Problems/Problem 5"
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Consider finding the number of subsets that do not contain any primes. There are four primes in the set: <math>2</math>, <math>3</math>, <math>5</math>, and <math>7</math>. This means that the number of subsets without any primes is the number of subsets of <math>\{4, 6, 8, 9\}</math>, which is just <math>2^4 = 16</math>. The number of subsets with at least one prime is the number of subsets minus the number of subsets without any primes. The number of subsets is <math>2^8 = 256</math>. Thus, the answer is <math>256 - 16 = 240</math>. <math>\boxed{D}</math> | Consider finding the number of subsets that do not contain any primes. There are four primes in the set: <math>2</math>, <math>3</math>, <math>5</math>, and <math>7</math>. This means that the number of subsets without any primes is the number of subsets of <math>\{4, 6, 8, 9\}</math>, which is just <math>2^4 = 16</math>. The number of subsets with at least one prime is the number of subsets minus the number of subsets without any primes. The number of subsets is <math>2^8 = 256</math>. Thus, the answer is <math>256 - 16 = 240</math>. <math>\boxed{D}</math> | ||
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| + | ==See Also== | ||
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| + | {{AMC10 box|year=2018|ab=B|num-b=3|num-a=5}} | ||
| + | {{MAA Notice}} | ||
Revision as of 15:28, 16 February 2018
Problem
How many subsets of 
contain at least one prime number?
Solution
Consider finding the number of subsets that do not contain any primes. There are four primes in the set: 
, 
, 
, and 
. This means that the number of subsets without any primes is the number of subsets of 
, which is just 
. The number of subsets with at least one prime is the number of subsets minus the number of subsets without any primes. The number of subsets is 
. Thus, the answer is 
. 
See Also
| 2018 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 3 |
Followed by Problem 5 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
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