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A={2, 4, 6, 8, 10} is given. How many subsets of A contain 4

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A={2, 4, 6, 8, 10} is given. How many subsets of A contain 4

by Max@Math Revolution » Tue Aug 27, 2019 11:38 pm

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[GMAT math practice question]

A={2, 4, 6, 8, 10} is given. How many subsets of A contain 4 and 6, but not 10?

A. 4
B. 6
C. 8
D. 9
E. 11
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by deloitte247 » Sat Aug 31, 2019 5:21 pm
We are looking for subsets of A that will include 4 and 6 but not 10
Subset 1 = {4, 6}
Subset 2 = {2, 4, 6}
Subset 3 = {2, 4, 6, 8}
Subset 4 = {2, 8}
So, from the superset A, there are 4 possible subsets containing 4 and 6 but not 10

Answer = option A
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by Max@Math Revolution » Sun Sep 01, 2019 9:08 pm
=>

Subsets of A must contain 4 and 6, but must not contain 10.
These subsets either contain 2, or don't contain 2. They also either contain 8, or don't contain 8. There are two possible outcomes for each of 2 and 8.

So, the number of subsets of A containing 4, 6 but 10 is 2^{5-3} = 2^2 = 4.

Therefore, A is the answer.
Answer: A
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