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The subsets of the set {a, b, c} are {a}, {b}, {c}, {a, b}, {a, c},

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KarunMendiratta
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The subsets of the set {a, b, c} are {a}, {b}, {c}, {a, b}, {a, c}, [#permalink] New post   09 Sep 2021, 10:02
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The subsets of the set {a, b, c} are {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}, and { } (the empty subset).

Quantity A
Quantity B
Number of subsets of the set {a, b, c, d} that contain a
10


A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
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B
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motion2020
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Re: The subsets of the set {a, b, c} are {a}, {b}, {c}, {a, b}, {a, c}, [#permalink] New post   09 Sep 2021, 11:59
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General direction: 3C3+3C2+3C1 AND 1 empty set result in (1+3+3)= 8 total arrangements

Solution: we need to find the total number of arrangements for subsets of set {a, b, c, d} and subtract from this all arrangements excluding 'a' OR all subsets of the set {b, c, d}.

4C4+4C3+4C2+4C1 AND 1 empty set less 3C3+3C2+3C1 AND 1 empty set = 1+4+6+4+1 - (1+3+3+1) = 8

Quantity A: 8
Quantity B:10

Quantity A > Quantity B
answer is B


KarunMendiratta wrote:
The subsets of the set {a, b, c} are {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}, and { } (the empty subset).

Quantity A
Quantity B
Number of subsets of the set {a, b, c, d} that contain a
10


A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
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Re: The subsets of the set {a, b, c} are {a}, {b}, {c}, {a, b}, {a, c}, [#permalink] New post   05 Jul 2024, 09:04
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Re: The subsets of the set {a, b, c} are {a}, {b}, {c}, {a, b}, {a, c}, [#permalink] New post   15 Dec 2024, 01:42
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It may be easier to just list all the possibilities since there's only 4 elements in the set and QB is 10. Goal is then to get as many sets with A as possible {a,b,c,d} we can get {a} , {a,b}, {a,c}, {a,d}, {a,b,c}, {a,b,d}, {a,c,d}, {a,b,c,d} which gives us 8 ways 8<10 so B is the ans. Also remember that order does not matter in sets (but it does in lists so if this was a lists question, we would also permute the answers)
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Re: The subsets of the set {a, b, c} are {a}, {b}, {c}, {a, b}, {a, c}, [#permalink]
15 Dec 2024, 01:42
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