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Let S and T be two sets
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18 Feb 2022, 10:06
18 Feb 2022, 10:06
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75% (02:05) correct
25% (03:16) wrong based on 4 sessions
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Let S and T be two sets such that the ratio of the number of elements in S to the number of elements in T to the number of elements in the set S∩T is 4 to 3 to 1. If the sum of the number of elements in S but not in T and the number of elements in T but not in S is 2520, what is the number of elements in S∩T?
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504
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Re: Let S and T be two sets
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18 Feb 2022, 15:30
18 Feb 2022, 15:30
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zperk525 wrote:
Let S and T be two sets such that the ratio of the number of elements in S to the number of elements in T to the number of elements in the set S∩T is 4 to 3 to 1. If the sum of the number of elements in S but not in T and the number of elements in T but not in S is 2520, what is the number of elements in S∩T?
Show: ::
504
Note: the elements in S∩T = the elements in BOTH S and T
We can solve this question using the Double Matrix Method (see video below)
If we combine all of the elements from sets S and T, some elements will be in both sets, some will be in just 1 set, but NONE will be in neither set. So our Matrix looks like this:
Given: the ratio of the number of elements in S to the number of elements in T to the number of elements in the set S∩T (in both S and T) is 4 to 3 to 1.
So, if we let x = the number of elements in both S and T, then the other two boxes look like this:
Finally, we can complete the matrix as follows:
Given: The sum of the number of elements in S but not in T (i.e., the top-right box) and the number of elements in T but not in S (i.e., the bottom left box) is 2520.
So, we can write: 3x + 2x = 2520
Simplify: 5x = 2520
Solve: x = 2520/5 = 504
Question: what is the number of elements in S∩T (i.e., the top left box)?
In other words, what is the value of x?
Answer: 504
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gmatclubot
Re: Let S and T be two sets [#permalink]
18 Feb 2022, 15:30
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