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Set A has 50 members and set B has 53 members. At least 2 of [#permalink]
03 Jul 2016, 16:18

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Set A has 50 members and set B has 53 members. At least 2 of the members in set A are not in set B. Which of the following could be the number of members in set B that are not in set A ?

Re: Set A has 50 members and set B has 53 members. At least 2 of [#permalink]
03 Jul 2016, 16:25

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Explanation

Let x be the number of members in the intersection of set A and set B. Then the distribution of the members of A and B can be represented by the following Venn diagram.

The question asks you to indicate which of the answer choices could be the number of members in set B that are not in set A. This is equivalent to determining which of the answer choices are possible values of 53 – x.

You are given that the number of members in set A that are not in set B is at least 2, and clearly the number of members in set A that are not in set B is at most all 50 members of A; that is, 2 ≤ 50 – x ≤ 50. Note that 53 – x is 3 more than 50 – x. So by adding 3 to each part of 2 ≤ 50 – x ≤ 50, you get the equivalent inequality 5 ≤ 53 – x ≤ 53. Thus the number of members in set B that are not in set A can be any integer from 5 to 53. The correct answer consists of Choices B, C, D, E, and F.

Re: Set A has 50 members and set B has 53 members. At least 2 of [#permalink]
13 Aug 2017, 06:04

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sandy wrote:

Set A has 50 members and set B has 53 members. At least 2 of the members in set A are not in set B. Which of the following could be the number of members in set B that are not in set A ?

Another approach is to use the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions). Here, we have a population of numbers, and the two characteristics are: - In set A or NOT in set A - In set B or NOT in set B

With the given information, we can set up our Matrix as follows: Our goal is to determine which values can go in the bottom left corner (marked with a star)

Let's start by seeing what happens if we minimize the number of values that are in the TOP RIGHT corner (the number of values that are in set A BUT NOT in set B) Since at least 2 values must be in this box, let's see what happens when there are 2 numbers there. We get: In this case, there are 5 numbers that are in set B but not in set A (bottom left box)

Now let's see what happens when we place a 3 in the box representing the number of values that are in set A BUT NOT in set B (i.e., the TOP RIGHT corner box): In this case, there are 6 numbers that are in set B but not in set A (bottom left box)

Now let's see what happens when we place a 4 in the box representing the number of values that are in set A BUT NOT in set B (i.e., the TOP RIGHT corner box): In this case, there are 7 numbers that are in set B but not in set A (bottom left box)

Now let's see what happens when we MAXIMIZE the box representing the number of values that are in set A BUT NOT in set B (i.e., the TOP RIGHT corner box): The biggest value that can go here is 50, since numbers in the top row of boxes must add to 50. In this case, there are 53 numbers that are in set B but not in set A (bottom left box)

So, the possible numbers that can be in the bottom left box range from 5 to 53 INCLUSIVE

Answer: B, C, D, E, F

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