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Set A consists of 40 integers, [#permalink]
26 Jan 2016, 01:02

Expert's post

00:00

Question Stats:

77% (00:40) correct
22% (00:19) wrong based on 54 sessions

Set A consists of 40 integers, and set B consists of 150 integers. The number of integers that are in both set A and set B is 20.

Quantity A

Quantity B

The total number of integers that are in set A or set B, or both

170

A)The quantity in Column A is greater. B)The quantity in Column B is greater. C)The two quantities are equal. D)The relationship cannot be determined from the information given.

Practice Questions Question: 4 Page: 465 Difficulty: hard

Re: Set A consists of 40 integers, [#permalink]
26 Jan 2016, 01:14

Expert's post

Solution

given that the number of integers in set A is 40, the number of integers in set B is 150, and the number of integers that are in both A and B is 20. You are asked to compare the total number of integers that are in set A or set B, or both, with 170.

The following Venn diagram is a representation of the integers in sets A and B.

Redrawing the Venn diagram so that the numbers are separated into three categories: the integers in A only, the integers in B only, and the integers in both A and B. The revised Venn diagram follows.

We observe that summing the numbers of integers in set A only, set B only, and both A and B yields the total number of integers that are in set A or set B, or both. Therefore, Quantity A is 20+130+20, or 170, and the correct answer is Choice C.

Re: Set A consists of 40 integers, [#permalink]
04 Oct 2016, 08:39

1

This post received KUDOS

Also, the formula for total number of items in sets A and B is Total = A + B - A and B. We are given A, B and A and B in the question, so you can plug in the numbers 40 + 150 - 20 = 170, so the answer is C. This saves the time required for drawing venn diagrams.

Re: Set A consists of 40 integers, [#permalink]
28 Jul 2017, 12:47

Expert's post

sandy wrote:

Set A consists of 40 integers, and set B consists of 150 integers. The number of integers that are in both set A and set B is 20.

Quantity A

Quantity B

The total number of integers that are in set A or set B, or both

170

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 integers, and the two characteristics are: - in Set A or not in Set A - in Set B or not in Set B

So, we can set up our diagram as follows:

Since there are 20 integers that are in BOTH set A and set B, we can add that to the diagram...

This allows us to fill in two other boxes...

Notice that we don't have enough information to fill in the last box, which means we also don't know the total number of integers combined. HOWEVER, we don't need this information.

Quantity A = The total number of integers that are in set A or set B, or both Notice that the 3 highlighted boxes represent integers that are in set A or set B, or both So, Quantity A = 20 + 20 + 130 = 170

So, Quantity A = Quantity B Answer: C

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