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.



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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.

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

RELATED VIDEO

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Is there any easy way?

Try the double matrix form it should make it a more straightforward approach

Quantity A asks for the highlighted part. Let me know if it is not clear

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