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# Set A contains 16 even integers, and set B contains 22 integers that

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Re: Set A contains 16 even integers, and set B contains 22 integers that [#permalink]
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Bunuel
Set A contains 16 even integers, and set B contains 22 integers that are all multiples of 3. If 7 of the integers fall into both sets A and B, how many integers are in exactly one of the two sets?

A. 21
B. 22
C. 23
D. 24
E. 25

The 16 integers in set A include the 7 integers in both sets. So 16 - 7 = 9 integers are in set A only. Similarly, the 22 integers in set B include the 7 integers that are in both sets. So 22 - 7 = 15 integers are in set B only. Thus, the number of integers that are in exactly one set will be 9 + 15 = 24.

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Re: Set A contains 16 even integers, and set B contains 22 integers that [#permalink]
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Bunuel
Set A contains 16 even integers, and set B contains 22 integers that are all multiples of 3. If 7 of the integers fall into both sets A and B, how many integers are in exactly one of the two sets?

A. 21
B. 22
C. 23
D. 24
E. 25

Let's combine the two sets make one population, and then use the Double Matrix Method. This technique can be used for 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

Given: Set A contains 16 even integers. Set B contains 22 integers. 7 of the integers fall into both sets A and B
Add this information to our diagram to get:

Important: Since we're combining the integers from set A and set B, we can conclude that there are ZERO integers that are in neither set. That's why we have 0 in the bottom-right box

From here, we can complete the matrix as follows:

Question: How many integers are in exactly one of the two sets?
On the diagram we can see that there are 9 integers that are in set A but not in set B, and there are 15 integers that are in set B but not in set A.
Total = 9 + 15 = 24

This question type is VERY COMMON on the GMAT, so be sure to master the technique.

EXTRA PRACTICE QUESTION

More questions to practice with:
EASY: https://gmatclub.com/forum/of-the-120-p ... 15386.html
MEDIUM: https://gmatclub.com/forum/in-a-certain ... 21716.html
HARD: https://gmatclub.com/forum/a-group-of-2 ... 24888.html
KILLER: https://gmatclub.com/forum/a-certain-hi ... 32899.html
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Re: Set A contains 16 even integers, and set B contains 22 integers that [#permalink]
Bunuel
Set A contains 16 even integers, and set B contains 22 integers that are all multiples of 3. If 7 of the integers fall into both sets A and B, how many integers are in exactly one of the two sets?

A. 21
B. 22
C. 23
D. 24
E. 25

Set A has 16 integers
Set B has 22 integers
Both = 7

Only Set A = 16 - 7 = 9
Only Set B = 22 - 7 = 15

Number of integers in exactly one set = 9 + 15 = 24