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

Question

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

Archit3110 · Answer

Set A= 16 even integers
Set B = 22 integers
set a & b overlap = 7 integers
so not in both ; 22+16-(2*7) ; 24
IMO D

Abhishek009 · Answer

( 16 - 7) + ( 22 - 7) = 9 + 15 => 24 , Answer must be (D)

ScottTargetTestPrep · Answer

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.

Answer: D

BrentGMATPrepNow · Answer

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 So we start with something like this: https://i.imgur.com/bDqB5Gx.png 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: https://i.imgur.com/YBtEM53.png 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: https://i.imgur.com/sEb6is6.png 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 Answer: D This question type is VERY COMMON on the GMAT, so be sure to master the technique. To learn more about the Double Matrix Method, watch this video: https://www.youtube.com/watch?v=jK-tiBrrf04 EXTRA PRACTICE QUESTION https://www.youtube.com/watch?v=DsbPUSH_Wu4 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

KarishmaB · Answer

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 Answer (D) Check this video on how to handle two overlapping sets: https://youtu.be/HRnuURqGhmg

bumpbot · Answer

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

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

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