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For sets A and B, define A*B to be

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by Max@Math Revolution » Mon Sep 02, 2019 12:10 am

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[GMAT math practice question]

For sets A and B, define A*B to be {(a, b)|a ∈ A and b ∈ B}. If the number of elements of A ∪ B is 8 and A ∩ B has 4 elements, what is the maximum number of elements of A*B?

A. 25
B. 32
C. 36
D. 42
E. 49
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by Max@Math Revolution » Tue Sep 03, 2019 11:29 pm
=>

Define n(X) to be the number of elements of a set X.
Since n(A ∪ B) = n(A) + n(B) - n(A ∩ B), we have n(A) + n(B) = n(A ∪ B) + n(A ∩ B) = 8 + 4 = 12.
Since n(A*B) = n(A)*n(B), the maximum value of n(A)*n(B), where n(A) + n(B) = 12, is 6*6 = 36.

Therefore, C is the answer.
Answer: C
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