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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 \(A*B\)?

\(A. 25\)

\(B. 32\)

\(C. 36\)

\(D. 42\)

\(E. 49\)
n(A U B) = n(A) + n(B) - n(A intersection B)
8 = n(A) + n(B) - 4
12 = n(A) + n(B)

To maximize the product, n(A) = n(B) = 6

Therefore, total sets = 6*6 = 36
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