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02 Sep 2019, 01:25
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C
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Difficulty:
65%
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Question Stats:
54% (01:45) correct
46%
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wrong
based on 161
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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 \(A*B\)?
\(A. 25\)
\(B. 32\)
\(C. 36\)
\(D. 42\)
\(E. 49\)
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 \(A*B\)?
\(A. 25\)
\(B. 32\)
\(C. 36\)
\(D. 42\)
\(E. 49\)
02 Sep 2019, 02:17
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For sets A and B, define A∗B to be {(a,b)|a ∈ A and b ∈ B}
set A has = 6 elements
set B has = 6 elements
for every element in set A there are 6 elements in set B to form ordered pair (a,b)
there are 6 elements in set A and 6 element in set B = so maximum ordered pair (a,b) = 6*6 = 36
maximum ---A∗B {(a,b)|a ∈ A and b ∈ B} = 6*6 = 36
set A has = 6 elements
set B has = 6 elements
for every element in set A there are 6 elements in set B to form ordered pair (a,b)
there are 6 elements in set A and 6 element in set B = so maximum ordered pair (a,b) = 6*6 = 36
maximum ---A∗B {(a,b)|a ∈ A and b ∈ B} = 6*6 = 36
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04 Sep 2019, 00:46
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=>
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
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
