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SAT Questions Gaja Mathematics Challenge Problems

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Define a set to be \(\textbf{selfish}\) if the number of elements it has is in the set. For example, \(X_{10}=\{1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7,\ 8,\ 9,\ 10\}\) is selfish because it has 10 elements, and 10 is in the set. How many selfish subsets does Xn have, where n is a positive integer?

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Question Type: Extended Constructed Response

Standard(s):HSN.RN.A.1

Standard Description: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5

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