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Three cubes are each formed from the pattern shown. They are then stacked on a table one on top of another so that the \(13\) visible numbers have the greatest possible sum. What is that sum?(A) \(154\) (B) \(159\) (C) \(164\) (D) \(167\) (E) \(189\) 정답 (C)

A function \(f\) has domain \([0, \; 2]\) and range \([0, \; 1]\). (The notation \([a, \; b]\) denotes \( \{ x\; : \; a \le x \le b \}\).) What are the domain and range, respectively, of the function \(g\) defined by \(g(x)=1-f(1+x)\) ? (A) \([-1, \; 1 ], \; [-1, \; 0]\)(B) \([-1, \; 1 ], \; [0, \; 1]\)(C) \([0, \; 2 ], \; [-1, \; 0]\)(D) \([1, \; 3 ], \; [-1, \; 0]\)(E) \([1, \; 3], \; [0, \; 1..

Points \(\rm A\) and \( \rm B\) lie on a circle centered at \( \rm O\), and \( \rm \angle AOB= 60 ^{\rm o} \). A ssecond circle is internally tangent to the first and tangent to both \( \overline{\rm OA}\) and \( \overline{\rm OB}\). What is the ratio of the area of the smaller circle to that of the larger circle? (A) \(\dfrac{1}{16}\) (B) \(\dfrac{1}{9}\) (C) \(\dfrac{1}{8}\) (D) \(\dfrac{1}{6}..

What is the area of the region defined by the inequality \(|3x-18| + |2y+7| \le 3 \) ? (A) \(3\) (B) \(\dfrac{7}{2}\) (C) \(4\) (D) \(\dfrac{9}{2}\) (E) \(5\) 정답 (A)

Let \(k=2008^2 + 2^{2008}\). What is the units digit of \(k^2 + 2^k\) ? (A) \(0\) (B) \(2\) (C) \(4\) (D) \(6\) (E) \(8\) 정답 (D)

The numbers \(\log \left ( a^3 b^7 \right ) , \log \left ( a^5 b^{12} \right ) \), and \(\log \left ( a^8 b^{15} \right )\) are the first three terms of an arithmetic sequence, and the \(12^{th}\) term of the sequence is \( \log \left ( b^n \right ) \). What is \(n\) ? (A) \(40\) (B) \(56\) (C) \(76\) (D) \(112\) (E) \(143\) 정답 (D)

Let \(a_1 , \; a_2 , \; \cdots\) be a sequence of integers determined by the rule \(a_n = \dfrac{a_{n-1}}{2}\) if \(a_{n-1}\) is even and \(a_n = 3a_{n-1} +1\) if \(a_{n-1}\) is odd. For how many positive integers \(a_1 \le 2008\) is it true that \(a_1\) is less thatn each of \(a_2 , \; a_3 ,\) and \(a_4\) ? (A) \(250\) (B) \(251\) (C) \(501\) (D) \(502\) (E) \(1004\) 정답 (D)