question: At a meeting of the 3 Joint Chiefs of Staff, the Chief of Naval Operations does not want to sit next to the Chief of the National Guard Bureau. How many ways can the 3 Chiefs of Staff be seated around a circular table?
Options:
(A) 120
(B) 480
(C) 960
(D) 2520
(E) 5040
answer: Stream of consciousness: Bunuel, I'm also a little confused with the number of arrangements of n distinct objects in a circle. Why is it given by (n-1)!. In theveritasanswer they say:answer C (960), should be the number of ways to arrange all 7 without the seating restriction given. Is this incorrect? The answer is (C).
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question: A girl is organizing her jellybean collection in which each color has its own row. In each row, there are as many jellybeans as the number of jellybean colors. Her little brother chops each jellybean into the same number of peices as the number of jellybean colors. If the final number of jellybean pieces is m, then:
Options:
(A) m is a perfect square
(B) m is an odd number
(C) m is an even number
(D) m is a perfect cube.
(E) None
answer: Stream of consciousness: For example, if there were 4 jellybean colors, the girl would have made a 4x4 arrangement. The boy chopped up each jellybean into 4, the number of pieces would be (4*4)*4 = 64 pieces, which is a cube of 4. The answer is (D).
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question: Sum of the local value and the face value of 4 in the numeral 153489216 is
Options:
(A) 40004
(B) 4004
(C) 4000004
(D) 400004
(E) 44
answer: Stream of consciousness: (Local value of 4) + (Face value of 4) = (400000 + 4) = 400004 The answer is (D).
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question: If the ratio of boys to girls in a class is B and the ratio of girls to boys is G; then 7 (B + G) is ?
Options:
(A) more than 7
(B) Less than 3
(C) More than 3
(D) Less than 1/3
(E) none of these
answer:
Stream of consciousness: Let number of boys = x
Let number of girls = y
Therefore x/y = B and y/x = G
7(B + G) = 7[(x/y) + (y/x)] = 7[(x2 + y2)/xy] > 7 The answer is (A).
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