Exactly six different essays will appear in a coming issue of a magazine. Three of the essays- G, I, and Jare by the writer K, and the other three essays-M, N, and P-are by the writer Y. Each essay will appear exactly once in the issue, and an essay must appear on each of the pages 3, 6, 9, 12, 15, and 18. The order in which the essays appear in the issue will be governed by the following conditions: The essays on pages 3, 9, and 15 must all be by the same writer. I must precede P. M must precede J. If G and N appear on pages 15 and 18, respectively, which of the following is a pair of essays that must appear on pages 3 and 6, respectively?
A. I and J
B. I and M
C. I and P
D. J and M
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Explanation: The pages are 3, 6, 9, 12, 15, 18. K essays: G, I, J. Y essays: M, N, P. Rules: (1) 3, 9, 15 must have the same writer. (2) I < P. (3) M < J. Given: **G is on 15** (K essay) and **N is on 18** (Y essay). Rule (1) \(\implies\) Pages 3, 9, 15 must all be K essays. Since G is on 15, {3, 9} must contain the remaining K essays, {I, J}. The remaining pages {6, 12, 18} must contain the Y essays {M, N, P}. Since N is on 18, {6, 12} must contain {M, P}. Rule (2): I < P. I is on 3 or 9. P is on 6 or 12. P is a Y essay, I is a K essay. I on {3, 9} precedes P on {6, 12} is always true. Rule (3): M < J. M is on 6 or 12. J is on 3 or 9. Since M must precede J, M must be on a page before J. If J is on 9, M must be on 6. If J is on 3, M cannot be on 6 or 12. Thus, **J must be on page 9** and **M must be on page 6**. Consequently, the remaining K essay, I, must be on **page 3**. The remaining Y essay, P, must be on **page 12**. The pair of essays that **must** appear on pages 3 and 6, respectively, is **I and M**. (The final arrangement is: I, M, J, P, G, N).
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