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 P appears on page 6, G must appear on which of the following pages?
A. 3
B. 9
C. 12
D. 15
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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: **P is on page 6**. P is a Y essay. Rule (1): Pages 3, 9, 15 must be either all K essays or all Y essays. **Case 1: Pages {3, 9, 15} are for Y writers {M, N, P}**. This is impossible as P is on page 6. **Case 2: Pages {3, 9, 15} are for K writers {G, I, J}**. This leaves the Y essays {M, N, P} on the remaining pages {6, 12, 18}. We know P is on 6. So, M and N are on {12, 18}. The K essays {G, I, J} are on {3, 9, 15}. Rule (2): I < P. I (K essay) must be before P (Y essay on 6). I must be on a page before 6, which is only **page 3**. So **I is on page 3**. Rule (3): M < J. M is on 12 or 18. J is on 3, 9, or 15. J cannot be on 3 (I is there). J cannot be on 9 (M must precede J, and M is on 12 or 18). J must be on **page 15**. So **J is on page 15**. The remaining K essay is G, which must be on **page 9**. So **G must appear on page 9**. (The rest of the arrangement would be M/N on 12 and N/M on 18, satisfying M < J, as J is on 15).
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