Pascal 2023 Part B - Question 15, CEMC UWaterloo
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Difficulty: 3
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(Pascal 2023, Part B, Question 15, CEMC - UWaterloo)
Nasim buys trading cards in packages of $5$ cards and in packages of $8$ cards. He can purchase exactly $18$ cards by buying two $5$-packs and one $8$-pack, but he cannot purchase exactly $12$ cards with any combination of packages. For how many of the integers $n = 24$, $25$, $26$, $27$, $28$, $29$ can he buy exactly $n$ cards?
$(A)$ $5$
$(B)$ $3$
$(C)$ $2$
$(D)$ $4$
$(E)$ $6$
Answer Submission Note(s)
Your answer should be a single capital letter, e.g. 'A'.
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