Ten new television shows appeared during the month of September. Five of the shows were sitcoms, three were hour-long dramas, and two were news-magazine shows. By January, only seven of these new shows were still on the air. Five of the shows that remained were sitcoms.

Given data

• Total new shows: 10 (5 sitcoms, 3 hour-long dramas, 2 news-magazines).
• By January, 7 shows remained; 5 of the remaining were sitcoms.

Concept/Approach

Use counts to deduce what must have been cancelled, without assuming audience preferences.

Step-by-step calculation
Initial non-sitcoms = dramas + news = 3 + 2 = 5.Remaining shows = 7 total; 5 are sitcoms ⇒ Remaining non-sitcoms = 7 − 5 = 2.Cancelled non-sitcoms = initial 5 − remaining 2 = 3.Max news-magazine cancellations = 2 (since only 2 existed).Therefore, at least one of the cancelled non-sitcoms must be a drama.

Verification/Alternative

Scenarios: (i) 2 news cancelled + 1 drama cancelled; (ii) 1 news cancelled + 2 dramas cancelled; (iii) 0 news cancelled + 3 dramas cancelled. In all, ≥1 drama is cancelled.

Common pitfalls

• Claiming exact counts for dramas/news remaining (A or B) — not uniquely determined.
• Inferring viewer preference from survival counts (D) — not justified.

Final Answer
At least one of the shows that was cancelled was an hour-long drama.