Read the given information carefully and answer the related questions:

Seven persons – A, B, C, D, E, F, and G – participate in different activities in seven different months of the same year: January, April, May, July, September, October, and November. The activities are Cooking, Gardening, Photography, Painting, Swimming, Sculpting, and Writing. Gardening is done in a month having 30 days. Three persons perform their activities between D and the one who does Gardening. One person performs their activity between D and E. The number of persons performing activities after E is the same as the number of persons performing activities before the one who does Painting. F performs their activity immediately before the one who does Photography. More than three persons perform their activities between F and G, who does Writing. Swimming is done in a month having 30 days before D. Cooking is done before C, who does not do Swimming.

Which activity is performed in October?

The correct answer is Sculpting.

Step-by-step Explanation:

1. Understanding the Month Schedule:

The seven months given in order with their respective number of days are:

1. January (31 days)
2. April (30 days)
3. May (31 days)
4. July (31 days)
5. September (30 days)
6. October (31 days)
7. November (30 days)

2. Deductions Step-by-Step:

Step A: Determine the positions of D and Gardening
• Gardening is performed in a month having 30 days (April, September, or November).
• Three persons perform their activities between D and Gardening. This implies a gap of 4 positions between D and Gardening.
• If Gardening is in April (2nd month), then D must be in October (6th month) because there are 3 months (May, July, September) between them.
• Testing Gardening in November (7th month) leads to a contradiction with the placement of other activities and persons.
• Therefore, Gardening is in April and D performs in October.

Step B: Determine the position of E and Painting
• One person performs between D (October) and E. Thus, E performs in July (4th month).
• The number of persons after E (July) is 3 (September, October, November).
• The clue states that the number of persons performing after E is equal to the number of persons performing before the one who does Painting.
• Since 3 persons perform after E, 3 persons must perform before Painting (January, April, May). Therefore, Painting is performed in July (by E).

Step C: Determine the position of Swimming
• Swimming is performed in a month having 30 days before D (October).
• The 30-day months before October are April and September.
• Since April is already assigned to Gardening, Swimming must be in September.

Step D: Determine the positions of F, G, Photography, and Writing
• F performs immediately before the one who does Photography.
• More than 3 persons perform between F and G (who does Writing).
• Placing G in November (doing Writing) and F in April (doing Gardening) gives exactly 4 persons between them (May, July, September, October), which satisfies "more than 3 persons".
• Since F performs in April, the person performing immediately after F (in May) does Photography.

Step E: Determine the positions of C, Cooking, and Sculpting
• The remaining months for activities are January and October.
• The remaining activities to assign are Cooking and Sculpting.
• Cooking is done before C, and C does not do Swimming (September). Therefore, C performs in May (Photography).
• Since Cooking is done before C (May), Cooking must be in January.
• The remaining activity, Sculpting, must be performed in October (by D).

3. Final Schedule Summary:

• January (31 days): Person A/B — Cooking
• April (30 days): F — Gardening
• May (31 days): C — Photography
• July (31 days): E — Painting
• September (30 days): Person B/A — Swimming
• October (31 days): D — Sculpting
• November (30 days): G — Writing

Thus, the activity performed in October is Sculpting.