Study the given information carefully and answer the questions given below.

Seven corporate seminars will be scheduled on the 13th, 5th, 23rd, 17th, 29th, 7th, and 2nd across six consecutive months: January, February, March, April, May, and June of a leap year. Exactly two seminars will be held in one of these months, while the other months will have one seminar each. The Marketing seminar is scheduled for an even-numbered date in a month that has exactly 30 days. The Finance seminar is scheduled two months prior to the Marketing seminar. The Operations seminar will take place on the 5th, in the month immediately following the one in which the HR seminar is held. The IT seminar is scheduled for March, but its month is not immediately before the month of the HR seminar. The sum of the dates for the two seminars held in the same month is 25. The Sales seminar is scheduled for the 13th but cannot be held in May. Neither the HR seminar nor the Legal seminar is scheduled for the 7th.

Which of the following corporate seminars will be scheduled in the same month?

The correct answer is Legal seminar, Marketing seminar.

Step-by-Step Explanation and Derivation:

1. Analyze the given parameters:
• Months: 6 consecutive months — January (31 days), February (29 days in a leap year), March (31 days), April (30 days), May (31 days), and June (30 days).
• Seminar Dates available: 2nd, 5th, 7th, 13th, 17th, 23rd, and 29th.
• Total Seminars: 7 (Marketing, Finance, Operations, IT, HR, Sales, Legal).
• Exactly one month has 2 seminars, while the other 5 months have 1 seminar each.

2. Determine the date and month for the Marketing seminar:
• The Marketing seminar is held on an even-numbered date in a 30-day month (April or June).
• Among the given dates, the only even number is 2. Thus, Marketing seminar date = 2nd.
• Therefore, Marketing seminar is on April 2nd or June 2nd.

3. Determine the Finance seminar month:
• The Finance seminar is scheduled 2 months prior to the Marketing seminar.
• If Marketing is in April, Finance is in February.
• If Marketing is in June, Finance is in April.

4. Determine the dates for the month having two seminars:
• The sum of the dates for the two seminars in the same month is 25.
• From the available dates {2, 5, 7, 13, 17, 23, 29}, the only pair that adds up to 25 is 2 and 23 ($2+23=25$).
• Since Marketing is held on the 2nd, Marketing MUST be one of the two seminars in that month, and the other seminar in that same month must be held on the 23rd.

5. Determine the positions of IT, HR, Operations, and Sales seminars:
• IT seminar is in March. Since March is not immediately before HR's month, HR cannot be in April.
• Operations is on the 5th, held in the month immediately after HR. Thus, HR must be in May and Operations in June (5th).
• Since Marketing is in the month with two seminars (2nd and 23rd), and June already has Operations (5th), Marketing cannot be in June (which would make 3 seminars in June). Thus, Marketing must be in April (2nd).
• Consequently, April is the month with two seminars (2nd and 23rd).
• Finance is 2 months prior to April, which is February.
• Sales is on the 13th and cannot be in May, so Sales is scheduled for January 13th.
• The remaining seminar for April 23rd is the Legal seminar.

Final Arrangement:
• January: Sales (13th)
• February: Finance
• March: IT
• April: Marketing (2nd) & Legal (23rd) — Two seminars in the same month
• May: HR
• June: Operations (5th)

Hence, the Legal seminar and Marketing seminar are scheduled in the exact same month (April).