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 seminars is scheduled two months after the IT seminar?

The correct option is HR.

Step-by-step Explanation and Logical Reasoning:

1. Given Information Analysis:

• Dates available: 2nd, 5th, 7th, 13th, 17th, 23rd, 29th.

• Months: January (31 days), February (29 days, since it is a leap year), March (31 days), April (30 days), May (31 days), June (30 days).

• Total seminars: 7 (Marketing, Finance, Operations, HR, IT, Sales, Legal).

• One month has exactly 2 seminars, while the other 5 months have 1 seminar each.

2. Deductions Step-by-Step:

• Marketing Seminar: Scheduled for an even-numbered date in a 30-day month. The only even date is 2nd. The 30-day months are April and June. If Marketing were in June, Finance (scheduled 2 months prior) would be in April. But let's evaluate Finance condition: "Finance is scheduled two months prior to Marketing".

• If Marketing is in April (2nd April), then Finance is in February. If Marketing is in June (2nd June), then Finance is in April.

• Sum of dates for the 2-seminar month: Two seminars happen in the same month and their dates sum to 25. Looking at the dates (2, 5, 7, 13, 17, 23, 29):

Possible pairs summing to 25: (2 and 23) or (7 and 18 - not in set) or (13 and 12 - not in set). So the two dates in the same month MUST be 2nd and 23rd.

Since the date 2nd is used for the Marketing seminar, the Marketing seminar is held in the month that has 2 seminars (on the 2nd)!

Thus, the month with 2 seminars has dates 2nd and 23rd, and one of these seminars is Marketing (on the 2nd).

• IT Seminar: Scheduled for March. It is explicitly stated that March is NOT immediately before the month of the HR seminar. Hence, HR cannot be in April.

• Operations Seminar: Held on the 5th, in the month immediately following the HR seminar. Since HR cannot be in April, Operations cannot be in May. Also, Operations is on the 5th.

• Sales Seminar: Held on the 13th, but NOT in May.

• Evaluating Marketing & Finance Month:

Case 1: Marketing is in April (2nd April). Then April is the 2-seminar month with dates 2nd and 23rd. Finance is 2 months prior, which is February.

Let's check HR & Operations placement in Case 1:

IT is in March.

HR month cannot be March (since March is not immediately before HR, so HR is not April). Since IT is in March, HR could be in January or February or May or June. But Operations is in the month immediately after HR.

If HR is in January -> Operations is in February (on 5th Feb). Then Finance is also in Feb? But only April has 2 seminars! So Feb can only have 1 seminar.

If HR is in April -> Contradicts "March is not immediately before HR".

If HR is in May -> Operations is in June (on 5th June). Then HR is in May (31 days). This works!

Let's check if HR is in May and Operations is in June (5th June):

Months overview:

- January: Sales (13th Jan)

- February: Finance (Feb date left: 7th, 17th, 29th)

- March: IT (March date)

- April (2 seminars): Marketing (2nd April) + Legal (23rd April)

- May: HR (May date)

- June: Operations (5th June)

Let's verify all constraints for this setup:

- IT is in March.

- Two months after IT (March) is May, where the HR seminar is scheduled.

Conclusion:

The seminar scheduled two months after the IT seminar (March + 2 months = May) is the HR seminar.