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 option is Legal seminar, Marketing seminar.

Step-by-Step Explanation:

Let's analyze the given clues step by step to determine the schedule for each corporate seminar.

1. Understanding the Dates and Months:

The dates available are: 2nd, 5th, 7th, 13th, 17th, 23rd, and 29th.

The six consecutive months in a leap year are:

• January (31 days)
• February (29 days - leap year)
• March (31 days)
• April (30 days)
• May (31 days)
• June (30 days)

There are 7 seminars across 6 months, meaning exactly one month has two seminars, and the other 5 months have one seminar each.

2. Determining the Month and Date of Marketing and Finance Seminars:

• "The Marketing seminar is scheduled for an even-numbered date in a month that has exactly 30 days."
The months with 30 days are April and June. The only even date available is the 2nd.
So, Marketing is on April 2nd or June 2nd.

• "The Finance seminar is scheduled two months prior to the Marketing seminar."
If Marketing is in June, Finance is in April.
If Marketing is in April, Finance is in February.
Let's check IT seminar placement: "The IT seminar is scheduled for March, but its month is not immediately before the month of the HR seminar."

• "The Operations seminar will take place on the 5th, in the month immediately following the one in which the HR seminar is held."
This means HR is in Month 'M' and Operations (on the 5th) is in Month 'M+1'.

• "The sum of the dates for the two seminars held in the same month is 25."
The dates available are 2, 5, 7, 13, 17, 23, 29.
Pairs from these dates adding up to 25:
- 2 + 23 = 25
- 13 + 12 (12 not in list)
So the two dates in the month with two seminars MUST be 2nd and 23rd.

Since the month with two seminars contains the 2nd and 23rd, and Marketing is on the 2nd, Marketing is in the month that has two seminars!

3. Deduction of the Complete Schedule:

• Since Marketing is on the 2nd and is in the month with two seminars (having 2nd & 23rd), Marketing must be in April (30 days). Thus, June is not the month with Marketing.
• Marketing: April 2nd.
• The other seminar in April is on the 23rd.
• Finance is scheduled two months prior to Marketing, so Finance is in February.

Now let's place HR and Operations:
• Operations is on the 5th, in the month immediately after HR.
• HR cannot be in February (before March) because IT is in March, and "IT's month (March) is not immediately before HR's month". Thus HR cannot be in April.
• Therefore, HR is in May, and Operations is in June on the 5th.

Now let's check Sales:
• "The Sales seminar is scheduled for the 13th but cannot be held in May."
• IT is in March. Sales is on the 13th, so Sales must be in January on the 13th (since March, April, May, June, Feb have their dates/constraints).

Now let's place Legal:
• "Neither the HR seminar nor the Legal seminar is scheduled for the 7th."
• The remaining dates to assign are 7th, 17th, 23rd, 29th.
• HR (May) cannot be 7th.
• Legal cannot be 7th.
• The seminars in April are Marketing (2nd) and one on the 23rd. The seminar in April on the 23rd must be Legal (making Legal and Marketing in April, the same month)!

Conclusion:

The month with two seminars is April, where both the Legal seminar (23rd April) and the Marketing seminar (2nd April) are held.