Explanation:

Correct option 3: G

There are eight candidates and four months: March, May, June, and July. Each month has two exam dates: 5th and 20th. This means there are a total of 4 months×2 dates/month=84 months×2 dates/month=8 available slots for the exams.

First, let's list the months and their number of days, which is crucial for some clues:

• March: 31 days
• May: 31 days
• June: 30 days
• July: 31 days

Now, let's break down each clue and fill in the schedule step-by-step:

Exam Schedule Deduction

1. Clue 1: "C has exam on 20th May and immediate before A."
   • This directly tells us C's exam is on May 20th.
   • Since C has exam "immediate before A", and May 20th is the last slot in May, A must have the exam in the very next available slot, which is June 5th.

   Current Schedule Snippet:

   • May 20th: C
   • June 5th: A
2. Clue 2: "Two candidates have exam between A and B."
   • We know A's exam is on June 5th.
   • Counting two slots after A:
     1. First slot after A is June 20th.
     2. Second slot after A is July 5th.
   • Therefore, B's exam must be in the slot immediately following these two, which is July 20th.

   Current Schedule Snippet:

   • June 5th: A
   • June 20th: (1st candidate between A & B)
   • July 5th: (2nd candidate between A & B)
   • July 20th: B
3. Clue 3: "D has exam in the month, which has 30 days."
   • Looking at our list of months, June is the only month with exactly 30 days.
   • In June, June 5th is already taken by A. So, the only remaining slot in June is June 20th.
   • Therefore, D's exam is on June 20th.

   Current Schedule Snippet:

   • June 20th: D
4. Clue 4: "E’s exam is immediately after D’s exam."
   • We just found that D's exam is on June 20th.
   • The slot immediately after June 20th is July 5th.
   • Therefore, E's exam is on July 5th.

   Current Schedule Snippet:

   • June 20th: D
   • July 5th: E
5. Clue 5: "F’s exam is immediately after G’s exam but not in same month."
   • This is a critical clue. It means G's exam must be on the 20th of a month, and F's exam must be on the 5th of the very next month.
   • Let's list the remaining empty slots:
     • March 5th: Empty
     • March 20th: Empty
     • May 5th: Empty
   • The only consecutive slots where the 20th of one month is followed by the 5th of the next month, and both are empty, are March 20th and May 5th. (April is not one of the months).
   • So, G's exam is on March 20th and F's exam is on May 5th.

   Current Schedule Snippet:

   • March 20th: G
   • May 5th: F
6. Clue 6: "H is one of the candidates."
   • We have placed 7 out of 8 candidates (A, B, C, D, E, F, G). The only remaining candidate is H, and the only remaining empty slot is March 5th.
   • Therefore, H's exam is on March 5th.

Final Exam Schedule

Let's compile the complete exam schedule for all eight candidates:

Identifying the Odd One Out

Now we need to find the odd one among the given options: H, G, E, F.

Let's check the exam dates for each of these candidates:

• H: March 5th (Exam on the 5th of the month)
• G: March 20th (Exam on the 20th of the month)
• E: July 5th (Exam on the 5th of the month)
• F: May 5th (Exam on the 5th of the month)

Upon reviewing the dates, we can observe a clear pattern:

• H, E, and F all have their exams on the 5th day of their respective months.
• G, however, has an exam on the 20th day of its month.

Therefore, G is the odd one out as its exam date pattern (20th of the month) differs from the others (5th of the month).