Directions: Study the following information carefully and answer the questions given below:

Six individuals – P, Q, R, S, T, and U – scheduled their vacation trips in three different months – March, June, and November – on two distinct dates, namely 11th and 18th of the same year. Each individual visits a different city – Boston, Dallas, Miami, Seattle, Chicago, and Denver. All the given information is not necessarily applied in the same order.

The one who visits Boston was scheduled two persons before R. Q was scheduled immediately before R on an even date. T was scheduled immediately before U on an odd date in a month having 30 days. Two persons were scheduled between U and the person visiting Miami. Two persons were scheduled between the ones visiting Boston and Chicago. P was scheduled before the one who visits Denver and two persons after the one who visits Seattle. U doesn’t visit Seattle.

Which of the following statements is/are incorrect?
I. T was scheduled before S.
II. No person was scheduled between Q and the person visiting Miami.
III. P was scheduled in a month having an even number of days and visits Chicago.

The correct option is Only I.

Step-by-step Explanation:

There are six vacation slots across three months on two distinct dates (11^th and 18^th):
1. March 11^th (31 days, Odd date)
2. March 18^th (31 days, Even date)
3. June 11^th (30 days, Odd date)
4. June 18^th (30 days, Even date)
5. November 11^th (30 days, Odd date)
6. November 18^th (30 days, Even date)

Step 1: Determine the positions of Q, R, T, and U
• Clue: "T was scheduled immediately before U on an odd date in a month having 30 days."
The odd dates in 30-day months are June 11^th and November 11^th. Therefore, T must be on June 11^th (with U on June 18^th) or T must be on November 11^th (with U on November 18^th).

• Clue: "Q was scheduled immediately before R on an even date. The one who visits Boston was scheduled two persons before R."
Since Q is on an even date, Q must be on March 18^th or June 18^th.
If Q were on June 18^th, R would be on November 11^th. But this would conflict with the placement of T and U. Thus, Q must be on March 18^th, and R must be on June 11^th.
Since the one visiting Boston is two persons before R (March 11^th), the person scheduled on March 11^th visits Boston.
Since June 11^th is occupied by R, T must be on November 11^th, and U must be on November 18^th.

Step 2: Determine Cities for R, Chicago, and P
• Clue: "Two persons were scheduled between U and the person visiting Miami."
U is on November 18^th (Slot 6). Counting two persons back, the person on June 11^th (R) visits Miami.

• Clue: "Two persons were scheduled between the ones visiting Boston and Chicago."
Boston is on March 11^th (Slot 1). Two persons between them means the person on June 18^th visits Chicago.

• Clue: "P was scheduled before the one who visits Denver and two persons after the one who visits Seattle."
Since P is scheduled two persons after the one visiting Seattle, P must be scheduled on June 18^th (visiting Chicago), and Q (March 18^th) visits Seattle.
The remaining individual, S, is scheduled on March 11^th (visiting Boston).

Final Arrangement Schedule:

Step 3: Evaluate the Given Statements
• Statement I: T was scheduled before S.
Incorrect. S is scheduled on March 11^th, whereas T is scheduled on November 11^th. Therefore, T was scheduled after S.

• Statement II: No person was scheduled between Q and the person visiting Miami.
Correct. Q is scheduled on March 18^th and R (who visits Miami) is scheduled immediately after Q on June 11^th.

• Statement III: P was scheduled in a month having an even number of days and visits Chicago.
Correct. P is scheduled on June 18^th. June has 30 days (an even number of days), and P visits Chicago.

Hence, the only incorrect statement is Statement I.