Question

Patrick goes to the disco on every Tuesday and Friday but does not go to the disco on any other day. Which day of the week is today?
I. He will not go to the disco two days later and he did not go to the disco four days earlier.
II. He did not go to the disco three days earlier and he will not go to the disco four days later.

• A. If the question can be answered by any one of the statements alone, but cannot be answered by using the other statement alone.
• B. If the question can be answered by using either statement alone.
• C. If the question can be answered by using both the statements together, but cannot be answered by using either statement alone.
• D. If the question cannot be answered even by using both the statements together.

Answer 1

The correct option is C If the question can be answered by using both the statements together, but cannot be answered by using either statement alone.

Using statement (I) alone, the day cannot be Sunday, Tuesday, Wednesday, and Saturday. It can be one of Monday, Thursday, and Friday.
Hence, statement (I) alone is not sufficient as there is no unique day.
Using statement (II) alone, this day cannot be Monday or Friday.
It can be any one of the other five days of the week.
Combining both the statements together, the day is Thursday. Thus, both the statements are required.