Question

a business is choosing which of 10 offices to rent. all of the offices with game rooms have kitchens, and some of the offices with kitchens have stairs. in the end, the business chose an office with stairs.

what is the most correct conclusion that can be made solely from the text above?

a the office must have a game room.
b the office must have a kitchen.
c the office must have a kitchen or a game room.
d the office could have no kitchen but have a game room.
e the office could have no kitchen and no game room.

Explanation:

Analyze the premises

Using the Logical Deduction knowledge point, let us break down the statements given in the text:

1. "All of the offices with game rooms have kitchens."

This can be written as: \(\text{Game Room} \implies \text{Kitchen}\).

1. "Some of the offices with kitchens have stairs."

This means there is an overlap between offices with kitchens and offices with stairs, but not necessarily all offices with stairs have kitchens, nor do all offices with kitchens have stairs.

1. "In the end, the business chose an office with stairs."

Let the chosen office be \(X\). We know \(X\) has stairs.

Evaluate the options

Using the Logical Inference knowledge point, we analyze what can be concluded about the chosen office \(X\) (which has stairs):

• Can we conclude \(X\) has a kitchen?

No. We only know "some offices with kitchens have stairs." This does not mean all offices with stairs have kitchens. There could be an office with stairs that has no kitchen.

• Can we conclude \(X\) has a game room?

No. Since we cannot even guarantee it has a kitchen, and a game room requires a kitchen, we certainly cannot guarantee a game room.

• Let us evaluate Option E: "The office could have no kitchen and no game room."

Since there is no rule stating that all offices with stairs must have kitchens or game rooms, it is entirely possible (i.e., "could") that the chosen office with stairs has neither a kitchen nor a game room. This is logically consistent with all premises.

Confirm the correct choice

Let us double-check the other options to ensure Option E is the most correct:

• (A) "The office must have a game room." (Incorrect, not guaranteed).
• (B) "The office must have a kitchen." (Incorrect, not guaranteed).
• (C) "The office must have a kitchen or a game room." (Incorrect, not guaranteed).
• (D) "The office could have no kitchen but have a game room." (Incorrect, because any office with a game room must have a kitchen according to Premise 1).
• (E) "The office could have no kitchen and no game room." (Correct, as this scenario is fully possible).

Answer:

• (A) The office must have a game room.
• (B) The office must have a kitchen.
• (C) The office must have a kitchen or a game room.
• (D) The office could have no kitchen but have a game room.
• (E) The office could have no kitchen and no game room. (Correct answer)