Is it possible that no square is green given that all squares are rectangles and some rectangles are green?

Is it possible that no square is green given that all squares are rectangles and some rectangles are green?

• A. No
• B. Cannot be determined
• C. Sometimes
• D. Yes

Answer: (D)

All squares are rectangles, but not all rectangles are squares. Saying some rectangles are green only tells us that there exists at least one green rectangle; it does not say anything about squares being green. If the green rectangles happen to be non-square rectangles, then none of the squares would be green, which fits the given information. For example, have one square that is not green and a non-square green rectangle; there are green rectangles, but no green squares. So it is possible for no square to be green.

All squares are rectangles, but not all rectangles are squares. Saying some rectangles are green only tells us that there exists at least one green rectangle; it does not say anything about squares being green. If the green rectangles happen to be non-square rectangles, then none of the squares would be green, which fits the given information. For example, have one square that is not green and a non-square green rectangle; there are green rectangles, but no green squares. So it is possible for no square to be green.