Which one of the following must be true?

Yoyo on June 6 at 10:35PM

Can you explain why the correct answer is D?

Even better if you could provide the setup! Thanks

1 Reply

Victoria on June 13 at 02:12PM

Hi @YoYo-Yin,

Happy to help!

The correct answer for this question that you've posted your question on is (A), but I'm happy to provide the setup and explain why this is the correct answer.

We know that there are six boxes numbered 1 through 6 stacked from the lowest box up to the highest.

1: _ 2: _ 3: _ 4: _ 5: _ 6: _

Each box holds a single ball which is either G, R, or W.

There are three conditions:

(1) There are more R than W

(2) There is a box containing G which is lower than ANY box containing R.
This means that there cannot be any R lower than the lowest G.

(3) There is a box containing W immediately below a box containing G.

We are looking for the answer choice which must be true. To eliminate answer choices, we just have to prove that there is at least one instance where it does not have to be true.

Answer choice (B) is incorrect because it is possible that there are no G higher than box 4:

1: G 2: W 3: G 4: R 5: R 6: R

Answer choice (C) is incorrect because it is possible that there are no R lower than box 4 (see above).

Answer choice (D) is incorrect because it is possible that there are no R higher than box 4:

1: G 2: R 3: R 4: W 5: G 6: G

Answer choice (E) is incorrect because it is possible that there are no W lower than 4 (see above).

Answer choice (A) must be true if we are to not violate any of the conditions. If the lowest G is in box 4, then there can only be a maximum of two R. We know that there must be a W immediately lower than G.

1: _ 2: _ 3: W 4: G 5: R 6: R

There are three possibilities from this diagram:

(1) We put W in boxes 1 and 2. This would mean there would be more W than R, violating condition 1

(2) We put G in boxes 1 and 2. This would mean there would be a G lower than box 4, meaning this answer choice would have to be true.

(3) We could add an additional R in box 2, but this would mean there would have to be a G in box 1, making this answer choice true.

Therefore, we either have to have a G lower than box 4 or violate condition 1, meaning that answer choice (A) must be true.

Hope this helps! Please let us know if you have any further questions.