Q21

[ElizabethC601]

Just wondering how to solve! Thank you!

[ohthatpatrick]

Hey, Elizabeth. Sorry for the long delay (I was on a weeklong vacation)

For all "which must be true" questions like Q21, I first start by looking at all the previous scenarios I've done to see if I can find a counterexample to each answer choice.

For example, I would be asking myself these questions:
(A) Could there be no G's in 1, 2, or 3?
(B) Could there be no G's in 5 or 6?
(C) Could there be no R's in 1, 2, or 3?
(D) Could there be no R's in 5 or 6?
(E) Could there be no W's in 1, 2, or 3?

I do all my "if" questions before I do unconditional questions, so I would also be pulling from my scenarios in Q22 and Q23.

I'm not going to re-create all the work I would have had for Q18, 19, 22, and 23, but I would have probably been able to kill at least a couple answers using those scenarios.

Instead, I'll just show you, in a vacuum, how you can eliminate the four wrong answers.

(A) Could there be no G's in 1, 2, or 3?
(B) Could there be no G's in 5 or 6? Sure. G W R R R R
(C) Could there be no R's in 1, 2, or 3? Sure. G W W R R R
(D) Could there be no R's in 5 or 6? Sure. G W R R G G
(E) Could there be no W's in 1, 2, or 3? Sure. G G G W R R

We can pick (A), since we found legal counterexamples to the other four answers.

Why does there HAVE to be a G in 1, 2, or 3?

Well, if we're not using G's, we're using R's or W's.

We can't put any R's in 1, 2, or 3, since we have to play a G before we're allowed to use any R's (rule 2).

We can't fill up spots 1, 2, and 3 with W's, since there have to be more R's than W's, so there would have to be 4 R's to outweigh those 3 W's.

Make sense?

[YarveyW703]

Instead, I'll just show you, in a vacuum, how you can eliminate the four wrong answers.

(A) Could there be no G's in 1, 2, or 3?
(B) Could there be no G's in 5 or 6? Sure. G W R R R R
(C) Could there be no R's in 1, 2, or 3? Sure. G W W R R R
(D) Could there be no R's in 5 or 6? Sure. G W R R G G
(E) Could there be no W's in 1, 2, or 3? Sure. G G G W R R

Hi, Patrick!

The condition says that "...a white ball...is immediately below...a green ball". But in your examples the green balls are below the white balls, so I was thinking that probably you made a small mistake.

I admitted that I was trapped by this question since I wrote the second condition wrong and forgot that there is no need for all green balls to be immediately below all the red balls. And the best way to solve this question in my opinion is to work through every choice and assume the opposite. If you can't find an example that can confirm the opposite situation, then you will have your answer and luckily we only need to do this for A. But for the record,

(from 1-6)

B: W G R R R R, there are no green balls higher than 4 (the highest is 2).
C: W G G R R R, there are no red balls lower than 4 (the lowest is 4).
D: W G R R G G, there are no red balls higher than 4 (the highest is 4).
E: G R R W G R, there are no white balls lower than 4 (the lowest is 4).