Suppose that none of the ticket sets are purple. If all of the other conditions remain the same, then which one of th...

Ravi on January 1, 2019

@Dijia-Xin,

Happy to help. This is a tricky problem, so it's important to have a
firm grasp of all of the rules so that you're not thrown for a loop
when they give you a new rule to substitute in for the rule that the
January tickets for line 2 are purple.

We are told that now, none of the tickets are purple. This means that
the rule that the January tickets for line 2 are purple no longer
applies. We're asked that if the other conditions remain the same,
then which of the following statements could be true?

Since we now know that there will be no purple ticket sets, then we
know that the ticket sets for each month, we will have one green, one
red, and one yellow ticket. We know this because each month can't have
repeating colors. We also know that we cannot have the same color for
both January and February tickets.

Answer A says that none of the January tickets are green. This cannot
be true because if it were true, then we would have to have a purple
ticket in January. However, the new rule states that there is no
purple, so this answer is out.

Answer B says that none of the February tickets are green. This cannot
be true because if it were true, then we would have to have a purple
ticket in February. However, the new rule states that there is no
purple, so this answer is out.

Answer D says that no line 1 or line 2 tickets are yellow. If this
were true, then that means that both yellow tickets would have to go
in line three since we cannot use purple and only have green, red, and
yellow to use. However, this would contradict the first rule of the
game (the rule that January and February cannot have the same color in
a given line). We can eliminate this answer.

Answer E says that no line 2 or line 3 tickets are red. If this were
true, then that means that both red tickets would have to go in line 1
since we cannot use purple and only have green, red, and yellow to
use. However, this would contradict the first rule of the game (the
rule that January and February cannot have the same color in a given
line). We can get rid of this answer.

This leaves us with answer C, which says that none of the line 2
tickets are green. Could this be true? Let's test it.

J F
1 Y G
2 R Y
3 G R

In this scenario, none of the line 2 tickets are green, but the game
board satisfies all of the other rules. We could put G in line 1 of
February and line 3 of January and still make a game board that works.
Additionally, we know that C is correct because the other answer
choices cannot be true.

Does this make sense? Let us know if you have more questions!