Which one of the following most be true?

on September 12, 2019

D vs E

Can someone please explain this question? It seemed to me that D could have been the answer too, since the we can't have a 2-2-2 set up.

Irina on September 14, 2019

@Minerva,

The game requires us to pick 6 stones out of 10. We have 3 rubies, 3 sapphires, and 4 topazes. The rules require us to pick a minimum of two topazes, but the game never says that we have to use all three types of stones, meaning it is possible that none of the rings are fitted with a ruby or a sapphire, e.g. 3 t, 3 s, and 0 r combination is valid, hence it is not the case that exactly one stone must be selected of at least one of the three types as (D) suggests.

The rules further tell us that if 2 sapphires are selected, 1 ruby is selected, hence we cannot have a 2 - 2 -2 combination as you correctly pointed out, and we cannot have a 4 T - 2 S - 1R combination because the rules tell that W and Z are both topazes and are mutually exclusive, meaning we could at most select 3 topazes in any valid combination.

Hence every valid combination must include either 2 or 3 T. If we only pick 2 T, we must select three out of one other group of stones, otherwise, we end up with a 2 - 2 -2 invalid combination:

2 T - 3 S - 1 R
2 T - 3 R - 1 S

Every other combination will require us to pick 3T, hence (E) is correct as we must always pick exactly three stones from at least one of the stone groups.

Let me know if this helps and if you have any further questions.