Thanks for the question! So this question tells us that large red shirts nor small blue shirts are available, and then asks us which one of the following Casey has to buy.
Theoretically, we have nine total shirt combinations. S = small, M = Medium, L = Large R = Red, Y = Yellow, B = Blue
SR MR LR SY MY LY SB MB LB
But we’re told in the game that there’s no SR or LB, so there’s really 7 combinations.
XX MR LR SY MY LY SB MB XX
And now we’re told that there’s no LR and SB for this question, leaving 5 combinations remaining.
XX MR XX SY MY LY XX MB XX
Now, remember that we can’t pick both a small shirt and a large shirt. So if we pick SY, we can’t pick LY, and vice versa. What does that mean? Well, it means we have to pick at least two medium shirts. Since if we pick LY, we can’t pick SY, so we have to pick two medium shirts; same if we pick SY, we can’t pick LY, so we have to pick two medium shirts; the only other combination is that we pick three medium shirts.
So now we know that we pick at least 2 medium shirts. Well, if that’s true, then it has to be true that we pick either a medium red shirt or a medium blue. Let’s say one of the medium shirts is the medium yellow. Well, then the other medium shirt has to be the medium red or blue! So at least one of those two has to be picked, and (D) is the correct answer.
Hope this helps! Feel free to ask any other questions that you might have.
kmccarthy10on July 15, 2020
thank you!
shunheon July 17, 2020
Glad I was able to help!
ilovethelsaton March 25, 2021
Why could we not have picked a medium yellow shirt? Why couldn't we have, say, small yellow, medium yellow, medium blue?
What did I miss in the rules that says you cannot have the same color twice? It says no two of the same type and then defines type as a combination of *both* size and color. You can't have two small yellows, but how does that preclude not having two of the same color shirts but different sizes?
on September 22, 2021
I am with Olivia on this one, this answer doesn't make sense. Please help.
Emil-Kunkinon December 9, 2023
We totally could pick a medium yellow. However, we must also pick at least one of the other two mediums. Since there is only one large and one small, we must have at least two mediums. So, we cannot fail to select two of the three mediums.
