We know that a store sells shirts in three sizes and three colours. The three sizes are S, M, and L and the three colours are R, Y, and B.
Casey buys exactly three shirts from the store.
Shirt 1: _ _ Shirt 2: _ _ Shirt 3: _ _ S C
Rule 1 - A shirt type consists of both a size and a colour
This is reflected in our diagram above.
Rule 2 - Casey does not buy two shirts of the same type
Rule 1 tells us that a shirt type consists of both a size and a colour. Therefore, Casey can buy multiple shirts of the same colour or multiple shirts of the same size, but they cannot buy multiple shirts that are the exact same colour and size.
Rule 3 - Casey does not buy both an S shirt and an L shirt
In other words, if Casey buys an S shirt, then they cannot buy an L shirt and vice versa
S --> Not L L --> Not S
Rule 4 - No SR shirts are available
Therefore, any R shirts must be either M or L.
Rule 5 - No LB shirts are available
Therefore, any B shirts must be either S or M.
So, what possible shirt combinations do we have?
SB MB __ __ MR LR SY MY LY
I've left blanks where the LB and SR shirts would be just to help with visualization.
Rule 3 tells us that Casey does not buy both an S shirt and an L shirt. We also know from our diagram above that there are only two possible S shirts and two possible L shirts. Therefore, to make three shirts, Casey must always buy at least one M shirt.
The question stem provides us with another condition: Casey buys an SB shirt. We are asked to find the answer choice which must be false (or cannot be true).
Shirt 1: S B Shirt 2: M _ Shirt 3: S/M _
We know that Casey has bought an S shirt. This means that they cannot buy an L shirt. Therefore, one of the remaining shirts must be M and the other must be either S or M.
We can immediately eliminate answer choices (D) and (E) because we can see from our deductions above that it is entirely possible that Casey buys two S shirts and one M shirt or two M shirts and one S shirt.
We know that at least one shirt has to be M. Therefore, we can eliminate answer choice (A) because it is possible that Casey buys both an SB and an MB shirt.
Finally, we can eliminate answer choice (C) because Casey could buy both an SY and an MY shirt.
This leaves us with answer choice (B). Why must this be false?
Rule 3 tells us that Casey does not buy both an S and an L shirt. We also know that there are no SR shirts and that Casey does not buy two shirts of the same type. This means that Casey can only buy one MR shirt.
Hope this helps! Please let us know if you have any further questions.
