Q13

[DenysK280]

Could you please walk me through the solution?

[ohthatpatrick]

Okay, so we can't have RO in any of our three groups.

We know we need two R's and at least one (or in this case, exactly one) O, so let's start those three groups
R __+
R __+
O __ +

Who's left? We still need to use a GP and a Y. Looking at the third rule, it says
...........Y -> ~G and ~O
O or G --> ~Y

Since O and Y can't be together, let's assign Y to one of those R groups.
R __ +
R Y
O __ +

What about GP? Y and G can't go together, so we could assign G to the first R group or to the O group. Let's just assign it to the first group, so that we're close to having a complete scenario.
R G P
R Y
O __ +

Everyone's been used at least once, but let's check that last rule:
~P --> O

If it's doesn't have a P, it's gotta have an O. The 2nd group doesn't have a P, so let's give it an O.

R G P
R Y O
O __ +

Wait a sec, Y and O can't go together. So let's fix that by giving the 2nd group a P.
R G P
R Y P
O __ +

Who could go with that O? It can't be R, because of the question stem. It can't be Y, because of rule 3. So it could go with G or P.

R G P
R Y P
O G/P

With a legal scenario in hand, to the answers we go:

(A) our scenario proves you don't NEED a GP group
(B) our scenario proves you don't NEED a GPO group
(C) our scenario proves you don't NEED a GO group
(D) our scenario proves you don't NEED a PO group
(E) YES, apparently we need an RYP.

That's how I would have done the problem during the test. In calmer reflection, we can see the logic in the correct answer.

When you combine rules 3 and 4, you have
Y --> ~G and ~O --> P

Since the R's and the O must be separated, and since Y can't go with O, we'll have to have an RY group.

And according to our chain, Y ----------> P.

So we'll have an RYP group. You can't throw in O, because of the question stem. And you can't throw in G because Y and G don't coexist.

Hope this helps.