The selection for the project is completely determined if which one of the following is true?

Alexandra on January 22 at 02:13AM

Is there a video explanation for this ?

I need some assistance with this questions

3 Replies

Ravi on January 22 at 03:11AM

@alymathieu,

Happy to help. We're told that seven workers (Q, R, S, T, V, W, and X)
are being considered for a special project. Three will be selected,
and one of the three selected will be a leader.

In Out
L _ _
_ _
_ _

This tells us that this is a group game with pieces that are in and out.

Rule 1 says Q or R can be in only if leading the project.

1) Q/R - >Q/R is leader

However, we're not done there. Since we know there's only one leader
in the project, we also know that Q and R can never be both selected.

2) Q - >/R
R - >/Q

The next rule says that if S is a project member, T must be as well

3) S - >T
/T - >/S

We're lastly told that if W is a project member, neither R nor V can be

4) W - >/R
W - >/V

R - >/W
V - >/W

That's our game setup.

Question 5 says, "The selection for the project is completely
determined if which one of the following is true?"

This question is best solved by running down the answers and seeing if
anything works.

(A) says neither Q nor S is selected.

If we put both Q and S out, we have

In Out
L _ Q
_ S
_ _
_

What else can we fill in for sure? Well, nothing really. R could be in
or out, and since the sufficient condition for rule 3 is failed, T
could also be in or out. The selection for the project is not
completely determined with this answer choice.

(B) says neither Q nor T is selected

In Out
L _ Q
_ T
_ _
_

Going back to rule 3, we know that if T is out, then S must be out too
since that's the contrapositive of the original rule.

In Out
L _ Q
_ T
_ S
_

In looking at rule 4, we know that if W is in, then R and V have to be
out. However, we only have room for one more piece to go out, so we
know that W can't be in. Therefore, W must be out.

In Out
L _ Q
_ T
_ S
W

Now that our out group is all full, all of the other pieces must go in
the in group. Additionally, since R is going into the in group, we
know that R must be a leader if it's in.

In Out
L R Q
V T
X S
W

If neither Q nor T is selected, then we can completely determine the
game board, so (B) is our correct answer choice.

Does this make sense for this question? If you have any other
questions on this game or anything else, please let us know—we're here
to help!

Alexandra on January 22 at 03:26AM

Thank you!

Ravi on February 13 at 07:07PM

@alymathieu, you're welcome!