#20 - Local

[Administrator]

Complete Question Explanation

The correct answer choice is (B).

Answer choice (A):

Answer choice (B): This is the correct answer choice.

Answer choice (C):

Answer choice (D):

Answer choice (E):


This explanation is still in progress. Please post any questions below!

[Bruin96]

Hello,

I got this question wrong but I am not exactly sure why. I have provided my set up below. I chose answer choice D
which is true. I am not exactly sure why Morse must work on Saturday? If someone can please add insight to this, I would really appreciate it!

Thursday:
Q
L
M

Friday:
Q
P
N

Saturday:
L
M
N

[euridyce]

Hello,

I got this question wrong but I am not exactly sure why. I have provided my set up below. I chose answer choice D
which is true. I am not exactly sure why Morse must work on Saturday? If someone can please add insight to this, I would really appreciate it!

Thursday:
Q
L
M

Friday:
Q
P
N

Saturday:
L
M
N

Hi!
So for this question, the prompt asks "which of the following must be true," not could be true. So while it's possible that Pang could work on Friday, D is incorrect because Pang could also work on Thursday and still fulfill the game's requirements.

E.g.,
Thursday -- P, N, Q
Friday -- N, M, L
Saturday -- M, L, Q

There's no way to follow the game's parameters for this question without putting Morse on Saturday. I personally found it helpful to try to do like two quick sketches of possible combinations for this question, which made it clear that Morse has to go on Saturday, and just doing that much didn't eat up too much of my time. Hope that helps!

[Zach Foreman]

Bruin,
Eurydice answered it quite well. I will add that your set up doesn't prove what "must be true" only what "could be true" because it is only one possibility. Your set up has L on Thursday, which fits with A, Morse on Saturday which fits with B, P on Friday, which fits D. Your set up only excludes C and E, which cannot be "must be true" because you found one instance where they are not true. To eliminate must be true answer choices, you need to make counter examples to eliminate wrong answers. Let's do one to try to eliminate D (P on Friday). Let's put P on Thursday only.

T: QNP
F:LMN
S: QLM

So, clearly it is not true that P must work on Friday. Therefore we eliminate D.

We could also try to try to have no M in S. If there is no M and no O then S must be LNQ. So far so good. Now we have six more slots to fill, P can only fill one of them and N is on Friday. 4 left. We can fill two more of them with ML, which leaves one slot left. It cannot be M (it would bring in L), N (three days), L (three days) or Q (three days) and it of course cannot be P. So, it is impossible.

[momgoingbacktoschool]

Bruin,
Eurydice answered it quite well. I will add that your set up doesn't prove what "must be true" only what "could be true" because it is only one possibility. Your set up has L on Thursday, which fits with A, Morse on Saturday which fits with B, P on Friday, which fits D. Your set up only excludes C and E, which cannot be "must be true" because you found one instance where they are not true. To eliminate must be true answer choices, you need to make counter examples to eliminate wrong answers. Let's do one to try to eliminate D (P on Friday). Let's put P on Thursday only.

T: QNP
F:LMN
S: QLM

So, clearly it is not true that P must work on Friday. Therefore we eliminate D.

We could also try to try to have no M in S. If there is no M and no O then S must be LNQ. So far so good. Now we have six more slots to fill, P can only fill one of them and N is on Friday. 4 left. We can fill two more of them with ML, which leaves one slot left. It cannot be M (it would bring in L), N (three days), L (three days) or Q (three days) and it of course cannot be P. So, it is impossible.

Still not sure what the most efficient way is to attack this game. I've tried to do two different set ups where P is on Thursday and P is on Friday and I feel overwhelmed by the possibilities of all of the other empty spaces. There seems to be too many possibilities to quickly and efficiently answer the questions (even with N on Friday and L on Saturday in both cases). Help.

[momgoingbacktoschool]

Bruin,
Eurydice answered it quite well. I will add that your set up doesn't prove what "must be true" only what "could be true" because it is only one possibility. Your set up has L on Thursday, which fits with A, Morse on Saturday which fits with B, P on Friday, which fits D. Your set up only excludes C and E, which cannot be "must be true" because you found one instance where they are not true. To eliminate must be true answer choices, you need to make counter examples to eliminate wrong answers. Let's do one to try to eliminate D (P on Friday). Let's put P on Thursday only.

T: QNP
F:LMN
S: QLM

So, clearly it is not true that P must work on Friday. Therefore we eliminate D.

We could also try to try to have no M in S. If there is no M and no O then S must be LNQ. So far so good. Now we have six more slots to fill, P can only fill one of them and N is on Friday. 4 left. We can fill two more of them with ML, which leaves one slot left. It cannot be M (it would bring in L), N (three days), L (three days) or Q (three days) and it of course cannot be P. So, it is impossible.

Still not sure what the most efficient way is to attack this game. I've tried to do two different set ups where P is on Thursday and P is on Friday and I feel overwhelmed by the possibilities of all of the other empty spaces. There seems to be too many possibilities to quickly and efficiently answer the questions (even with N on Friday and L on Saturday in both cases). Help.

It finally clicked. With these types of questions, it's best to first look at the most restricted variables. So if P is only once, then M has to be twice. We already know L must be on Saturday, so if M is twice, can M go Thursday and Friday? No, because that would mean L also needs to go Thursday and Friday and that is not possible because of the rule that states it can't go three times. So, since M must go twice, then the only place for it to go is Friday and Saturday. Therefore, M must be Saturday.

[elijahpitt123]

What is the fastest way to approach this question? I initially skipped it during my section because I thought it would take too much time but is there a way to do it without just making hypotheticals?

[Rachael Wilkenfeld]

Hi Elijah,

I'd start on this one by looking at the most restricted variable(s). Did you do a numerical distribution? Once you have the one (and only one) solo variable you know all the other variables occur on two days. That means that M and L in a block occur twice. We can only place that block in three combinations: Thurs Fri, Fri Sat, or Thurs Sat. I tried each of those to see if they worked. Thurs Fri didn't work because it didn't leave enough space for P and 2 Qs on non-Saturdays. We can use 1 Q on a Saturday, but the second Q and the P both need to be on other days. That tells us that ML must be on Sat, and I'd look for that as an option, which is answer choice (B). I would not necessarily do full templates/scenarios.

Overall, it should take only about a minute to answer. If it takes more than that, it's certainly fine to skip it, and only attempt when you have time at the end.

Hope that helps!