# Which one of the following could be an accurate list of three of the courses Alicia takes?

shenricus on August 19, 2019

Hi I was wondering if someone could please explain how E is correct if S 9am---->no WH How can Statistics and World History be taken together?

Replies

Irina on August 20, 2019

It is possible to take statistics at 3 pm, then 9 am condition would not be apply. The only scenario when statistics must be taken at 9 am if one of the courses chosen is psychology, since it is not the case here, she could be taking the 3 pm statistics section.

ulino23 on January 18, 2020

How do we know that is the statistics at 3pm and not the one at 9am. Both rules 3 and 4 imply Stats9am. The answer choice, itself, does not address which stats is taken. This is confusing.

ulino23 on January 18, 2020

In addition, wouldn't it be more correct to say that since W - >NotS9am - >NoTP because we don't have statistics as a choice for answer choice C or D. Because if P is in, then statistics9am must be in per rule 4. Or can we just say that since P is in and no stats9am is in, on both C&D answers it violates rule 4, thus incorrect.
For answer choice E: if W is in then stats9am is out, however, doesn't meant stats3pm is out, so we can still have a stats. Russian being in doesn't trigger anything so its fine. Thus Russian, stats and world history can be the three chosen.

Skylar on January 19, 2020

@shenricus and @ulino23, happy to help.

First, let's look at the game setup:

G J M P R S(9)/S(3) WH

__ __ __ __ | __ __ __
IN OUT

Rule 1: Not R -> J
Not J -> R
So either J or R must be in, possibly both,
Rule 2: M -> Not J
J -> Not M
So J and M cannot both be in.
Rule 3: S(9) -> Not WH
WH -> Not S(9)
So WH and S(9) cannot both be in.
Rule 4: P -> S(9)
Not S(9) -> Not P
Combining Rules 3 and 4 gives us:
P -> S(9) -> Not WH
WH -> Not S(9) -> Not P
So WH and P cannot both be in.
Rule 5: G or WH must be in, BNB

Now, let's look at the answer choices:

(A) is incorrect because it has both G and WH in, which violates Rule 5.
(B) is incorrect because it has both J and M in, which violates Rule 2.
(C) is incorrect because the combination of Rules 3 and 4 show that, since P is in, S(9) must also be in, and WH must be out. However, here both P and WH are in.
(D) is incorrect for the same reason that (C) is incorrect.
(E) is correct because R S(3) WH (J/M) is a valid possible group of courses Alicia could take.

Note that Rules 3 and 4 only apply to S(9), not to S(3). In the scenario described in (E) the time of the statistics course is left open, meaning that we can pick whichever time works- which is S(3) in this case. Moreover in (E), Rule 5 tells us that we could not have G in, and the combination of Rules 3 and 4 show that we cannot have P in either. However, if either J or M fill the last "in" spot, the scenario is valid.