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 Dave Killoran
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#72679
Complete Question Explanation

Must, #%. The correct answer choice is (A).

The stimulus contains a Fact Set and begins by indicating that every Harrison University student lives in either Pulham or Westerville. This doesn't need to be diagrammed but we will do so to help with this explanation:

  • ..... ..... ..... ..... Pulham
    Harrison ..... :arrow: ..... or
    ..... ..... ..... ..... Westerville
From this basis, the stimulus continues on to provide two separate percentage figures, and you must read closely in order to not mistake which groups are being referenced.

The first figure references all of Harrison University, and states that 38% of all students take at least one night class; the second figure references just Westerville, and states that 29% of Westerville students take at least one night class. For purposes of explanation, let's add this to our diagram form above:

  • ..... ..... ..... ..... ..... Pulham
    Harrison (38%) ..... :arrow: ..... or
    ..... ..... ..... ..... ..... Westerville (29%)
Since the percentage for Westerville students is lower than the overall percentage for all Harrison students, at this point you can conclude that the Pulham percentage must be higher than 38% in order to raise the overall percentage back to 38% (remember, these two residence halls represent the entire university).

If the above doesn't make sense, stop for a moment and consider what would happen if the Pulham percentage was, say, also 29%. If that was the case, 29% of the Pulham students would take a night class, and 29% of the Westerville students would take a night class. Since those are the only two groups, that would mean that 29 of Harrison students as a whole students would take a night class. But that's too low, and immediately you can conclude that the Pulham percentage must be higher than 29%, and also must be higher than 38% in order to raise the overall up to 38%.

Note that one common error here was to read the 38% as being in reference to Pulham, but a close reading shows that the percentage relates to all of Harrison. Unsurprisingly, with this easy reading error built into the stimulus, the question stem is a Must Be True. As you search the answers, consider carefully that in this #% question that the correct answer is more likely to address just the percentages, and far less likely to address hard numbers (of which there could be many more scenarios).


Answer choice (A): This is the correct answer choice. As noted above, to meet the requirement that 38% of Harrison students take at least one night class, Pulham must have a percentage higher than 38% in order to offset the lower percentage reported for Westerville students.

Answer choice (B): While this answer is possible, we cannot be certain that it is true. For example, if the number of Pulham and Westerville students is identical, then the Pulham figure would only need to be 47% (47% + 29% divided by 2 = 38%).

Answer choice (C): While this is also possible, it also does not have to be true and thus is incorrect. This answer is also suspicious since it address actual student numbers and not percentages.

Answer choice (D): The stimulus only addresses students taking "at least one night class," and there is no information about students taking "more than one night class." Thus, there is no information to prove this answer and it is incorrect.

Answer choice (E): This answer is suspicious since it address actual student numbers and not percentages, but in any event there is no information in the stimulus about the number of night classes, their enrollment, or specific day class numbers.
 sparrrkk_
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#74383
Hi,

I keep getting stumped on this question :(

I understand why C, D & E are wrong. I was able to cross out B by drawing out a counterexample.

However, I'm trying to understand how A is right.

So, in general, if the % of the total is 39% and % of Westerville is 29%, then the % of Pulham has to be higher then 39%?
So, if the % of Westerville was instead 50%, then would the % of Pulham have to be lower then 39%?

What happens when the % of Westerville is 39%?

Thank you! :)
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 KelseyWoods
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#74406
Hi sparrrkk_!

Think of that 38% as an average. ALL of the students at Harrison live in either Pulham or Westerville, so they are basically the only 2 groups making up the whole of Harrison. And 38% of all students at Harrison is the average between Pulham and Westerville. So if only 29% of Westerville students take night classes, we have to have more than 38% at Pulham taking night classes so that the average between both residence complexes is 38%.

Let's make up some numbers to illustrate this. Let's say that there are 200 total students at Harrison and 100 live in each residence:

Total at Harrison: 200
% taking night classes: 38%
# taking night classes (38% of 200): 76

# at Westerville: 100
% taking night classes: 29%
# taking night classes: 29

# at Pulham: 100
# taking night classes (76 total taking night classes at Harrison-29 taking night classes at Westerville): 47
% taking night classes: 47%

Again, all of the students at Harrison are accounted for between these 2 dorms. So if I have 38% of Harrison students total taking night classes but only 29% of Westerville students taking night classes, I have to have a higher percentage (47%) of Pulham students taking night classes.

Hope this helps!

Best,
Kelsey
 sparrrkk_
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#74539
Thank you so much! :)
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 amys45
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#86142
Hi Kelsey!

Thanks for the explanation. I'm confused however, because doesn't this answer choice require that we make a very strong assumption that the residence halls are equal in terms of the number of residents in each hall, even though we're not told that anywhere?

For example, what if there are 100 students total, and 90 live in Westerville and 10 live in Pulham. In this case, 38 students take a night class. However, in this case, only 26 students in Westerville would take a night class, which means that at least 12 students from Pulham would need to take night classes, which is impossible in this scenario.

So, I'm essentially asking how LSAT can expect us to make the assumption that the halls have somewhat equal numbers of residents when there is no evidence for that in the stimulus. If you don't assume this, it seems that the numbers don't make sense at all.

Thanks for your help!
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 KelseyWoods
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#86145
Hi Amys45!

So your example shows us exactly why we can assume that the total numbers in the residence halls, while not necessarily equal, have to be within a certain range of each other!

Things we are 100% certain of:
38% of Harrison students take a night class
29% of students living in Westerville take a night class

We know that these things are true. Anything else that must be true because of these two things would also be something we can be certain of. We're not certain of the exact split between our two residence halls. But as your example shows, the 90/10 split doesn't work. We can't have that be true at the same time that the other things we know to be true are true. So the facts the stimulus gives us are enough for us to be certain that the split can't be as extreme as 90/10.

We're not assuming that the residence halls have to be closer in number than the 90/10 split. The facts are telling us that they have to be closer in number.

It also doesn't mean the residence halls have to be totally equal. We could make numbers like this work:

Total at Harrison: 1500
% taking night classes: 38%
# taking night classes (38% of 200): 570

# at Westerville: 1000
% taking night classes: 29%
# taking night classes: 290

# at Pulham: 500
# taking night classes (570 total taking night classes at Harrison-290 taking night classes at Westerville): 280
% taking night classes: 56%

Answer choice (A) doesn't assume any more about the split between the two residence halls than the stimulus facts tell us. The 90/10 split doesn't work because of the stimulus, not because of answer choice (A). But answer choice (A) must be true for any valid split between the two residence halls that allows for 38% of students at Harrison to be taking night classes and only 29% of students in Westerville to be taking night classes.

Hope this helps!

Best,
Kelsey
 2020//Vision
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#89348
Thank you for these full explanations!
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 mnhigh
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#103658
Hi!

Ive reviewed this question and the answer explanation a couple times, yet I'm not understanding the explanation given. When working through this stimulus, I understood the group of students taking at least one night class totaling only 38% at Harrison. However, out of that 38%, 29% of them are students from Westerville. So, following that train of thought, the remaining 9% are students from Pulham.

Please highlight what I am overlooking and/or misinterpreting.

Thank you!
 Adam Tyson
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#103660
That's not quite how percentages work, mnhigh! 38% of the total of all students combined is not the same as 29% of one group plus 9% of another group. To illustrate that, let's say there are 100 students in each dorm. 29% of one dorm would be 29 students, while 9% of the other dorm would be 9 students. That's 38 students, but only 19% of the 200 total students in the two dorms. In this case, to get 38% of all 200 students, the second dorm would need to have 47 students in night classes, for a total of 76 students out of 200. That's 38% of the total!

That 38% must be the average between the two dorms. If one dorm is below that average, the other must be above that average.

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