Q21 - All of the students at Harrison University

[Laura Damone]

Question Type:
Inference (Must Be True)

Stimulus Breakdown:
No argument here so we just need the facts: All students at Harrison live in either Pulham or Westerville. Overall, 38% of Harrison students take at least one night class. Only 29% of students living in Westerville take at least one night class.

Answer Anticipation:
Inference questions that include percentages are probably testing the relationship between those percentages and actual amounts, so let's think about what is and is not implied here. The percentage of students taking a night class in Westerville is lower than the percentage of students taking a night class overall. That must mean that, at Pulham, more students are taking a night class than the overall rate of 38%. We can't, however, infer anything about the actual number of students taking night classes. There aren't, for example, more students in Pulham taking night classes than there are students in Westerville, because Westerville might be a much larger facility. Therefore 29% of Westerville students could amount to a larger number of students than a greater percentage of the Pulham students.

Correct answer:
A

Answer choice analysis:
(A) A ha! A perfect match to our prephrase. Select.

(B) Without knowing the relative population of Pulham vs. Westerville, we can't calculate exactly what percentage of Pulham students take a night class. Eliminate.

(C) Nope. We don't know the relative population of Pulham vs. Westerville.

(D) No way. We only have info about those taking "at least one night class." We can't conclude anything about students taking more than one.

(E) Tempting! We’re told that night classes are just a small fraction of the classes offered at Harrison. So if 38% of students take at least one night class, does that mean night classes have higher average enrollments? Not necessarily. It could be the case that almost all the students who take a night class take a particular one, leaving the rest with really low enrollment. Even if those enrollments are averaged, it wouldn't necessarily put the average enrollment of those classes above that of the day classes.

Takeaway/Pattern:
When it comes to questions that test percentages and amounts, know what you know, and, as importantly, know what you don't. The extent to which information about percents doesn't imply anything concrete about amounts is almost always at the crux of these questions.

#officialexplanation

[TijanaS421]

Hi, could you please explain this argument in more depth? I have trouble understanding why, given that only 29% of W students take at least one night class, that must mean that the % of P students taking a night class must be above 38%? I cant seem to understand the logic here.

Thanks!

[LoganS285]

Hi, could you please explain this argument in more depth? I have trouble understanding why, given that only 29% of W students take at least one night class, that must mean that the % of P students taking a night class must be above 38%? I cant seem to understand the logic here.

Thanks!

You can think about it this way: we know 38% of the total population has a certain characteristic, and we know that there are two groups, a and b. This means that a certain percentage of a has the characteristic, and a certain percentage of b has the characteristic, and together 38% of a + b has that characteristic. If we want to think about it slightly more symbolically, we can show that:

.38(a + b) = some percentage of a + some percentage of b

Now let's stipulate, as the stimulus does, that we actually know one of these undefined percentages: we know that 29% of one of those groups has the characteristic. Let's say it's a. So now we know that:

.38(a + b) = .29a + xb, where x is some unknown percentage.

If we play by the rules of algebra, we can work out a few inferences here. Let's look closely. If 38% of a + b has a characteristic, that's like saying that 38% of a has that characteristic and 38% of b has that characteristic. In other words, .38(a + b) is the same thing as saying .38a + .38b (FOIL makes a comeback!), which means:

.38a + .38b = .29a + xb

Looking at this representation of the stimulus, it might already be clear what the inference is. The only way that 38% of a and 38% b can be the same thing as 29% of a and some unknown percentage of b is if that unknown percentage of b is higher than 38%. Intuitively, does it make sense to say:

.38a + .38b = .29a + .35b

Does it even make sense to say that:

.38a + .38b = .29a + .38b

No, and it even kinda looks funny. Remember, while a and b may be different numbers, the a on the left side of the equation is the same as the a on the right side of the equation. The same goes for b. So how could 38% of group a plus 38% of group b come out to the same thing as (some number less than 38)% of group a and (some number less than 38)% of group b?

It can't. If one of those percentages is lower than 38%, then the percentage of the other group must be higher than 38% to compensate.

Sorry for the math, but I think the symbolic representation is helpful in this case. Hope that helps!

[Jay W717]

Yes, there is a lot of math involved. Unfortunately, it is difficult for me to calculate these percentages because of my poor level of knowledge. Yes, not only mathematics is my weakness, but I also do not like to write various texts. For studies, I try to use a website https://newyorkessays.com/examples/dedication/ that helps me to write quality materials with good grades. To be more specific, on this website you can find free samples of essays on the topic of dedication. Studying is quite a complicated process and sometimes you have to look for ways to solve many problems.

Unfortunately, we started for math calculations and ended up talking about essay writing. I'm very upset.

[Akyla T135]

So a simpler way that helped me understand the inference is to apply the "is over of % method"

29 = is
38 = of

Step 1: 29 / 38 = x / 100
Step 2: cross multiply (38x = 2900)
Step 3: divide both sides by 38 to find x (Answer: x = 76%)

76% of students that live in Pulham attend night classes

This is what (A) is saying. More than 38% of students at Harrison who live in Pulham attend night classes