PT16.S2.Q20

Ashley2018-1

I need help understanding why the correct answer is correct. I eliminated A and B because I felt they were both hypotheticals that could not be proven given the information. I took out D because I could not show the standards had risen higher than any other college's and took out C because the proportion of students who are not Marylanders may have decreased, but the number of students could have remained the same. I just don't get why E is correct. And for this stimulus, is "proportion" the same thing as percentage?
Any help appreciated!

canihazJD

Students from outside Markland pay twice as much tuition
Students from outside Markland account for ⅔ enrollment
Over past 10 years academic standards have risen
Proportion of students from outside Markland has dropped to around 40%

A. Academic standard improvement → outside Markland high tuition

We don’t know this. We know the high tuition pre-existed, and that there is a correlation between standards increase and proportion change.

B. /academic standard improvement → /change in proportion

Same as A.

C. Number of Markland students increased and the number of outside Markland students decreased

This doesn’t have to be true. Either one could have happened alone.

D. Academic standards have risen more than any other college.

What? We don’t know about any other college. This is in no way supported.

E. If per capita revenue from tuition has remained the same, tuition fees have increased.

This is the answer. If per capita revenue is the same while the proportion of students paying a higher rate dropped, tuition must have increased in some capacity to retain the same revenue.

@"ashley.tien" said:
I just don't get why E is correct.

If we have 10 students total and receive $5 from 5 and 10$ from 5 that gives us $75 or $7.5 per capita.

If we then lose 2 of the $10 students (leaving 3@$10) and gain 2 $5 students (resulting in 7@$5) we now have $65 or $6.5 per capita.

Having lost some of my higher paying students and replaced them with lower paying ones, the only way I can retain my $7.5 per capita rate is if I somehow increase the overall amount I receive to make of for the $10 difference (75-65) and bring me back up to $75.

@"ashley.tien" said:
And for this stimulus, is "proportion" the same thing as percentage?

Yes. Proportions can be expressed as percentages.

Hope that helped!

LOWERCASE EVERYTHING

@"ashley.tien" said:
I eliminated A and B because I felt they were both hypotheticals

this is not a reason why a and b are wrong.
e (correct answer) is also a hypothetical: we don't know if the college's per capita revenue has remained the same; but if it has, it must be the case that tuition fees have increased.

a: is wrong, because we have no information on why the academic standards were improved.
b: is wrong, because we have no information on why the proportion of non-markland students decreased.

note that a and b are trying to trick us into thinking that there’s a causation relationship, while the only information we have in the stimulus is correlation.

e: we know that non-markland students were paying more tuition than markland students; we also know that the proportion of these non-markland students (who were paying more tuition) dropped from +66% to 40%.

so if “per-capita revenue from tuition” (average price paid for tuition) stayed the same, that must mean that markland college must have raised tuition that made of for the difference.

Ashley2018-1

Per Capita means the total cost divided by number of students; all info we have is just percentage of non-markland has decreased, so how can we get any info about the amount of money each student pays?

Ashley2018-1

I was thinking that it may be true non-markland students pay more but the markland students could make up that amount since there are more of them.

canihazJD

@"ashley.tien" said:
Per Capita means the total cost divided by number of students; all info we have is just percentage of non-markland has decreased, so how can we get any info about the amount of money each student pays?

We don't need to know how much each student pays. No matter what they pay, we know there is a group that pays more and a group that pays less. If the percentage of higher paying students decreases, the per capita revenue will go down, all else held equal.

Maybe look at it like an RRE question. We know the percentage of higher paying students has in fact decreased. Now add in the premise that the per capita revenue has remained constant in spite of this. The only way this can happen is if tuition was increased.

LOWERCASE EVERYTHING

@canihazJD well said.

@"ashley.tien" not sure if looking at it mathematically will help. if it just confuses you more, just ignore this comment.

i think this question can well be a gmat question. in this question, it is possible to calculate the value for "per-capita revenue from tuition."

as you said, per capita means the total tuition school collects divided by total number of students.

t(m): tuition for 1 markland student
t(n): tuition for 1 non-markland student
total tuition school collects: t(m) x # of markland students + t(n) x # of non-markland students
s: # of total students

"non-markland students pay twice as much as markland students" means t(n) = 2t(m)

total tuition school collected: t(m) x (0.33s) + 2t(m) x (0.66s)
if you divide that by s,
you get: 1.65t(m)

after 10 years, this changes to:
total tuition school collected: t(m) x (0.60s) + 2t(m) x (0.40s)
if you divide that by s,
you get: 1.40t(m)

so, per-capita tuition was 1.65t(m), but it decreased to 1.40t(m).
the only way for them to be equal is that you increase the value of t(m), which is tuition for markland students.

note: if you increase the tuition for markland students, tuition for non-markland students also increases (remember, t(n) = 2t(m) ).
so it's fair to say that tuition for all increased, which is answer choice e.

Help2222

I agree with all the comments above, that this is a tuition problem. We could also assume that the reason non-Markland students decreased is because the tuition increased. So, E must be true.

canihazJD

@Help2222 said:
We could also assume that the reason non-Markland students decreased is because the tuition increased.

Well... we could, but that would not be supported by the stimulus. That assumption is attractive, and I'm surprised this question didn't target it. If that were a MBT or even a MSS AC, I pretty sure it'd be a wrong answer. What if the double tuition they pay is still the lowest in the area available to them? We don't have enough info. Consider that it could have also been say the rising academic standards, or many other reasons. In fact the increase in standards at least correlate with the decrease in non-M students.

canihazJD

@"ashley.tien" If you haven't seen it and don't mind looking, 75.1.19 has a similar feel to it

Ashley2018-1

I had a lot of issues with that question as well. I couldn't anticipate any answers and so went to the stimulus wondering how wages could go up in each region while decreasing in the country.
A.) Doesn't explain why wages went up in each region
B.) Am I supposed to assume after the employers moved those jobs, the wages decreased?
C.) Unemployment rate unrelated to wages
D.) Doesn't get at the discrepancy between region and country
E.) The stimulus is talking about full-time jobs in general and not specific to manufacturing or service and still doesn't explain the discrepancy

canihazJD

@"ashley.tien" said:
I had a lot of issues with that question as well. I couldn't anticipate any answers and so went to > the stimulus wondering how wages could go up in each region while decreasing in the country.

B.) Am I supposed to assume after the employers moved those jobs, the wages decreased?

No that assumption isn't required.

You were probably thinking something like this:

Start of last year
Region 1 - $2/hr average
Region 2 - $10/hr average

Overall average $6/hr

End of last year increased averages
Region 1 - $3/hr average
Region 2 - $11/hr average

Overall average $7/hr

So how could the average of the two regions combined actually decrease?

We want the overall average for the whole country, so you have to consider the number of people used to calculate the average in each region as opposed to considering the regions as single numbers:

Start of last year
Region 1 - $2/hr average (5 people - $1, $1, $2, $3, $3)
Region 2 - $10/hr average (5 people - $9, $9, $10, $11, $11)

Total people: 10
Overall average $6/hr

End of last year increased averages with large population shift toward low wage regions
Region 1 - $3/hr average (9 people - $2, $2, $2, $2, $3, $4, $4, $4, $4)
Region 2 - $11/hr average (1 person - $11)

Total people: 10
Overall average $3.80/hr

These two questions exhibit what is a not-uncommon focus in LR. I'm not sure what your timeline looks like, but consider running through some basic statistics, probability, and survey lessons... maybe on Khan Academy. It'll help, even if only by training you to adopt a mindset that allows you to see the effects of different variables. If anyone else has a better resource please post it.

Ashley2018-1

but how do you know to focus on the movement of people rather than the jobs themselves?

canihazJD

@"ashley.tien" said:
but how do you know to focus on the movement of people rather than the jobs themselves?

I'm pretty sure that's the only way the overall average could have decreased. If a larger number of individual people had a wage below the previous average.

The question you should ask yourself is, "given a increase in regional wage averages, how could the national average drop?"

Or for the original question, "given the percentage of higher paying students has fact decreased how could the per capita revenue have remained constant?"

The reason I recommended some statistics exposure, is that it will prime you to see, when asked questions like the two above, what the possible (or only) causes would be.

Ashley2018-1

Going back to the previous question about Markland, I think my issue was that I was comparing the 40% to the original 2/3rd's in terms of the number of students paying tuition; to avoid confusion, should I just think of it as percentage of students paying double decreasing so you would expect an overall decrease in amount of tuition paid so that means per capita should decrease as well?

canihazJD

@"ashley.tien" lets try this:

A. (10, 2, 9, 2, 9, 1, 10, 0, 1, 1, 1, 10, 9)
B. (5, 4, 5, 11, 4, 3, 3)

Which is the higher average?

or

Last year I donated $5 a month to PETA, and $10 a month to the Red Cross.
This year I only donated to the Red cross.
But the total value of my charitable contributions this year was the same as last year.

How is this possible?

or

Last month my state had a 50% positive covid test rate.
This month my state had a 20% positive covid test rate.
Despite this decline, the number of covid cases detected in my state this month is double the number detected last month.

How is this possible?

or

The average GPA in each of the 10 classes offered by the university has risen compared to last year.
The average GPA of the student body as a whole at the university has dropped.

How is this possible?

You don't like have to actually answer me... But just think about how you'd resolve them and why it works. Not nearly as good as the test writers, but I tried to gradually ease into the type of reasoning behind those two questions.

Ashley2018-1

1.) Without using a calculator, I'm guessing the second one has the higher average because it has fewer numbers to divide against.
2.) Eh...I am not sure about this one. Since you're only donating to RC now, maybe that amount makes up for the P donations that are left out?
3.) More people were tested in the state with 20% positivity; a smaller percentage of a bigger number can be greater than a bigger percentage of a smaller number.
4.) People with higher GPA's sneaked into each of the classrooms so the average GPA of each classroom went up but I'm not sure why that would mean the university's average GPA decreased since overall number of people are the same
Is there any way to approach these without using numbers to try out? On the exam, I know I won't have time to do that.

Ashley2018-1

4.) Same concept as the jobs moving from one region to another; should I think of jobs=people like gpa=students?

canihazJD

@"ashley.tien"

1.) Without using a calculator, I'm guessing the second one has the higher average because it has fewer numbers to divide against.

The averages are the same. They are both 5. The point here is that the distribution and N value can change radically but still be tuned to average the same. Conversely, two sets of data could look similar but be saying very different things.

2.) Eh...I am not sure about this one. Since you're only donating to RC now, maybe that amount makes up for the P donations that are left out?

The only way my total donation amount could be the same is if I increased my donation amount to RC. Similar reasoning to the tuition question you originally mentioned.

3.) More people were tested in the state with 20% positivity; a smaller percentage of a bigger number can be greater than a bigger percentage of a smaller number.

Good. A common theme in the test. Numbers vs. percentages. Though I suspect you missed that it was the same state being referenced, which was intended to make it slightly harder. Consider the opposite... what if volume of positives dropped but percentage of positives went up?

4.) People with higher GPA's sneaked into each of the classrooms so the average GPA of each classroom went up but I'm not sure why that would mean the university's average GPA decreased since overall number of people are the same

I don't know about snuck in, but there would have to be a rise in the number of lower GPAs distributed foused in classes that already had low GPAs to begin with.

There's an analogy about section stacking in here somewhere too.

4.) Same concept as the jobs moving from one region to another; should I think of jobs=people like gpa=students?

Yes!

Is there any way to approach these without using numbers to try out? On the exam, I know I won't have time to do that.

The thing is that the numbers are what make them hard, and this is how they'll show up.

Try the second one:

Last year I donated each month to both PETA and the Red Cross. This year I only donated to the Red cross. But the total value of my charitable contributions this year was the same as last year.

So I just gave all my money to the Red Cross right?

The numbers are there to see if you can pull the reasoning out from behind them.