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# Students from outside the province of Markland, who in any

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Re: Students from outside the province of Markland, who in any  [#permalink]

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30 Nov 2010, 08:45
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The catch in E is that the per capita revenue remaining the same. Even If the absolute number of non- Marklanders increases, despite the percentage coming down, (which is possible) the per capita revenue will not rise. This is because, for every higher contribution by the non- Marklanders, there is a much more increase in the number of the Marklanders, who contribute half of their counterparts, thus pulling down the average.

The best way is to a make a simulated arithmetic, and one can see that whatever the situation, the per capita revenue will not remain the same in the new permutation, unless there is an actual rise.

E is the safest inference
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Re: Students from outside the province of Markland, who in any  [#permalink]

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12 Jan 2012, 22:57
Good job with explanation Karisma.+1 for you!
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Re: Students from outside the province of Markland, who in any  [#permalink]

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30 Apr 2014, 07:31
Can somebody please explain why is C not right. If the proportion of outsiders has decresed then can't it be inferred that number of outsiders has decreased .

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Re: Students from outside the province of Markland, who in any  [#permalink]

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30 Apr 2014, 23:46
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282552 wrote:
Can somebody please explain why is C not right. If the proportion of outsiders has decresed then can't it be inferred that number of outsiders has decreased .

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A decrease in proportion does not imply a decrease in numbers.

Say there used to be 100 students - 70 outsiders (70%) and 30 Marklanders (30%)

Say now there are 500 students - 200 outsiders (40%) and 300 Marklanders (60%)

So though the proportion of outsiders has decreased from 70% to 40%, their number has actually increased (from 70 to 200) because total number of students has increased. Since we know nothing about the number of students, we cannot say what happened to the actual number of outsiders in the last 10 years.
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Re: Students from outside the province of Markland, who in any  [#permalink]

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04 May 2014, 02:15
I still don't understand why the answer is E. What if the actual number of non-Markland students increase? According to CR Bible, decreasing porportion does not necessarily imply decreasing numbers.

This is a "MUST" question, so should not be tricky by "implying Number and %".
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Re: Students from outside the province of Markland, who in any  [#permalink]

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20 Sep 2014, 15:05
Good practice for those who aim for 700+!
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Re: Students from outside the province of Markland, who in any  [#permalink]

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27 Oct 2015, 04:50
I still don't understand why the answer is E. What if the actual number of non-Markland students increase? According to CR Bible, decreasing porportion does not necessarily imply decreasing numbers.

Nice try, but...

E is correct due to the following logic:

"If the college’s per capita revenue from tuition has remained the same, tuition fees have increased over the past 10 years."

The fact is that the college's per capita revenue from tuition only remained the same. Nobody can dispute that. Now imagine this example (someone already had the same idea above): there are 100k students enrolled. First, 66k were paying let say 10k for tuition. The other third was paying 5k. From this we can get the average (per capita) tuition/revenue. Now if the number of first students from the first group dropped to 40k, 40k people would now be paying 10k tuition (in old terms) and 60k people would be paying 5k tuition (also in old terms). Consequently, the total revenue from tuition would drop significantly, hence also the average tuition.
Now E) states, as already mentioned, that the revenue hasn't changed, thus the tuition per capita HAD to increase.

It is true that the total number of students might have increased and therefore the total revenue might have increased as well, but this is irrelevant as the argument is relying on the average numbers, not the absolute numbers.

Btw, I chose answer C and while I was writing this post I realised my mistake - proportions vs. absolute. Funny

Hope this helps.
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Re: Students from outside the province of Markland, who in any  [#permalink]

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27 Oct 2015, 09:18
noboru wrote:
Students from outside the province of Markland, who in any given academic year pay twice as much tuition each as do students from Markland, had traditionally accounted for at least two-thirds of the enrollment at Central Markland College. Over the past 10 years academic standards at the college have risen and the proportion of students who are not Marklanders has dropped to around 40 percent.

This one has really been a sitter for me ( And trust me the more challenging the game becomes the better it feels)

noboru wrote:
Students from outside the province of Markland, had traditionally accounted for at least two-thirds of the enrollment at Central Markland College

Situation 10 Yrs ago -

Total students = 60
Non Markland = 40 ( Considering 2/3rd)
Markland = 20

noboru wrote:
who in any given academic year pay twice as much tuition each as do students from Markland

Let the tution fees 10 years ago be as follows -

Non Markland = 20
Non Markland = 10

Total tution fees collected by Central Markland College was -

(20*40) + (10*20) = 1000

Per Capita Revenue is 1000/60 =>16.67

noboru wrote:
Over the past 10 years academic standards at the college have risen and the proportion of students who are not Marklanders has dropped to around 40 percent.

Situation 10 Yrs ago -

Total students = 60
Non Markland = 16 ( 40% )
Markland = 44

Considering tution fees and No of students remaining the same

Tution fees now -

Non Markland = 20
Markland = 10

Total tution fees collected by Central Markland College was -

(20*16) + (10*34) = 660

Per Capita Revenue is 660/60 =>11.00

Which one of the following can be properly inferred from the statements above?

(A) If it had not been for the high tuition paid by students from outside Markland, the college could not have improved its academic standards over the past 10 years.

We can not infer anything about the standard of education because nothing has been explicitly mentioned in the stimulus.

(B) If academic standards had not risen over the past 10 years, students who are not Marklanders would still account for at least two-thirds of the college’s enrollment.

We can not infer anything about the standard of education because nothing has been explicitly mentioned in the stimulus.

(C) Over the past 10 year the number of students from Markland increased and the number of students from outside Markland decreased.

This might seem a probable answer choice but be very very careful this statement talks about " the number of students " and the passage keeps on mentioning Percentage - Increase/Decrease in %gae doesn't mean a corresponding increase/Decrease in number.

(D) Over the past 10 years academic standards at Central Markland College have risen by more than academic standards at any other college in Markland.

We can not infer anything about the standard of education.

(E) If the college’s per capita revenue from tuition has remained the same, tuition fees have increased over the past 10 years.

This sounds very interesting , lets check.

Per Capita Revenue 10 years ago was 1000/60 =>16.67
Per Capita Revenue now is is 660/60 =>11.00

Now to keep per capita revenue same we must have to increase the tution fees to 1000 now , this will defintely mean a increase in Per capita tution fees.

Hence IMHO (E)
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Re: Students from outside the province of Markland, who in any  [#permalink]

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28 Oct 2015, 11:25
Hi,

Brilliant question.

The answer choices B and C are trap. One can arrive at those options by making certain out of argument assumptions. So they are clearly not the choices.

E is more of a mental math choice.

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Re: Students from outside the province of Markland, who in any  [#permalink]

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22 Apr 2017, 07:50
Let's say there were 100 students enrolled at Central Markland College (hereafter referred to as CMC) and the tuition for residents was \$100. Since at least 2/3 of the student body comprised of non-residents who paid double the residents' tuition (\$200), let's suppose, for the purpose of simplification, that 70% of the student body were non-residents.

In sum, 10 years ago, we had 30 resident students each of whom paid \$100 and 70 non-resident students each of whom paid double that amount, i.e. \$200.

To compute the average tuition (tuition revenue received by CMC per head) = ( \$100 x 30 + \$200 x 70 ) / 100 = \$170 per capita or per student

After 10 years, IF CMC is still earning per capita revenue of \$170 and that the proportion of nonresidents has decreased to 40%, it MUST BE TRUE that the amount of contribution by residents has increased.

Let me give you another hypothetical situation.

After 10 years, the number of student body has increased. Say, the number of residents and nonresidents have BOTH increased to a total of 200. Here, since nonresidents make up 40% of the student body, there are 80 of them and the rest are residents (160 students).
See how (C) doesn't have to be true here for nonresident students' proportion to decrease relative to that of the residents?

So if the college is still earning \$170 from each student, let's denote the new tuition as NT and see if NT equals \$100 (which was the tuition for residents a decade ago).

170 = { ( NT x # of residents ) + ( double NT x # of nonresidents) } / new total number of students

170 x 200 = ( NT x 120 ) + ( 2NT x 80 )
34000 = 280NT
New Tuition (NT) = \$121.something
So the tuition has indeed increased! (by \$21 in our hypothetical example)
Hence E is correct.
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Re: Students from outside the province of Markland, who in any &nbs [#permalink] 22 Apr 2017, 07:50

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