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Sajjad1994
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For question 1, can someone please explain to me why 330 is can't be a possible number of in-state undergrads?
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For 1st:

Let total students be x
Under grads = 60x/100 = 6x/10

Foreign Undergrads = (1/8)*(45x/100)*(6x/10)
=27x/800

In-State Undergrads = (55/100)*(6x/10)
= 33x/100

Out of-State Undergrads = (6/8)*(45x/100)*(6x/10)
= 162x/ 800
Now, trial and error

We want to see if In-State i.e.33x/100 could be any of those 3 values:

1. 33x/100 = 200
x = 20000/33 , Not an integer, disqualified

2. 33x/100 = 330
x = 33000/33 = 1000

Check for rest:
Foreign = 27x/800 = 27000/800 = Not an integer, disqualified


3. 33x/100 = 1320
x = 132000/33 = 4000 Integer

Check for:
Foreign: 27x/800 = 127*4000/800 = Integer, Qualified

Other = 162x/ 800 = 162*4000/800 = Integer, Qualified

Hence, 3rd can only be the number of in-stateundergrads
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Q3:

Hi!

The reply to the previous email about less in-state student is that:
Even if there is a smaller percentage of in-state graduate students this year, our overall number of students is not appreciably different from last year. We are not suffering from an abundance of empty spaces. It has been my experience from my tenure at other schools that when a particular demographic of student decreases, others will rush to fill their places. This is especially true of foreign students. At Western State University, for example, we had to turn away 50% of our qualified foreign applicants. Those are students who would be glad to get in to a qualified school such as Syrandon.

The VP seems to be very confident about getting enough foreign students to fill the spot by using an example (Western State University) to support his claim. However, the school the VP is in is a private college so the VP must have assumed state school example can apply to private college.

Hope it helps :)
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There is some confusion on how to answer question 1. The simplest way is:

Foreing students must be an integer, thus, if T is the total number of sudents in the school

Foreing Students = (6/10) * (45/100) * (1/8) * T = (27/800) T -> For this to be an integer, T must be a multiple of 800, thus T = k * 2^5 * 5^2

In-state Graduates = (6/10) * (55/100) * T = (33/100) T -> For this to be an integer, T must be a multiple of 100 (but it also must be a multiple of 800 as we saw above thus the first is more restrictive and T must be a multiple of 800).

We can then express In-state Graducates as = (33/100) T = (33/100) * k * 2^5 * 5^2 = 11*3*2^3 * k

Going through the choises:
1. 200 = 2^3*5^2 -> cannot be, we are missing a 3 and a 11
2. 330 = 11*3*2*5 -> Cannot be, we are missing a 2^2
3. 1320 = 2^3*5*3*11 -> Yes, we have all factors of T

hope it helps!
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natkoo
For question 1, can someone please explain to me why 330 is can't be a possible number of in-state undergrads?
Let's say 330 is the number of in-state undergraduate students. Since percentage of in-state undergraduate students is 55%, we can find out the number of Foreign & Out state students, that comes out to be 270
( if 55% is 330 then 1% is 330/55 then 45% is (330/55)*45 which is equals to 270)
we have given that number of out-states students are 1/8th of the Foreign & Out state students, so that will make 270/8=33.75 which is not possible since number of students can't be in decimals.

Hope that solves your query.
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You are saying - " we have given that number of out-states students are 1/8th of the Foreign & Out state students"

but this contradicts what is given

we are given foreign make up 1/8 of the number of out of state undergrads

let's say if OS are 8a , then Foreign are a

so 9a = 45% of 60% of total undergrads

if we suppose total undergrads are 60x

in state are 33x
Out of state + foreign = 27x
27x = 9a
so a = 3x

if 33x = 330, x is 10

this means foreign students are 30
and out of state are 240

don't know why is 330 marked a no

monarchme

Let's say 330 is the number of in-state undergraduate students. Since percentage of in-state undergraduate students is 55%, we can find out the number of Foreign & Out state students, that comes out to be 270
( if 55% is 330 then 1% is 330/55 then 45% is (330/55)*45 which is equals to 270)
we have given that number of out-states students are 1/8th of the Foreign & Out state students, so that will make 270/8=33.75 which is not possible since number of students can't be in decimals.

Hope that solves your query.
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Not a good question. Archiving it.