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# Can anyone please explain this math problem?

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Intern
Joined: 18 Nov 2015
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18 Nov 2015, 20:34
1
This post was
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Attached. Much obliged!
Attachments

1.png [ 86.56 KiB | Viewed 1293 times ]

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Math Forum Moderator
Joined: 02 Aug 2009
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18 Nov 2015, 21:18
1
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Expert's post
porkery wrote:
Attached. Much obliged!

Hi,
lets see what all we have..
1) year 1999..
number of students=5500
number of faculty=5500/R..

2) year 2004.....
number of students=5500(100-S)/100..where S is the % change over 5 academic years
number of faculty=5500/R*(100+F)/100..where F is the % change over 5 academic years..
so number of students/number of faculty members=
[5500(100-S)/100]/[5500/R*(100+F)/100]
=(100-S)/(100+F) * R
ans D
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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Manager
Joined: 15 Apr 2016
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17 Sep 2016, 02:34
chetan2u wrote:
porkery wrote:
Attached. Much obliged!

number of students=5500(100-S)/100..where S is the % change over 5 academic years
number of faculty=5500/R*(100+F)/100..where F is the % change over 5 academic years..

Hi chetan2u,
Can you please tell me how you got the below step ?
100-S and 100+F ..

chetan2u wrote:
number of students=5500(100-S)/100..where S is the % change over 5 academic years
number of faculty=5500/R*(100+F)/100..where F is the % change over 5 academic years..

i din understand from where 100 came all of a sudden.. is there anything i am missing ?

just a query, is the answer (100-S)/(100+F) * R ?
cause the one mentioned in screenshot is different.
_________________

Cheers,
Shri
-------------------------------
GMAT is not an Exam... it is a war .. Let's Conquer !!!

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Math Forum Moderator
Joined: 02 Aug 2009
Posts: 4771

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17 Sep 2016, 04:55
1
KUDOS
Expert's post
Shrivathsan wrote:
chetan2u wrote:
porkery wrote:
Attached. Much obliged!

number of students=5500(100-S)/100..where S is the % change over 5 academic years
number of faculty=5500/R*(100+F)/100..where F is the % change over 5 academic years..

Hi chetan2u,
Can you please tell me how you got the below step ?
100-S and 100+F ..

chetan2u wrote:
number of students=5500(100-S)/100..where S is the % change over 5 academic years
number of faculty=5500/R*(100+F)/100..where F is the % change over 5 academic years..

i din understand from where 100 came all of a sudden.. is there anything i am missing ?

just a query, is the answer (100-S)/(100+F) * R ?
cause the one mentioned in screenshot is different.

Hi,
There is a decrease in the number of students, say s%...
Then the student who were initially 5500 goes down to 5500*(100-s)/100..
Example.. the decrease was 20%, so number is 5500*(100-20)/100=5500*80/100..
Similarly for increase in faculty (100+F)/100..
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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Manager
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17 Sep 2016, 09:43
chetan2u wrote:

Hi,
There is a decrease in the number of students, say s%...
Then the student who were initially 5500 goes down to 5500*(100-s)/100..
Example.. the decrease was 20%, so number is 5500*(100-20)/100=5500*80/100..
Similarly for increase in faculty (100+F)/100..

Thank you so much chetan2u for your explanation Kudos to you ..
(100+S)/(100+F) * R

Since Students decrease, it should be 100-s right ?
_________________

Cheers,
Shri
-------------------------------
GMAT is not an Exam... it is a war .. Let's Conquer !!!

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Intern
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27 Sep 2016, 13:57
1
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Shrivathsan wrote:
(100+S)/(100+F) * R

Since Students decrease, it should be 100-s right ?

I think the process used is completely right, but there is a minor flaw.
S represents the change and not the decrease itself. The change has to be used as +S, and when the change is on the negative side (there is a decrease), S will assume a -ve value.

Example: If there is an increase, S = +5%, or in case of decrease, S = -7%
Over here in the working provided, in case of increase, S = -5% and in case of decrease, S = 7%. The general way of depiction is wrong.

Working is totally fine though.

Hope it helps

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Manager
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29 Sep 2016, 06:11
testprepabc wrote:
The general way of depiction is wrong.

Thanks testprepabc

But they have provided S is decreasing right ?
Since the value is not given .. we are giving a general expression ?
_________________

Cheers,
Shri
-------------------------------
GMAT is not an Exam... it is a war .. Let's Conquer !!!

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Intern
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01 Oct 2016, 01:08
Shrivathsan wrote:
But they have provided S is decreasing right ?
Since the value is not given .. we are giving a general expression ?

The question defines S to be a percentage change in the number of students. We need a formula which will generalize both the increase and the decrease. Hence the positive sign.
Small example: Let's say the question had 2 parts - One with a x% increase and the other with a x% decrease.
The easiest way to answer this is to write a formula which will satisfy both the equation instead of writing 2 formulae one with +S and the other with -S. Rather you would probably write a formula with +S and replace +S = x% for increase and +S = -x% for decrease.
A mathematical corollary would be formula for compound interest. We do not change the +ve sign in the bracket to -ve for decreasing Rs in A=P[1+(R/100)]^n, rather replace R with a -ve value.

Remember, formulae should be general and conventional.

Hope this explains and helps you

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Re: Can anyone please explain this math problem?   [#permalink] 01 Oct 2016, 01:08
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