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this is the question on gmat official site.. can some1 help

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this is the question on gmat official site.. can some1 help [#permalink] New post 06 Jun 2012, 11:23
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Organization A currently has 1,050 members. Organization B currently has 1,550 members. The number of members of Organization A and the number of members of Organization B are increasing annually, each at its own constant rate. Analysts project that if each of these organizations maintains its constant annual rate of membership increase, five years from now they will for the first time have the same number of members, and in subsequent years Organization A will have more members than Organization B.

In the table below, identify a rate of increase, in members per year, for Organization A and a rate of increase, in members per year, for Organization B that together are consistent with the analysts’ projection. Make only one selection in each column.


Organization Organization B Rate of increase(members per year)


10


30


40


120


130


150
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Re: this is the question on gmat official site.. can some1 help [#permalink] New post 06 Jun 2012, 11:26
the question isnt shown properly.. these are the options... for both organization A as well as organisation B .. we have to find out rate for both from these options only
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Re: this is the question on gmat official site.. can some1 help [#permalink] New post 06 Jun 2012, 20:55
shradhagrover18 wrote:
Organization A currently has 1,050 members. Organization B currently has 1,550 members. The number of members of Organization A and the number of members of Organization B are increasing annually, each at its own constant rate. Analysts project that if each of these organizations maintains its constant annual rate of membership increase, five years from now they will for the first time have the same number of members, and in subsequent years Organization A will have more members than Organization B.

In the table below, identify a rate of increase, in members per year, for Organization A and a rate of increase, in members per year, for Organization B that together are consistent with the analysts’ projection. Make only one selection in each column.


Organization Organization B Rate of increase(members per year)


10


30


40


120


130


150


I don't quite get the IR.

But here's my take on the problem:

Let x be the number of people Org A adds in its work force per year
y be the number of people Org B adds in its work force per year

Now, problem states that after 5 years the two will have the same number of workforce.

1,050 + 5x = 1,550 + 5y
5x - 5y = 1,550 - 1,050
5 (x - y) = 500
x - y = 100

So what do we do about what?

I don't get it haha
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Re: this is the question on gmat official site.. can some1 help [#permalink] New post 07 Jun 2012, 00:28
Let me try and see:

This is a linear growth problem (y=mx + c) and we know initial membership quantities:

Organization A: y = mx +1050
Organization B: y = nx + 1550

m and n are the respective growth rates for Organizations A and B.

At year 5, the membership qty becomes equal

mx+1050 = nx+1550 when x = 5

Thus: 5(m-n) = 1550 - 1050
m-n = 500/5
m-n = 100

Intuitively speaking. the growth rate for Org A is greater than B since after year five, it has more members.

Looking at the choices:
Org A : 130
Org B : 30

These values work because 130-30 = 100.

Is this the correct answer?
And where did you get this question from anyways?
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Re: this is the question on gmat official site.. can some1 help [#permalink] New post 19 Jun 2012, 07:59
macjas wrote:
Let me try and see:

This is a linear growth problem (y=mx + c) and we know initial membership quantities:

Organization A: y = mx +1050
Organization B: y = nx + 1550



Your answer is Same as Official Answer. Question is from MBA.com

However, tell me why do you think this is linear growth problem. What is given in question stem is "Number of members are increasing at constant rate" NOT "Number of members are increasing by constant number "
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Re: this is the question on gmat official site.. can some1 help [#permalink] New post 19 Jun 2012, 08:05
anordinaryguy wrote:
macjas wrote:
Let me try and see:

This is a linear growth problem (y=mx + c) and we know initial membership quantities:

Organization A: y = mx +1050
Organization B: y = nx + 1550



Your answer is Same as Official Answer. Question is from MBA.com

However, tell me why do you think this is linear growth problem. What is given in question stem is "Number of members are increasing at constant rate" NOT "Number of members are increasing by constant number "


The fact the the question stem states constant rate indicates that its a linear growth problem. The other option is exponential growth but the question does not state this . Usually a constant rate IMO refers to linear growth unless specified otherwise. Hope this is somewhat helpful!
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Re: this is the question on gmat official site.. can some1 help [#permalink] New post 19 Jun 2012, 10:56
macjas wrote:
The fact the the question stem states constant rate indicates that its a linear growth problem. The other option is exponential growth but the question does not state this . Usually a constant rate IMO refers to linear growth unless specified otherwise. Hope this is somewhat helpful!


It definitely fits this question and I can not doubt MBA>com as well. However, by constant rate I always understood constant percentage.
For Ex.
Increase of 20 on 100 is 20% growth
and Increase of 24 on 120 is 20% growth.

So I can say, initial amount (100) grew at a constant rate(20%) for 2 periods, even though amount it grew by (20 Vs 24) was different during two periods.

Nevertheless, thanks for quick post. I'll be wary about this term going forward, although not sure about correct interpretation yet.
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Re: this is the question on gmat official site.. can some1 help [#permalink] New post 20 Jun 2012, 00:06
You make a good point. A percentage growth is an exponential growth pattern. Lets assume that we're dealing with exponential growth.

T_n = a*(r^{n}) general expression for exponential growth, where T_n is the final quantity and n/m is the discrete time interval.

Then,
Org A: A_5=1050*r^{5} where r is the growth rate for Org A
Org B: B_5=1550*s^{5} where s is the growth rate for Org B

At time=5 (years) A_5=B_5
Then,
1050r^{5} = 1550s^{5}

\frac{1050}{1550} = \frac{s^{5}}{r^{5}}

Now testing this would take too much time (I didn't bother checking).
IMO, I doubt if you will see this kind of exponential growth problem in IR.
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Re: this is the question on gmat official site.. can some1 help [#permalink] New post 20 Jun 2012, 00:47
I feel ,that if GMAC states 'factor' it implies exponential growth and if they state constant rate it means linear growth. Experts, please correct me if you think this is wrong. Take for example this OG12 question:

Attachment:
Capture.JPG
Capture.JPG [ 42.54 KiB | Viewed 1876 times ]


If you consider linear growth, the answer is 12.2
If you consider exponential growth, the answer is 12.

The OA is 12 so the question implies exponential growth
Re: this is the question on gmat official site.. can some1 help   [#permalink] 20 Jun 2012, 00:47
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