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

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Intern
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this is the question on gmat official site.. can some1 help [#permalink]

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06 Jun 2012, 12:23
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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
Intern
Joined: 26 May 2012
Posts: 9
GMAT Date: 07-04-2012
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Kudos [?]: 5 [0], given: 8

Re: this is the question on gmat official site.. can some1 help [#permalink]

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06 Jun 2012, 12:26
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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06 Jun 2012, 21:55
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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Senior Manager
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Kudos [?]: 1277 [0], given: 100

Re: this is the question on gmat official site.. can some1 help [#permalink]

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07 Jun 2012, 01:28
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.

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]

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19 Jun 2012, 08:59
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

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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Senior Manager
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GMAT 1: 620 Q42 V33
GMAT 2: 680 Q44 V38
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Kudos [?]: 1277 [0], given: 100

Re: this is the question on gmat official site.. can some1 help [#permalink]

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19 Jun 2012, 09:05
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

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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19 Jun 2012, 11:56
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.

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Senior Manager
Affiliations: UWC
Joined: 09 May 2012
Posts: 393
GMAT 1: 620 Q42 V33
GMAT 2: 680 Q44 V38
GPA: 3.43
WE: Engineering (Entertainment and Sports)
Followers: 31

Kudos [?]: 1277 [0], given: 100

Re: this is the question on gmat official site.. can some1 help [#permalink]

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20 Jun 2012, 01:06
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.
Senior Manager
Affiliations: UWC
Joined: 09 May 2012
Posts: 393
GMAT 1: 620 Q42 V33
GMAT 2: 680 Q44 V38
GPA: 3.43
WE: Engineering (Entertainment and Sports)
Followers: 31

Kudos [?]: 1277 [0], given: 100

Re: this is the question on gmat official site.. can some1 help [#permalink]

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20 Jun 2012, 01:47
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 [ 42.54 KiB | Viewed 3959 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, 01:47
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