Organization A currently has 1050 members, Organization B currently

Question

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.

vmelgargalan · Accepted Answer

1050 + 5x = 1550 + 5y

5x - 5y = 500

(Divide both sides by 5)

x - y = 100

Only two digits were x - y = 100 is 130 and 30

Rahul885 · Answer

I absolutely agree with you, even I tried solving it using a GP.
Just saying "  constant annual rate of member increase  " is  AMBIGUOUS.  As it can mean both:
1. constant additive growth or linear growth  OR 
2. constant percentage increase or compound growth

BUT!!!

NOTICE THE UNITS GIVEN IN THE TABLE.  "Rate of increase   (members per year)  " 
Now if I say organization increases with a constant rate, it does clearly means increase in members per year is constant, and hence in AP or linear growth.
 
I hope this helps 
(PS" even I stayed frustrated by this question for a long time)

brajeshc · Answer

If this is the case it will match numbers in a year or so ..

1050+1050*1.30 and 1550+1550*.3 ....

In my opinion 40 and 30 should be Answer

Baps · Answer

It is said that after 5 years, the number of employees in organization A will be equal to the number of employees in organization B. 
If we take 40 and 30 then after 5 years, the result will be :

Org A : 1,050 + (40*5) = 1,250

Org B : 1,550 + (30*5) = 1,700

It doesn't match, so it can't be our answers.

However, if you take 130 and 30 :

Org A : 1,050 + (130*5) = 1,700

Org B : 1,550 + (30*5) = 1,700

It's a match !

Answers : 130 and 30.

Vidhi96 · Answer

1050+5x=1550+5y x-y=100 Only 130 and 30 suffice

CRACKGMATNUT · Answer

Whats the OA? Shouldnt the andwer be A>40 and B>30 ?

Sajjad1994 · Answer

OA is updated

Organization A: 130
Organization B: 30

Thank you!

Rogerper123 · Answer

Why do we solve by means of an arithmetic progression and not a geometric prgression?

What I initially did was 1050*a^5 = 1550*b^5. a and b being A and B respective constant rates.

djangobackend · Answer

is my approach correct ?

Initally they have difference of 1550-1050 = 500 in b/w them and this 500 needs to be covered in 5 yrs and since rates are same so each year they will cover 500/5 = 100 ka difference 
now, since A surpasses B afterwards so A's rate is more than B and only 130 and 30 can be valid options since only then the difference of 100 in a year can be covered 
A moved ahead by 130, B moved ahead by 30 so overall difference b/w is 100

Rahul885 · Answer

Yes,  Your approach is correct as well, and it works because of the constant additive rates.
To clarify it lets look at this more mathematically:

1050 + 5a = 1550 + 5b
(Here a is the constant additive rate by which org A is growing and likewise for B)

1550-1050 = 5(a-b)
(a-b)=500/5 ---- This is what you arrived at directly
a-b =100

Hope this helps!
Regards.

Annukiran · Answer

Here there is a fault- the question explicitly states the number of member increases by a constant rate(not constant number) so there will a compounding of the number every year. if the question would have said by a constant number then we could use your method............

vmelgargalan

1050 + 5x = 1550 + 5y

5x - 5y = 500

(Divide both sides by 5)

x - y = 100

Only two digits were x - y = 100 is 130 and 30

AnushkaKala · Answer

I generally struggle with understanding if a question is on linear growth or exponential growth. how do we identify it in such questions?

egmat · Answer

Hi AnushkaKala,

This is a great question, and it's exactly the confusion Rogerper123 and Annukiran raised in the thread when they tried a geometric-progression setup ( 1050·a^5 = 1550·b^5 ). Rahul885 pointed to the fix, and it's worth spelling out as a general rule you can reuse.

The single strongest clue: the units

Look at what the rate is measured in.

-  A rate given as an absolute amount per time  - "members  per year ," "dollars per month," "liters per hour" - means you  add the same fixed number  each period. That's  linear  (arithmetic) growth.
-  A rate given as a percent  - "grows  5%  per year," "increases by a  factor  of  1.1 ," "doubles every decade" - means you  multiply  each period. That's  exponential  (geometric) growth.

In this question the table literally says  "Rate of increase (members per year)" . That unit - a count of members added each year - locks it as linear. So each year Org A adds the same fixed number, and after  5  years it has  1050 + 5a . No compounding.

Why "constant rate" felt ambiguous

The phrase "constant rate of increase"  sounds  like it could go either way, and that's the trap. The word "rate" alone doesn't decide it -  the units do . Percentages compound; fixed quantities add.

A quick test to build the habit

Read these two versions of the same sentence and sort each one:

- "Membership grows by  40 members  each year." - add  40  every year -  linear .
- "Membership grows by  4%  each year." - multiply by  1.04  every year -  exponential .

Same word ("grows"), different unit, different model. Whenever you're unsure, ask:  am I told a number to add, or a percent to multiply by?  That question alone will settle it almost every time.

Answer: Column 1 (Organization A) = 130; Column 2 (Organization B) = 30

KarishmaB · Answer

Constant rate can mean either - "100 members per year" or "5% increase in the number of members per year"
That is why it is important to keep an eye on the options. The answers are in terms of 'members per year'. So rate of increase is a simple addition of members year or year.

Organization A currently has 1050 members, Organization B currently

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Organization A	Organization B	Rate of increase (members per year)
		10
		30
		40
		120
		130
		150

GMAT Two-part Analysis (TPA) Questions

Organization A currently has 1050 members, Organization B currently

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