Appletons population is 400 greater than Berryvilles population. If

Question

Appleton’s population is 400 greater than Berryville’s population. If Berryville’s population were reduced by 900 people, then Appleton’s population would be 3 times as large as Berryville’s population. What is Berryville’s current population?

A. 1550
B. 1650
C. 1750
D. 1850
E. 1950

Kudos for a correct solution.

A. 1550
B. 1650
C. 1750
D. 1850
E. 1950

mvictor · Answer

let's assign variables for Appleton (A) and Berryville (B)
Appleton's population is 400 greater than Berryville's. Let's write this with variables that we have assigned: A = B +400
If Berryville’s population were reduced by 900 people, then Appleton’s population would be 3 times as large as Berryville’s.
A=3(B-900)
What is Berryville’s current population? or what is B?

We have 2 equations with 2 unknowns:
A=B+400
A=3(B-900)
substitute A in the second equation:
B+400=3B-2700
3100 = 2B
1550 = B

Population of Berryville is 1550. Answer choice A.

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION appletonandberryville_text(2).png

EMPOWERgmatRichC · Answer

Hi All,

This question can certainly be solved using a 2-variable "system" of equations. Since the prompt asks for B's CURRENT population, and the answers are numbers, we can TEST THE ANSWERS.

We're told that:
1) A's population is 400 greater than B's population.
2) If B's population were reduced by 900, then A's population would be 3(B's population).

We're asked for B's CURRENT population.

Let's TEST Answer B....
IF....
B's current population is 1650
A's current population is 2050

B - 900 = 1650 - 900 = 750
3(750) = 2250.....which is TOO BIG (in this scenario, it's supposed to be 2050).
This means that there should be FEWER people in both locations....

Knowing this, you can now pick the correct answer. Here's the proof though:

IF...
B's current population is 1550
A's current population is 1950

B - 900 = 1550 - 900 = 650
3(650) = 1950...which is a MATCH for what we were told.

Final Answer:  A

GMAT assassins aren't born, they're made,
Rich

PareshGmat · Answer

Answer = A = 1550

...................... Appleton .............................. Berry

Current population (x+400) .............................. x

Reduction by 900 ............................................... (x-900)

Given that 3(x-900) = x+400

x = 1550

OptimusPrepJanielle · Answer

Given that A = 400 + B Also, A = 3(B - 900) Equating both the equations, 400 + B = 3(B - 900) So, 400 + B = 3B - 2700 So, 3100 = 2B So, B = 1550 Hence option A. -- Optimus Prep's GMAT On Demand course for only $299 covers all verbal and quant. concepts in detail. Visit the following link to get your 7 days free trial account: https://www.optimus-prep.com/gmat-on-demand-course

Mohafez · Answer

Shouldn't "Berryville’s current population" be (B-900) as in the previous sentence it' said that the population was reduced by 900 people? 
In this case the answer would be 650

OptimusPrepJanielle · Answer

The sentence reads "were reduced by 900". Hence this is a hypothetical situation.
Therefore the current population would be B and after the situation takes place, it would be B-900

Does this help?

Mohafez · Answer

MAGOOSH OFFICIAL SOLUTION appletonandberryville_text(2).png Shouldn't "Berryville’s current population" be (B-900) as in the previous sentence it' said that the population was reduced by 900 people? In this case the answer would be 650 The sentence reads "were reduced by 900". Hence this is a hypothetical situation. Therefore the current population would be B and after the situation takes place, it would be B-900 Does this help? Thanks Janielle, but is it "If were" put together that makes it hypothetical, or just "were"? If the sentence reads "If Berryville’s population was reduced" would it still be hypothetical?

OptimusPrepJanielle · Answer

Shouldn't "Berryville’s current population" be (B-900) as in the previous sentence it' said that the population was reduced by 900 people? 
In this case the answer would be 650

The sentence reads "were reduced by 900". Hence this is a hypothetical situation.
Therefore the current population would be B and after the situation takes place, it would be B-900

Does this help?

Thanks Janielle, 
but is it "If were" put together that makes it hypothetical, or just "were"? If the sentence reads "If Berryville’s population was reduced" would it still be hypothetical? 
Hi Mohafez,

Yes both "If" and "were" contribute towards the hypothetical situation. 
Have you started preparing for SC questions?

Mohafez · Answer

Hi Mohafez,

Yes both "If" and "were" contribute towards the hypothetical situation. 
Have you started preparing for SC questions?

No, not yet

OptimusPrepJanielle · Answer

I think you should start preparing for the Verbal section too. You should try to keep you Verbal and Quants sections balanced else you face the risk of lagging behind in one.
How long have you been studying?

Mohafez · Answer

I think you should start preparing for the Verbal section too. You should try to keep you Verbal and Quants sections balanced else you face the risk of lagging behind in one.
How long have you been studying?

Been studying for 3 weeks now but only for the quantitative section.

OptimusPrepJanielle · Answer

I would recommend you to start studying for the Verbal part as well.

1. When do you plan to take the GMAT?
2. Which course material have you been following?

You need to build the concepts/fundamentals before you jump in solving the problems. You can do so by choosing one of the following ways:

1. In person classes/private tutoring
2. Online classes
3. Self paced online preparatory course
4. Book heavy approach

Whatever you choose, make sure that you choose one. Because GMAT tests you on some concepts and fundamentals that you can learn from a course. Most of the preparatory companies including ours offer a free trial of our course. You can take the trial and see if the course suits your needs.

In addition to the preparatory material, buy the Official Guides(both the Official Guide and the Verbal Review), Question Pack 1 and the 4 official mock CATs. They should be an indispensable part of your preparation.

You need close to 3 months to prepare well for the GMAT.

1. Understand the concepts and fundamentals before jumping into problem solving
2. Solve full length CATs including AWA and IR. You can get two free GMAT Prep mock CATs and can purchase two more from mba.com
3. Make sure you solve the official questions from the Official Guide

loserunderachiever · Answer

I solved it like this , 
 A=400+B -> (i)
3(B-900) = A 
Or 3B - 2700 = A --> (ii)
Now plug in the values of A in equation (ii) , 
Or 3B - B = 2700 + 400
Or 2B = 3100
Or B =1550 
I took 120 seconds , I'm sure there would be better ways than this .

Bunuel  , do these questions come in the category of Word Problems ? I'm sorry if it sounds stupid , I've started participating in your maths forum. Started with Quantitative at first.

ScottTargetTestPrep · Answer

Solution:

We can let A = Appleton's population and B = Berryville's population and create the equations:

A = B + 400

and

A = 3(B - 900)

Substituting B + 400 for A in the second equation, we have:
 
B + 400 = 3(B - 900)

B + 400 = 3B - 2700

3100 = 2B

1550 = B

Answer: A

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Appletons population is 400 greater than Berryvilles population. If

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