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Population Question

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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Population Question

by milanproda » Mon Dec 20, 2010 4:45 am
Hello, I am having trouble with this population question:

The population of Country S is 10 million people less than the population of country J. If in 5 years, Country J has twice as many people as country S, how many people will live in Country S in three years given that each country has a constant population growth of .5 million people per year?

A-6

B- 7.5

C-9 (CORRECT)

D-10.5

E-12

Thanks!
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by Geva@EconomistGMAT » Mon Dec 20, 2010 7:54 am
The main sticky point for this question is remembering that time passes for both countries. If each country has a .5 pop growth per year constant, then 5 years from now they would both have 5*.5 = 2.5 million people more than they currently have.
Thus, the following two equations can be formed:
S is 10 million people less than J:
(1) S = J-10
in 5 years, j will be twice as S:
(2) J +2.5 = 2(S+2.5)

and then solved by adding the two equations together, left side to left side, right to right:

S+J+2.5 = J-10+2(S+2.5)
Js cancel out to get:
S+2.5 = 2S - 5
7.5 = S

Two problems with this approach:
1) possible mistakes in forming the equations (accidentally interpreting the first one as S-10=J, for example)
2) By the time you have finished solving the equations, you will simply choose B, and forget to notice that the question actually asked how many people will live in country S in three years - which is equal to 7.5+3*.5 = 9.
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by Geva@EconomistGMAT » Mon Dec 20, 2010 8:28 am
continued:
The great room for error is why I'd actually prefer the second approach: Plug in the answer choices back into the question.

The question asks for the number of people in S in 3 years. Let's assume that C is the right answer, meaning that in 3 years' time, S will have 9 million people. Take this a few steps further and see if everything checks out:
If in 3 years time S will have 9 million, then S now has 7.5 million. We know that S is 10 million less than J, so J now has 17.5 million people.

How do we know if this answer is correct? the last sentence says that in 5 years time, J should have twice as many people as S. Take the entire problem 5 years into the future:
S now has 7.5 million, so in 5 years S will have 10 million.
J now has 17.5 million, so in 5 years J will have 20 million.
Since 20 million is twice as many as 10 million, everything checks out and the answer is C.

Doing the same for the other answer choices will yield some problem with the "twice times rule", proving that they are not the right answer choice. Of course, if you begin with c as you should and find that c is the right answer, there's no need to repeat the process with the other answer choices.
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by milanproda » Mon Dec 20, 2010 1:29 pm
Geva,

Thank you very much for the reply!

I found this question to be very tricky. I kept getting answers like J is equal to 5 or S is equal to 10. I also did not structure the problem out correctly. Furthermore, the question is extra tricky because you have to remember to add those extra 2.5 million, because the 7.5 is the present.

The second approach was remarkably simple! However I am not sure if I will have the time to work through each answer question on the GMAT to find the correct choice.

Thank you again!
Milan Prodanovic
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