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[jmuduke08]

mods please delete. ty

[jnelson0612]

If a town of 25,000 people is growing at a rate of approx. 1% per year, the population of the town in 5 years will be closest to?

OA: C) 28,000

Can anyone help me to do this in under two minutes? I understand 25,0000 (1.05)^5 but that still seems to take me too long to do in my mind. Thanks in advance!

Hi,
Happy to help, but is the town growing at a rate of 1% or 5% per year? Thanks!

[jmuduke08]

It is 1% per year. I know the general formula of 25,000(1.01)^5, but just wondering if there was a quicker way to do this problem.

[tim]

ah, that's a little easier! :) with a number SUPER close to 1 (such as 1.01), you can basically just multiply the percentage by the number of years to get (1.01)^5 is approximately equal to 1.05. of course, this gives us an answer that is nowhere near 28000. can you give us the source of this problem so we can figure out what's wrong?

[crusade]

Hi Tim,

Could you please explain how you got 1.01^5=1.05?

I got stuck at trying to solve 1.01^5 -- is there a quick way to solve indices like these?

Thanks

[tim]

I guess what I was trying to say was THAT'S the trick: 1.01^5 is about 1.05. Sounds like you're asking for a derivation though, which I'm happy to provide because it's fun. :) A warning though: the HOW of this is pretty complicated, and you do NOT have to know this to apply the trick. As such, please do not expect me or any other instructor to explain the derivation any further, as it is for informational purposes only and as far as the GMAT is concerned you will only need to know WHAT the trick is, not HOW it works.



WHAT the trick is (you need to know this):

If x is tiny, (1+x)^y is approximately 1+xy



HOW it works (not for the faint of heart):

By the Binomial Theorem, (1+x)^y = yC0*1 + yC1*x + yC2*x^2 + yC3*x^3 + ... + yCy*x^y. The first two terms are 1+xy. Now for sufficiently small x, all remaining terms are negligible. As an example, if x = .01 and y = 5 as in the original problem, the first two terms give you the 1.05 approximation, and the third term only adds 10*1/10000, or .001.