GMAT Math : Small number powers

Let’s start with an example:

What is the number closest to (1.001)50?

A. 1.05

B. 1.10

C. 1.15

D. 1.09

E. 2

Readers are encouraged to take some time to give this a go!

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There is a particular approximations which can help simplify a “small number raised to n” power question.

(1 + x)n ~= (1+nx)  when -1 < x < 1

Coming to the original question:

(1.001)50 = (1 + 0.001)50 ~= 1 + 50*(0.001) = 1 + 50/1000 = 1 + 0.05 = 1.05

So we go with option (A)

Do you know what the actual value of (1.001)50 is? It is 1.05124483243

Our approximation is surprisingly close, isn’t it? J

(1 + x)n ~= (1+nx) becomes increasingly more accurate as x comes closer to 0.

Remember this nifty trick when you see small number raised to a power question in the GMAT quant and you want to move rapidly to the next question. J

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