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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