This question is a great example of using the answer choices to our advantage.

When we check the answer choices, we see that we have a gigantic spread.
For example, 10 is 900% greater than 1, which is 900% greater than 0.1, which is 900% greater than 0.01, which is 900% greater than 0.001.

In comparison to the significant differences between each answer choice, I'm going to make some a incredibly minor changes to the values in our calculation.

\(\frac{999}{100+\frac{1}{999}} ≈ \frac{1000}{100} ≈ 10\)

Answer: A

Aside:
Changing \(999\) to \(1000\) represents a change of approximately 0.1%
Similarly, changing \(100+\frac{1}{999}\) to \(100\) represents a change of approximately 0.001%.
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Good exercise in approximation.

We can approximate the numerator to be 1000.
For the denominator, 1/999 is MUCH less than 100, so we can disregard it completely. (1/999 = 0.001001..., so 100.001 ≈ 100)
The expression now becomes 1000/100 = 10

Answer: A
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Is there a way to solve this using the (a+b)(a-b) construction? I've seen problems similar to this in the past where you used the sum of perfect squares strategy. Or is approximation the best way to solve since we don't need to solve for an exact number?

Hi All,

We're asked which of the following numbers is closest to the value of the given fraction. While it might appear that some of the answers are 'close' to one another, the reality is that each answer is 10 TIMES greater than the answer immediately below it - meaning that we can use estimation to answer this question (and avoid any step-heavy calculations).

This fraction can be rewritten as approximately 1000/100 = 10. From a logical standpoint, that's the only answer that's even remotely close - so it must be the answer.

Final Answer:

GMAT assassins aren't born, they're made,
Rich
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Since it is an approximation, we can say that \(\frac{1}{999}\) is so small (almost 0.001) that we can neglect the same.

What remains is the simple fraction of \(\frac{999}{100} = 9.99\). The closest answer is 10.


Option A

Arun Kumar
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