GMAT Official Practice Tes #6

Since we're asked what the value is *closest* to, Marty is right - we don't have to do complicated math, we can just estimate with the larger numbers.

But, for a lot of exponent questions with addition or subtraction, we can't simply add or subtract the bases, but we can FACTOR:
\(10^8-10^2\) ---> \(10^2(10^6-1)\)
and
\(10^7-10^3\) ---> \(10^3(10^4-1)\)

So, we can rewrite the problem as:
$$\frac{10^2\left(10^6-1\right)}{10^3\left(10^4-1\right)}$$

$$\frac{\left(10^6-1\right)}{10^1\left(10^4-1\right)}$$

$$\frac{10^6-1}{10^5-10}$$

Since \(10^6\) is so much greater than 1, \(10^6-1\) is effectively equal to \(10^6\) for the purposes of estimating. So, we essentially have \(\frac{10^6}{10^5-10}\) . Again, the -10 makes very little impact, so for the purposes of estimating, this is very close to \(\frac{10^6}{10^5}\), which would equal \(10^1\).

The answer is B.