Hi All,
We're asked to choose the answer that is CLOSEST in value to (10^8-10^2)/(10^7-10^3). While you might be tempted to try lots of 'math steps', if you consider how the answer choices are written, you can use a bit of estimation and logic to get to the correct answer without doing too much math.
To start, when the answer choices are based around increased exponents, it's worth noting that those answers are NOT "close" to one another. Each of the answers here is a 'power of 10', and each answer is 10 TIMES greater than the one immediately above it.
With the numerator of the given fraction, instead of factoring, consider how 10^8 compares to (10^8 - 10^2)....
10^8 = 100,000,000
10^2 = 100
Difference = 99,999,900
100,000,000 is essentially the same as 99,999,900. Next, we can think about the denominator in the same terms...
10^7 = 10,000,000
10^3 = 1,000
Difference = 9,999,000
This means that 10,000,000 is essentially the same as 9,999,999...
Thus, we're essentially just asked to divide 10 million by 1 million... and that equals 10.
Final Answer:
GMAT assassins aren't born, they're made,
Rich