Whoa - careful!
10^8 - 10^2 is NOT 10^6. It's actually almost exactly 10^8. If you expand them you'll see:
10^8 = 100,000,000
10^2 = 100
If you subtract the two, you're not subtracting very much at all. The same goes for 10^7 - 10^3 which is NOT 10^4
10^7 = 10,000,000
10^4 = 1,000
Again, if you subtract the two, you don't end up very far at all from 10^7.
So....
For this one you can simply estimate, given the knowledge that the magnitude of the larger exponents renders the smaller ones insignificant (the answer choices all differ by a factor of 10), and get:
10^8 / 10^7 = 10
OR, you can factor the numerator and denominator to get even closer to a quick estimate:
10^8 - 10^2 = 10^2 * (10^6 - 1)
10^7 - 10^3 = 10^3 * (10^4 - 1)
Then divide those two. 10^2 / 10^ 3 gives you 1/10
And (10^6 - 1) / (10^4 - 1) is a pretty easy estimate to 10^2.
So with 10^2 / 10 you'd get to 10.
The biggest key here is to recognize the order of magnitude for exponents. 10^8 and 10^7 are so large that 10^2 and 10^3 really don't matter at all in comparison.
Brian Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep
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