Putting this into words, we can express it this way:

Let \(x\) by the factor of increase.

So if magnitude goes from 0 to 10, then intensity increases from 0 to 10.
If magnitude goes from 10 to 20, then intensity increases tenfold, so it goes from 10 to 100.
Magnitude increases from 20 to 30, then intensity increases from 100 to 1000.
And so on.

Following this pattern, we can say that:

\(10x => 10^x\), or that \(10x\) corresponds to \(10^x\).

Now we can solve for \(x\) in both magnitude scenarios and find their corresponding intensities:

Magnitude = 165

\(10x = 165\)
\(x = 16.5\)

Which means that:

\(10^x = 10^{16.5}\)


Magnitude = 125

\(10x = 125\)
\(x = 12.5\)

Which means that:

\(10^x = 10^{12.5}\)


Now that we have our intensities, we can compare them:

\(\frac{10^{16.5}}{10^{12.5}} = 10^4 = 10,000\)

So the answer is E

Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.