A certain college has a student-to-teacher ratio of 11 to 1.

Hi obs, if you're intent on solving the question through ratios, then you can, but it's not necessarily the best approach. That being said, let's attack it as a ratio problem.

Firstly, there's a slight typo in how you copied the math, it's actually \(26t = 3,380\). You can then figure out that whatever t is, if you multiply it by 11 you'll get the number of students. So yes \(\frac{s}{11}=\frac{t}{1}\), and you already have \(26t = 3,380\) so \(t= \frac{3,380}{26}\). Now solve t for 130, and then \(11t=s\). s is 1430.


A sneakier way to solve this:

The GMAT will always try and trap you, so if it asks for the number of students (s), the number of teachers (t) will also be a trap answer somewhere on the list. If you recognize this, then all you have to do is look for the two answer choices that are 11 away from one another. The bigger one will be the answer and the smaller will be the trap. This kind of "fourth wall" shortcut isn't for everyone, but it can be very helpful when crunched for time or unsure about the math.

Hope this helps!
-Ron