PWN the SAT Q&A

This one is brutal. I’d say the easiest way to do it is to plug in, but you’ve gotta be a bit clever about how you do so, because of the way the question is set up. 

Since the question tells you that all of the answer choices except one are equivalent, scan them all for two that look IMMEDIATELY equivalent. See how (C) and (D) are the same exact choices, only flipped? Those both have to be equivalent, so choose the numbers you’ll plug in based on them.

Let’s say a = 2, c = 4, f = 10, and b = 5. Those numbers work in (C) and (D) of course. Let’s see which other choices they work in:

(A) 2/10 = 4/5 NO
(B) 10/4 = 5/2 YES
(E) (2x10)/(5x4) = 1/1 YES

So (A) is the only one that doesn’t work. That’s your answer.

(Of course, there’s always an algebraic solution, too. You can manipulate all of these to be the same except (A).)

The one last brutal thing about this question is that they made (A) the answer. That means, if you started by plugging in values that work in (A), nothing else will work for you. Logically, that means (A) must be the answer, but seeing that under time pressure requires more mental energy, I think, than plugging in based on (C) and (D), which are clearly equivalent.