Exponent Simplification Troubles

[JamilA33]

I seem to be having issues with solving certain exponent problems within the 2 minute timeframe. This problem showed on a MGMAT CAT. I ended up cutting my losses and only spent 1:51. I've come across similar problems and would get them right but would spend between 2:45 - 3:00 minutes. Are there any techniques I could utilize to solve faster? Or should I cut my losses and move on if I determine it'll take me too long?

(6.804)^6 * (1.701)^ - 13
-----------------------------------
2^19 * (3.402)^ -7

The correct answer is 1.

[Chelsey Cooley]

First of all, sincere congrats on cutting your losses right before the two-minute mark. It's so easy to say "I know that I've almost spent two minutes, but I feel like if I just had another 15 seconds, I could totally get this one" - and we all know what happens next, you look up at the four minute mark and realize that the GMAT just played you for a fool.

This particular problem is a fantastic illustration of why you should spend more time reading quant problems than you probably think you should. Even if the problem isn't a word problem, slowing down your reading process will speed you up on average. Let's spend some time looking at that problem with a critical eye – the first thing you notice that it's an exponent problem, but then, take a look at those bizarre numbers. The GMAT very often gives you weird numbers in a problem for a very specific reason, and figuring out that reason as you read the problem is part of solving it. In this case, 1.701, 3.402, and 6.804 are all multiples of 1.701!

(Exercise for the reader: how would you get yourself to notice that fact quickly? What would you have to be looking for?)

The savvy test-taker sees that, and deviates slightly from their standard 'solving an exponent problem' approach to focus on using the information they've just figured out. How? Well, if 6.804 is just a multiple of 1.701, write it like that:

(4*1.701)^6 * (1.701)^ - 13
-----------------------------------
2^19 * (2*1.701)^ -7

Working it out from there using the exponent rules, step-by-step, will suddenly be a lot faster because a lot of terms will combine together or cancel out. The trick is noticing the special information in the problem on your first read through, instead of waiting until you've exhausted your regular approach and are giving up. And the first step to doing that is reading the problem like a detective, not like someone browsing a magazine.

On solving exponent problems fast in general: Exponent problems really lend themselves to drill sets. Sometimes you're not slow for a strategy reason - you're just slow because you need to work faster! You want to use the right rule automatically and do it correctly every single time. There are a few good sources for exponent drills in our materials (the Algebra strategy guide, etc.) and you can also find some online with a bit of searching. If you know all of the rules, and you can solve problems correctly very consistently, but you're just taking too long to do the math, then targeted, repetitive practice might be just the thing.

[Chelsey Cooley]

And as for your other question - yes, you absolutely should cut your losses wherever you can. In many situations, spending a very long time on a problem and getting it right can be worse than getting the same problem wrong quickly. 'Cut your losses' even when you're practicing, to reinforce the habit (the difference, of course, is that when you're just practicing you can always come back to the problem to spend more time on it later.)

[RonPurewal]

also, there's nothing particularly bad about spending 2:45-3:00 on a problem in the first place.

remember—'two minutes per problem' is an AVERAGE. even if you're doing amazingly well, you'll probably go over that amount just as often as you go under it; that's the nature of averages.