Problem Solving

Matt@VeritasPrep wrote:301*201*201 - 300*200*200
= (300 + 1)(201)(201) - (300)(200)(200)
= (300)(201)(201) + (1)(201)(201) - (300)(200)(200)
= 300(201*201 - 200*200) + 201*201
= 300(201+200)(201-200) + 201*201
= 300(401) + 201*201
= 300(400+1) + (200+1)(200+1)
= 120000 + 300 + 40000 + 400 + 1
= 160701

^^ This is ... impressive. (I certainly wouldn't think of these steps, even if I had 2 hours for this one problem.)

The problem with putting forward too many approaches like this one, though, is that they discourage students from simply "getting out the shovel and digging".
These steps are VERY non-obvious, and, in my experience, it's not very likely that someone will think of them in real time, especially on a high-pressure exam. (More importantly, anyone who can execute these steps fast enough on the test won't have any reason to look at this thread in the first place.)

I've seen this a lot with tutoring students. After seeing enough "elegant" / "cute" / "clever" solutions like this one, they become reluctant to just do the work. They won't just multiply the numbers, or do long division, or whatever, because they become singularly obsessed with finding "tricky" ways to solve the problems instead.
Which is great if you can think of such tricks ... but not if you can't.

So, again, I think this solution is really cool. No way I'd ever come up with it myself, not in a million zillion years. But I think we'd be remiss to post it without something like "... if you don't immediately think of this, just pick up the shovel and start digging".
Multiplying out 300*300*200 is trivial, so "get the shovel out and dig" just boils down to multiplying out 301*301*201. That's not even a lot of digging.

ngalinh wrote:Fair enough. I see the world of people who were traditional-great-students is very different from the world of mediocre students (like mine). They can approach a problem from many elegant doors as quickly as from normal doors.

In my case, it's more like "I give up easily."
o_O

... but, seriously, that's what it is. I'm a very lazy person with this kind of work (though not with, say, training dogs or working out). In any sort of testing environment, if something is not working right away, I just quit.
Perhaps ironically, that right there is 99% of the basis for ideal time management on the GMAT.

When you're lazy and you quit easily, you start finding lots of "doors".