Smart Numbers

[AdrianaH256]

Hi Stacey,

How do we know when it is a good idea to use "Smart Numbers". I've noticed that some of your solutions use smart numbers to "guess and check" certain possibilities or answer solutions.

I have a hard time adapting to this strategy - I am an engineering student, and the professors at my school constantly emphasize "solving for the most general case using variables". Therefore, no matter how complicated the variables may become, my first instinct is always to solve problems using a set of variables. However, there are definitely times when this takes me longer than 2 min/question. While finding an answer in terms of variables is definitely the most complete way to solve any math problem, I know it is not always necessary when the goal is to pick from list of A-E answers.

[RonPurewal]

hi,
fyi, stacey hasn't posted in this folder for several years. she moderates only the General Questions folder.

I have a hard time adapting to this strategy - I am an engineering student, and the professors at my school constantly emphasize "solving for the most general case using variables"

what you're basically saying here is 'other people tell me to do something, so i do it'—which is THE WORST possible mentality with which to take this exam.
the whole point of this exam is that the problems are unpredictable, so that you need mental flexibility to do well on it.

[RonPurewal]

no matter how complicated the variables may become, my first instinct is always to solve problems using a set of variables

here you need to use your everyday common sense, along with some basic observations about how this test works.

by 'basic observations' i mean, essentially, that NO problem on this exam should be 'labor-intensive'. if you've done more than five or six distinct steps, you're probably doing something wrong.

with that in mind, you just need to make VERY HONEST assessments of 'is this actually going somewhere?' as you go. if the answer is 'no' then IMMEDIATELY stop what you're doing and try another strategy.

--

we all have certain instincts. that's fine, as a FIRST reaction... but the point is that (as in real life) you need to change up your strategy if it's maladaptive in any given situation.

analogy:
i'm a sprinter.
if someone challenges me to a race, my instinct is to run as fast as i possibly can.

on the other hand, if i discover that the race is 2 miles long, then this would be a pretty silly thing to do, now, wouldn't it?
(:
(...and if i started running before discovering this, then, well, i'd slow down!)

[RonPurewal]

...and, perhaps most importantly, this:

there are definitely times when this takes me longer than 2 min/question

...?
why would this be a bad thing?

'2 minutes' is an AVERAGE.
if you're an engineering student, then of course you know how averages work. some data lie above the average, others below it.
most probably, LOTS of problems will take longer than two minutes. so what? that's the nature of averages.
there will also be problems that take less than 1 minute.

'time management' consists of exactly two things:
1/ BE VERY HONEST about 'is this going anywhere?',
2/ STOP WHAT YOU'RE DOING if the answer is 'no'.
that's it. that's the whole thing.
time management has NOTHING to do with minutes and seconds. in fact, if you have good time-management skills, you should NEVER have to look at a timer (although you may do so once or twice per section just for psychological reassurance).

i wrote about this here:
mgmat-advance-quant-book-doubt-t32280.html#p116804