semidevil wrote:so I"m going over the OG 11 math, and I find myself solving the problems in my own way, rather then the from the answer key.
I do a lot of 'plugging' in, 'counting,' and just doing it in my head rather than laying out the formula going line by line.
we love you.
you should of course study raw content, but these sorts of "secondary methods" are where you're going to make the big gains.
this is EXACTLY what you should be doing.
in fact, i'm a bit extreme about this, but i believe in the "10-15 second mental shot clock", a lot like the shot clock in basketball.
if you don't think of a theory-type method within 10-15 seconds of the time you finish reading the problem, then move on to secondary methods, NOW.
never stare at problems. they don't like to be stared at, and may bite you.
in the real test, does the test try to use figures in such a way that prevents you from doing that and force you to use traditional formulas?
dear lord, no.
in fact, many of the most difficult problems on the test are, ironically,
more amenable to such backdoor solutions.
you see, each step of a problem usually admits some probability of a non-traditional solution. since harder problems are usually not only more conceptually difficult but also more complicated (i.e., have more steps), that translates into a higher probability of alternative solutions.
in fact, the
only problems i've found to have a single, orthodox method of solution are very easy problems.
For practice purposes, should I force myself in laying out formula step by step?
dear lord, no.
you should
indulge your tendency to use secondary methods. "forcing yourself to lay out formulas" is a recipe for horrible time management; it's an attitude that will make you spend too much time on solution methods that simply aren't working.
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by the way, as jim said, many of the og solutions aren't so hot.
especially in word translations, where they NEVER use ANY charts, tables, or other such devices that i consider absolutely essential for solving such problems.
do remember that gmac is
not in the business of helping you ace their own tests.
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in fact, i've gone so far as to FORMALIZE a PROBLEM SOLVING HIERARCHY that incorporates the sort of methods of which you speak, because most students rarely or never think to use such methods under the time constraints imposed on the test.
here it is.
PROBLEM SOLVING:
1. can i find a
"textbook method" to solve the problem?
- i.e., can i find an 'opener' that might be in an answer key, etc.?
IF NOT,
2. can i
"plug in numbers"?
- note that there are two kinds of "plugging in numbers" for problem solving:
(a) plugging in YOUR OWN numbers, and working through the problem in the normal direction with your numbers instead of variables (VIC style problems),
(b) plugging in the ANSWER CHOICES and working the problem backwards (used if the answer choices are numbers and there's a decently easy path "backwards" through the problem).
IF NOT,
3. can i
estimate, or perform
process of elimination in any other way?
- if the answer choices are NUMBERS and there's a decent spread - i.e., not all of the answer choices are extremely close together - then you may be able to eliminate answers based on estimation. this goes especially for geometry problems, which have DIAGRAMS and are therefore easier to estimate, but it goes for all sorts of other problems as well.
IF NOT,
4.
guess
- if you get to this point, DO NOT DELIBERATE - just guess. remember that any random guess is as good as any other random guess. if you're an extreme "deliberator", then, as weird as it may sound, you may want to have an actual method for random guessing. this could be as simple as "pick the first one of the remaining choices", but anything you can do to prevent staring at the problem is good.
DATA SUFFICIENCY:
1. can i find a
"textbook method" to solve the problem?
- i.e., can i find an 'opener' that might be in an answer key, etc.?
IF NOT,
2. can i
"plug in numbers"?
- note that NUMBER PLUGGING WORKS DIFFERENTLY FOR DATA SUFFICIENCY. with problem solving, all you have to do is plug in one set of numbers (VICs) or plug in one answer choice at a time (working backwards). with data sufficiency, though, you have to plug in MULTIPLE numbers or sets of numbers, with the goal being to TRY FOR 'INSUFFICIENT'.
in other words, you should try multiple values, with your goal being to get both a 'yes' and a 'no' (if it's a yes/no question) or two different values (if it's a value question).
if it's a number properties problem, you should make sure that you figure out the TYPES of numbers being tested, and plug in accordingly. for instance, if the problem involves absolute values, then it's likely that you'll have to plug in both positive and negative numbers.
IF NOT,
3. can i use the "easy statement", or perform
process of elimination in any other way?
- always use the "easy statement" first, if there is one, and choose the grid (ad/bce or bd/ace) accordingly.
ironically, the hardest problems commonly have one very "easy" statement out of the two (such as a statement that doesn't contain one of the relevant variables).
IF NOT,
4.
guess
- if you get to this point, DO NOT DELIBERATE - just guess. remember that any random guess is as good as any other random guess. if you're an extreme "deliberator", then, as weird as it may sound, you may want to have an actual method for random guessing. this could be as simple as "pick the first one of the remaining choices", but anything you can do to prevent staring at the problem is good.
