yo4561 Wrote:To clarify, is this statement just discussing the problem (if 2x+y=18 and x+2y=12, what is the value of x+y)? Or, is this the general rule for combos?
Yeah, I think the Relationship & Ratio comment was specific to this example (and, others like it). But as you point out, it might be too limited to apply to every combo example.
yo4561 Wrote:Can't you use combos to solve when there is more than one variable (e.g., 2x^2+y= 18 and x^2+2y=12) or mismatching variables (x^2+y^2=12 and x^3+y=14) where you can convert them to like terms before combining? Note that my made-up examples may have been impossible to solve, but do you see what I mean? Or can you only have single variables in combos?
I'll try to make up an example based on your ideas:
What is x^2 + y ?
(1) 2x^2 + y= 18
(2) x^2 + 2y=12
The answer is (C). With either statement alone, the combo in either statement and the question do not match. But if you stack-and-add the statement equations, you get 3(x^2 + y) = 30, so the answer is x^2 + y = 10. In summary, you can't manipulate either statement alone to be like the combo in the question, but you can manipulate the statements together to make the combo in the question. Not sure whether that is what you were getting at; let me know.
yo4561 Wrote:On a related note, when you solve for combos, do you generally want the variables on the left side of the equation equal to a single numeric value or could you solve combos having the equation equal to a numeric value and one of the variables also on that side (or is it just a matter of lining everything up and order does not necessarily matter (e.g. I noticed the setup below in the quant companion and didn't know if you could perhaps move the 3w to one side)?
-x+3w=-2
2x + 3w= 12
--> What I mean is... can't you also set it up like this?
-x= -3w -2
2x= -3w + 12
The equations above are equivalent, so you CAN do that. But what you SHOULD do on Combo problems is
try to create the question combo as you manipulate the statements (or vice versa). The idea is just to minimize work. Think matching, not solving.
So on this one, where I am assuming that the equations were the two DS statements, it would depend on the question. If the question was "What is x + 6w ?" I would leave it the first way:
-x + 3w = -2
+(2x + 3w = 12)
----------------------
x + 6w = 10
And the answer would be (C). Neither statement alone matches, but together they can be made to match.
If the question was "What is -2x + 6w ?" I would also leave it the first way, because this question combo can be matched to the first equation:
-x + 3w = -2 ----> Does match the question combo, if you multiply it by 2.
2x + 3w = 12 ---> Does not match the question combo
And the answer would be (A). The first statement can be made to match but the second one can't.
If the question was "What is 3x?" I might isolate x as you did in the second setup and stack-and-subtract:
2x = -3w + 12
- (-x = -3w - 2)
----------------------
3x = 0w + 14
And the answer is (C). This one is less "combo"-like, though, as it only cares about one variable.
