newdimension wrote:
I remember from school that we need as many equations as unknown variables to be able to find the values of unknowns.
I just came across a DS problem where they were able to find a value of a variable using two equations in a three variable problem.
So now I'm wondering, I know we need 3 equations to solve for 3 variables. Are there any rules of how many equations we need to find 1 or 2 out of the 3 variables?
Hello,
newdimension, and welcome to the forum. There are times in which you can look at two multivariable equations with three unknowns to solve a question asking about one of them, but a certain framework would have to be in place to allow you to answer the question. An example from a DS question I am making up on the spot:
What is the value of z?
(1) x + y + z = 22
(2) 3x = 42 - 3y
In this case, you could definitively answer the question--z = 8--whether you had substituted algebraically into the first equation or had manipulated the second to eventually read, x + y = 14 and then substituted out x + y in the first equation. You will never know what either x or y may be individually, but you can pin down how they interact when added, and that is all that matters to answer the question being asked.
I would advise you to focus on getting the fundamentals down before worrying too much about shortcuts. Always ask yourself the following:
1) What is the question asking?
2) What information do I have?
3) What is the core concept being tested?
Together, this three-step process can help you get the ball rolling on just about any problem, once your foundational knowledge is in place, or can help you understand that you can get the answer, in some cases, without doing all the work. You might call that a shortcut, but I prefer to think of it more as a way to use the test against itself. The GMAT™ tests analytical
reasoning ability, not necessarily mathematical prowess. (You can read all about the theory by following the link in the signature of any post by
Bunuel to the Ultimate GMAT Quant Megathread.)
Good luck with your studies.
- Andrew