Data Sufficiency

benjiboo wrote:Everybody says that in order to solve two variables, you need two equations. I am confused, because is this not true here:

"A man sells oranges ("O") for $2 and grapefruits ("G") for $3. How many oranges did he sell?

1) Last week the man made a total of $5.00
2) Irrelevant for the point of this question

-Can we not conclude that O=1 and G=1?... And thus we just solved two variables with one equation?

-When does this hold true? Because, I keep getting DS questions wrong thinking that this will be some sort of trick in higher level DS questions.

Great observation. This is a common myth that will hurt students when they're solving DS questions.

That myth along with several more can be found in our free DS videos:
- https://www.gmatprepnow.com/module/gmat- ... cy?id=1106
- https://www.gmatprepnow.com/module/gmat- ... cy?id=1107

Cheers,
Brent

If you are restricted to whole numbers, then NONE of your traditional algebra rules will be reliable.
Algebraic methods don't distinguish between whole numbers and non-whole numbers -- so algebra simply won't be able to tell you when there will and won't be whole-number solutions.

If you get things like this, you'll just have to test cases, and see whether you can get more than one possibility. If you can, then "not sufficient"; if you can't -- i.e., if you can only get 1 possibility -- then "sufficient".

For instance, try solving the following:
* 5p + 7q = 47 (if p and q have to be positive integers)
* 5a + 7b = 48 (if a and b have to be positive integers)
One of these only has one solution; the other has two. (I'll leave it to you to investigate and figure out which is which.) There's no algebraic way to determine that; you just have to slog through the possibilities and see whether you can get more than one of them to work.