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Two variables, 1 equation, sufficiant?

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Two variables, 1 equation, sufficiant?

by benjiboo » Tue Aug 28, 2012 11:21 am
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.
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by Brent@GMATPrepNow » Tue Aug 28, 2012 1:07 pm
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
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by lunarpower » Mon May 13, 2013 4:04 am
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.
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by fcabanski » Wed May 15, 2013 10:25 am
"-Can we not conclude that O=1 and G=1?... And thus we just solved two variables with one equation? "

Those myth videos are excellent.

No, you didn't solve for two variables with one equation. You used common sense to pick numbers that worked for the unknowns. You plugged in numbers. But you would not have been able to find both unknowns (variables) using algebraic manipulation.

Plugging in numbers is a valid method for solving an equation.
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