One equation,...two variables??

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One equation,...two variables?? [#permalink]

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10 Sep 2009, 09:08

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I curious,... I thought that in order to solve an equation (or in the case of a D.S. question - in order to know if one possibility is "SUFF"), that an equation must have only one variable.

In other words, if we are given the equation:

2a + 5b = 20

then we can't solve it without any other info. But if we try to simplify it down to finding "a" then we get:

2a = 20 - 5b or a = 10 - (5/2)b

If we try to plug in the equation again we get:

2[10 - (5/2)b] + 5b = 20 or 20 - 5b + 5b = 20 or

20 = 20

which leaves us with nothing.

But if a question has two equations, then we could use this plug-n-play approach to find the variables.

So, after trying to tackle the attached Kaplan D.S. question, I'm left wondering..... In both possibilities, it states that there is one equation, two variables but the first possibility states that we move to the second and then, all of a sudden, it's possible to solve one equation, two variables ??

What's going on here?

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Re: One equation,...two variables?? [#permalink]

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10 Sep 2009, 10:08

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Expert's post

Hi Stilite,

You're slightly misremembering the rule, though it's understandable as the distinction is subtle.. The rule is that in order to solve for all variables in a system of equations, we need at least as many equations as we have variables. It is mathematically impossible for a single equation to give us values for both a and b. However, since we only need the value of one variable in this problem, b, it is possible for a single equation to give us a solution; we just need an equation where we can get rid of all the A's.

In this case, because we have +a on both sides, the a's cancel out--leaving us with a single variable equation with nothing but b's and numbers. This is a common trap in DS questions. Keep your eyes peeled for variables that aren't really there!
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Eli Meyer
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Re: One equation,...two variables?? [#permalink]

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11 Sep 2009, 07:52

KapTeacherEli wrote:

Probably the best/clearest response I've ever received. Many thanks for that!