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# m23#17

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Math Expert
Joined: 02 Sep 2009
Posts: 36549
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Kudos [?]: 93148 [0], given: 10553

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01 Aug 2012, 06:33
voodoochild wrote:
Bunuel,

If Ay + B = C and A, B and C are known, then there should be only one value of y = (C-B)/A.

1) C>B This should be sufficient because A, B and C are known. Correct? If C = 5, B = 4, A = 2, I will get a unique value of 'y'.

2) A>1 => Again,...All three variables are known. Hence, Sufficient.

I am really not able to follow the OE about #1 - Consider A= 0 and A=1..Why? A,B and C are known...I am lost.

Thanks

This question is removed from the set. So, I wouldn't worry about it.
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Kudos [?]: 889 [1] , given: 43

Quant - Linear equations with parameters [#permalink]

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01 Aug 2012, 08:16
1
KUDOS
Relevant to an old question (was M03-Q23):
m23-74149.html

Consider the the equation $$Ax=B$$, where $$A$$ and $$B$$ are given real numbers, and $$x$$ is to be found.
There are three possible scenarios:

1) $$A\neq0$$. In this case, the given equation has a unique solution given by $$\frac{B}{A}$$. Doesn't matter who is $$B$$, it can be also 0, as 0 divided by a non-zero number is 0.
2) $$A = 0$$ and $$B = 0$$. In this case, the given equation has infinitely many solutions, as for any number $$x$$, $$0 * x = 0$$.
3) If $$A = 0$$, but $$B\neq0$$, then the given equation has no solution, because $$Ax = 0 * x = 0 \neq{B}$$.

I hope the above can help when discussing any linear equation with one unknown and parameters (letters instead of numbers as coefficients).
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PhD in Applied Mathematics
Love GMAT Quant questions and running.

Quant - Linear equations with parameters   [#permalink] 01 Aug 2012, 08:16

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# m23#17

Moderator: Bunuel

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