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I am trying a GRE question, and I have the following:

Given $a=bc$ and $c\geq 1$ and $b\neq 0$,

Answer A: $a$ > $(b+c)$

Answer B: $a$ < $(b+c)$

Answer C: $a$ = $(b+c)$

Answer D: The relationship cannot be determined from the info given.

Now, trying to reason out the problem statement, we get:

$a \geq b$ and $b+c=b+\frac{a}{b}$ which gives $b+c=b$+{some value greater than or equal to 1}

Now, my hunch is that the answer is option D, but for whatever values I try to plug in, I seem to get option B. Is there a way to say with certainty that option B is the correct answer?

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  • $\begingroup$ What about the sign of $b$? $\endgroup$ – mrs Jan 22 '14 at 11:30
  • $\begingroup$ $b$ is nonzero. $\endgroup$ – Joebevo Jan 22 '14 at 11:31
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  • If $b=2, c=4$ then $a=8$, so the first one would be right.

  • If $b=-2, c=4$ then $a<b+c$ so the second one could be right. So I think D is our choice.

Note that I makes some examples because this is a GRE-exam.

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  • $\begingroup$ See here * $\endgroup$ – mrs Jan 22 '14 at 16:08
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Take: $$b = -0.5$$ $$c = 1$$ Then : $$a = -0.5$$ In this case , $a = b + c = -0.5$ Similarly prove that for some example options $A,B$ also hold true and hence option $D$ is correct.

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  • $\begingroup$ Good points and counter-examples. +1 $\endgroup$ – mrs Jan 22 '14 at 14:26

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