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Just because this is so important in so many questions: if ac = 5, and a and c are integers, there are four possibilities, not two: a and c can be 5 and 1, in either order, or they can be -5 and -1, in either order.ceilidh.erickson wrote: (2) \(a\cdot c = 5\)
If both of these are integers, it must be 1*5 or 5*1. Since we don't know which is which, though, this is insufficient.
Ian has an excellent point here! The question doesn't specify non-negative. I think this shows how we all really synthesize before we extrapolate - after reading statement 1, when I read statement 2 I immediately thought "well a=5, but I don't know that from this one alone" and didn't further pick apart what I already knew to be insufficient. But Ian's point is important - we can't assume a non-negative constraint where none is specified.Ian Stewart wrote:Just because this is so important in so many questions: if ac = 5, and a and c are integers, there are four possibilities, not two: a and c can be 5 and 1, in either order, or they can be -5 and -1, in either order.ceilidh.erickson wrote: (2) \(a\cdot c = 5\)
If both of these are integers, it must be 1*5 or 5*1. Since we don't know which is which, though, this is insufficient.
Of course, when we combine the two statements, we can discard the negative solutions, but from Statement 2 alone, we have four possible values of a.
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