Ravixxx wrote:
If \(\frac{a}{|a|}\) < a and a≠o, then which of the following cannot be true?
(A) \(a>1\)
(B) \(a<-1\)
(C) \(|a|>1\)
(D) \(\frac{a}{|a|}=1\)
(E) \(\frac{a}{|a|}=-1\)
Source: Ready4Gmat.
If a > 0, then \(\frac{a}{|a|} = 1\) and we would be given \(1 < a\), therefore \(a > 1\) describes all the positive solutions.
If a < 0, then \(\frac{a}{|a|} = -1\) and we would be given \(-1 < a\). Therefore \(-1 < a < 0\) is the only region for negative a's.
Then note the question is asking for "which of the following CANNOT BE TRUE", we have to find a region that has absolutely no solutions.
(A) \(a>1\), this is the solution for positive a's.
(B) \(a<-1\), we don't have any solution that satisfies this so this is our answer.
(C) \(|a|>1\), when a is positive we can satisfy this.
D and E refer to the case "a is positive" and "a is negative", there are solutions for both cases.
Ans: B
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