If a/|a|

Question

If \frac{a}{|a|} < a and a ≠ 0, 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.

ArunSharma12 · Answer

(A)  a>1 : all numbers > 1 satisfies the condition
(B)  a<-1 : any negative number less than -1 will not satisfy the condition
(C)  |a|>1 : this will be true for positive numbers greater than 1
(D)  \frac{a}{|a|}=1 : this is true for positive numbers
(E)  \frac{a}{|a|}=-1 : this is true for negative numbers 
Ans: B

Abhishek009 · Answer

Plug in the value of the options given, only (B) fits in perfectly as shown by  ArunSharma12

TestPrepUnlimited · Answer

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

chetan2u · Answer

The ALGEBRAIC approach... \frac{a}{|a|}a.......a(|a|-1)>0 ... Two cases.. 1) a>0, then |a|>1....a>1......A, C and D can be true.... 2) a<0, then |a|<1...But as a<0...-1

RamaSubramanian · Answer

I did this algebraically a(1/modA - 1) < 0 --> a < 0 (or) --> 1/modA < 1 ==> modA > 1 but clearly a can be greater than 1 ; where am I going wrong ; any help please, and how to learn these concepts

Bunuel · Answer

Here is an easier way to do it. If a > 0, then |a| = a, and we get a/a < a, which simplifies to 1 < a. If a < 0, then |a| = -a, and we get a/(-a) < a, which simplifies to -1 < a. Since we're considering the a < 0 range, this gives -1 < a < 0. So, if a > 0, then options A, C, and D could be true. If -1 < a < 0, then E could be true. Only B is never true. Answer: B.

If a/|a| < a and a 0, then which of the following cannot be true?

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