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

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If a/|a| < a and a≠o, then which of the following cannot be true?  [#permalink]

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New post 15 Apr 2020, 23:08
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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.
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Re: If a/|a| < a and a≠o, then which of the following cannot be true?  [#permalink]

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New post 15 Apr 2020, 23:19
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) \(\frac{a}{|a|}=-1\)



    (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
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Re: If a/|a| < a and a≠o, then which of the following cannot be true?  [#permalink]

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New post 16 Apr 2020, 07:34
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.

Plug in the value of the options given, only (B) fits in perfectly as shown by ArunSharma12
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If a/|a| < a and a≠o, then which of the following cannot be true?  [#permalink]

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New post 16 Apr 2020, 09:26
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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Re: If a/|a| < a and a≠o, then which of the following cannot be true?  [#permalink]

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New post 16 Apr 2020, 18:24
By taking values we get B
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Re: If a/|a| < a and a≠o, then which of the following cannot be true?  [#permalink]

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New post 16 Apr 2020, 20:44
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.



The ALGEBRAIC approach...
\(\frac{a}{|a|}<a........|a|a>a.......a(|a|-1)>0\)...
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<a<0, so B cannot be true and E can be true

B
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Re: If a/|a| < a and a≠o, then which of the following cannot be true?   [#permalink] 16 Apr 2020, 20:44

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

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