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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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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) $$\frac{a}{|a|}=-1$$

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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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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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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) $$\frac{a}{|a|}=-1$$

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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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) $$\frac{a}{|a|}=-1$$

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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16 Apr 2020, 18:24
By taking values we get B
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Joined: 02 Aug 2009
Posts: 8738
Re: If a/|a| < a and a≠o, then which of the following cannot be true?  [#permalink]

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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) $$\frac{a}{|a|}=-1$$

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