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# If |A| < |B|, which of the following numbers is always negative?

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Manager
Joined: 24 Jul 2009
Posts: 243
If |A| < |B|, which of the following numbers is always negative?  [#permalink]

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09 May 2010, 04:58
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Difficulty:

85% (hard)

Question Stats:

51% (02:20) correct 49% (02:17) wrong based on 764 sessions

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If |A| < |B|, which of the following numbers is always negative?

A. $$\frac{A}{B} - \frac{B}{A}$$

B. $$\frac{A - B}{A + B}$$

C. $$A^B - B^A$$

D. $$A \frac{B}{A - B}$$

E. $$\frac{B - A}{B}$$
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Joined: 02 Sep 2009
Posts: 52164
Re: If |A| < |B|, which of the following numbers is always negative?  [#permalink]

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09 May 2010, 06:23
6
3
nverma wrote:
If $$|A| \lt |B|$$ , which of the following numbers is always negative?

* $$\frac{A}{B} - \frac{B}{A}$$

* $$\frac{A - B}{A + B}$$

* $$A^B - B^A$$

* $$A \frac{B}{A - B}$$

* $$\frac{B - A}{B}$$

$$|x|<|y|$$ means there are 4 scenarios possible:

1. ------------$$0$$----$$a$$----$$b$$---, both positive;
2. -------$$a$$----$$0$$---------$$b$$---, $$b$$ positive, $$a$$ negative;
3. --$$b$$---------$$0$$----$$a$$--------, $$a$$ positive, $$b$$ negative;
4. --$$b$$----$$a$$----$$0$$-------------, both negative.

A.$$\frac{A}{B} - \frac{B}{A}$$ - is positive for scenario (2) or (3);

B. $$\frac{A - B}{A + B}$$ - is negative for all scenarios (either numerator positive, denominator negative ot vise-versa).;

C. $$A^B - B^A$$ - is positive for scenario (2), ($$a$$ negative integer, $$b$$ positive even);

D. $$A \frac{B}{A - B}$$ - is positive for scenario (4);

E. $$\frac{B - A}{B}$$ - is positive for all scenarios.

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Re: If |A| < |B|, which of the following numbers is always negative?  [#permalink]

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26 Jul 2013, 23:59
6
1
This problem in a simplest way:

|A| < |B| => A^2 < B^2

Option (B).

(A-B)/(A+B)

Multiplying by (A+B) both in the numerator and denominator we get

(A^2 - B^2)/(A+B)^2

=> Denominator is always +ve ,and we know that A^2 < B^2

Hence (B) !!
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Re: If |A| < |B|, which of the following numbers is always negative?  [#permalink]

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09 May 2010, 07:12
3
IMO B,

One quick way to solve this was.

For option A..

a/b - b/a = (a^2-b^2)/ab , here numerator is always -ve, as its given |b|>|a| thus it all depends upon a and b , thus this is not always -ve.

in B. (a-b)/(a+b) is -ve when (a-b)*(a+b) is -ve, when a^2-b^2 is -ve
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Re: If |A| < |B|, which of the following numbers is always negative?  [#permalink]

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27 Jul 2013, 09:26
Option C is always -ve in my calculation

bunnel - i took scenario 2 and it is coming -negative.. where i am going wrong..

a = -2
B = 3
then it is -ve
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Re: If |A| < |B|, which of the following numbers is always negative?  [#permalink]

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20 Sep 2014, 02:01
I have solved this by putting the test numbers considering all the scenarios which satisfy the condition |A| < |B| .

Regards
Siva
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Re: If |A| < |B|, which of the following numbers is always negative?  [#permalink]

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08 Nov 2015, 23:22
1
|A|<|B|

pick numbers: |2|<|3|

4 possibilities: 2 & 3, -2 & 3, 2 & -3, -2 & -3

we need option giving only negative in all 4 cases. If any positive, discard

A/B-B/A, second case is positive. Out

A-B/A+B, all case are negative

B
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Re: If |A| < |B|, which of the following numbers is always negative?  [#permalink]

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23 Apr 2018, 13:12
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Re: If |A| < |B|, which of the following numbers is always negative? &nbs [#permalink] 23 Apr 2018, 13:12
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