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

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

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New post 09 May 2010, 05:58
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A
B
C
D
E

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

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New post 09 May 2010, 07:23
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.


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

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New post 27 Jul 2013, 00:59
6
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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New post 09 May 2010, 08:12
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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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New post 27 Jul 2013, 10:26
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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New post 20 Sep 2014, 03:01
I have solved this by putting the test numbers considering all the scenarios which satisfy the condition |A| < |B| .

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

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New post 09 Nov 2015, 00:22
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

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

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New post 23 Apr 2018, 14:12
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Re: If |A| < |B|, which of the following numbers is always negative? &nbs [#permalink] 23 Apr 2018, 14:12
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