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09 May 2010, 05:58
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B
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Difficulty:
75%
(hard)
Question Stats:
55% (02:19) correct
45%
(02:19)
wrong
based on 1163
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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. \(\frac{B - A}{B}\)
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. \(\frac{B - A}{B}\)
27 Jul 2013, 00:59
Kudos
Bookmarks
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) !!
|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) !!
09 May 2010, 07:23
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nverma
\(|x|<|y|\) 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.
