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28 Jun 2024, 00:56
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
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Question Stats:
68% (02:08) correct
32%
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based on 421
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If a^3 + b^3 > 0, which of the following must be true?
I. 1/a < -1/b
II. a^2 > b ^2
III. a > -b
A. I only
B. II only
C. III only
D. I & II only
E. I & III only
I. 1/a < -1/b
II. a^2 > b ^2
III. a > -b
A. I only
B. II only
C. III only
D. I & II only
E. I & III only
If a^3 + b^3 > 0, which of the following must be true?
I. 1/a < -1/b
II. a^2 > b ^2
III. a > -b
A. I only
B. II only
C. III only
D. I & II only
E. I & III only
Take the cube root:
Thus, III is always true.
Let's check other options:
I. 1/a < -1/b
II. a^2 > b ^2
Answer: C.
I. 1/a < -1/b
II. a^2 > b ^2
III. a > -b
A. I only
B. II only
C. III only
D. I & II only
E. I & III only
a^3 + b^3 > 0
a^3 > -b^3
a^3 > -b^3
Take the cube root:
a > -b (so a +b > 0).
Thus, III is always true.
Let's check other options:
I. 1/a < -1/b
1/a + 1/b < 0
(a + b)/(ab) < 0
We know that a + b is positive. However, ab can be positive as well as negative. For example, consider a = 2 and b = 1 AND a = 2 and b = -1.
(a + b)/(ab) < 0
We know that a + b is positive. However, ab can be positive as well as negative. For example, consider a = 2 and b = 1 AND a = 2 and b = -1.
II. a^2 > b ^2
This option is also not always true. That would imply that a is further from 0 than b is. However, from a + b > 0 (from the fact that the sum of two numbers is positive), we cannot say which one is further from 0.
Answer: C.
17 Aug 2026, 17:07
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But, shouldnt we get I also correct if we inverse the inequality III?
Bunuel
