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If a < b < 0, which of the following numbers must be positive? Indicate all such numbers
If a < b < 0, which of the following numbers must be positive? Indicate all such numbers
admin
2014-08-13
43
问题
If a < b < 0, which of the following numbers must be positive?
Indicate
all
such numbers
选项
A、a - b
B、a
2
-b
2
C、ab
D、a
2
b
E、a
2
b + ab
2
答案
B,C
解析
In this question, you are given that a < b < 0 and are asked to determine which of the answer choices must be positive. Note that the condition a < b < 0 means that a and b are negative and that a
Choice A: a - b. In the question, it is given that a
Choice B: a
2
- b
2
. Since a and b are negative, you can square both sides of the inequality a < b to get the inequality a
2
> b
2
. Then you can subtract b
2
from both sides of the inequality a
2
> b
2
to conclude that a
2
- b
2
> 0. So a
2
- b
2
must be positive. Alternatively, note that a
2
- b
2
can be factored as(a - b)(a + b). The factor a - b is, Choice A, which must be negative, and the factor a + b is the sum of two negative numbers, which also must be negative. Thus, a
2
- b
2
is the product of two negative numbers, so it must be positive.
Choice C: ab. Because a and b are negative, you can conclude that their product ab must be positive.
Choice D: a
2
b. Because a
2
b can be written as(a)(a)(b), which is the product of three negative numbers, you can conclude that a
2
b must be negative.
Choice E: a
2
b + ab
2
. By the reasoning in the explanation of Choice D, Choice E is the sum of two negative numbers. Therefore, you can conclude that a
2
2b + ab
2
must be negative.
Choices B and C must be positive, and Choices A, D, and E must be negative. The correct answer consists of Choices B and C.
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本试题收录于:
GRE QUANTITATIVE题库GRE分类
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GRE QUANTITATIVE
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