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# xy < 0

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xy < 0 [#permalink]  09 Aug 2017, 15:30
Expert's post
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Question Stats:

79% (00:26) correct 20% (00:39) wrong based on 67 sessions

$$xy < 0$$

 Quantity A Quantity B | x + y | |x| + |y|

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: xy < 0 [#permalink]  16 Oct 2017, 00:05
This is the so called triangular inequality which states that $$|x+y|\leq|x|+|y|$$. Thus, the answer is B or C.

Since xy < 0 it must be that either x or y are negative. Thus, in this case it is impossible to have an equality for whatever number we fit in the equation. E.g. x = 1, y = -2; then, $$|1-2|\leq|1|+|-2|$$ which becomes $$1<3$$.

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Re: xy < 0 [#permalink]  07 Feb 2018, 00:55
1
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xy<0, in here when x is negative, y will be positive. When x is positive, y will be negative.
Q.A | x + y |
Q.B |x| + |y|
Q.B will be greater because it sums up two positive numbers.
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Re: xy < 0 [#permalink]  07 Feb 2018, 01:44
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Re: xy < 0 [#permalink]  17 Feb 2018, 01:18
It's not a hard question.

Simply, the product of two numbers is negative, so one must be negative and other one must be positive.
Therefore, combined mode will always be less than the sum of individual modes.

Choice B correct.
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Re: xy < 0 [#permalink]  17 Feb 2018, 16:04
IlCreatore wrote:
This is the so called triangular inequality which states that $$|x+y|\leq|x|+|y|$$. Thus, the answer is B or C.

Since xy < 0 it must be that either x or y are negative. Thus, in this case it is impossible to have an equality for whatever number we fit in the equation. E.g. x = 1, y = -2; then, $$|1-2|\leq|1|+|-2|$$ which becomes $$1<3$$.

never heard of this inequality, where have you seen in featured before?
Re: xy < 0   [#permalink] 17 Feb 2018, 16:04
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