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Is |x+y|=|x|+|y|?

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Is |x+y|=|x|+|y|?  [#permalink]

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New post 13 Jan 2017, 01:49
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Is |x+y|=|x|+|y|?

1) xy>0
2) x<0

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Re: Is |x+y|=|x|+|y|?  [#permalink]

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New post 13 Jan 2017, 02:48
1
MathRevolution wrote:
Is |x+y|=|x|+|y|?

1) xy>0
2) x<0


From statement1:

xy>0 => x, and y will have the same sign.

Hence above result will hold true. Sufficient.

From statement2:

x < 0 , but no information about y. When y < 0 then the above statement will hold true, else not. Hence NOT sufficeint.

Answer (A).

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Re: Is |x+y|=|x|+|y|?  [#permalink]

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New post 14 Jan 2017, 11:54
Is |x+y|=|x|+|y|?

1) xy>0

It means x & y have the same sign

Let x= 1 & y=3...... |1+3|= 4 = |1|+|3|.......Answer is YES

Let x=-1 & y=-3.... |-1-3|= 4 = |-1|+|-3|.......Answer is YES

Sufficient


2) x<0

We do not know anything about y.

Insufficient

Answer: A
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Re: Is |x+y|=|x|+|y|?  [#permalink]

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New post 15 Jan 2017, 18:42
==> When you modify the original condition and the question, \(|x+y|^2=(|x|+|y|)^2?, x^2+2xy+y^2=x^2+2|xy|+y^2\)? is derived. If you delete \(x^2 y^2\) from the both equations, 2xy=2|xy|?, xy=|xy|? is derived, which becomes xy≥0?. Then, in a case of 1), it is yes and sufficient.

Answer: A
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Is |x+y|=|x|+|y|?  [#permalink]

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New post 02 Apr 2018, 07:23
MathRevolution wrote:
==> When you modify the original condition and the question, \(|x+y|^2=(|x|+|y|)^2?, x^2+2xy+y^2=x^2+2|xy|+y^2\)? is derived. If you delete \(x^2 y^2\) from the both equations, 2xy=2|xy|?, xy=|xy|? is derived, which becomes xy≥0?. Then, in a case of 1), it is yes and sufficient.

Answer: A


So, does |x+y|^2 is same as (X+Y)^2 , going by the expanded form as explained above
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Re: Is |x+y|=|x|+|y|?  [#permalink]

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New post 02 Apr 2018, 07:50
cruiseav wrote:
MathRevolution wrote:
==> When you modify the original condition and the question, \(|x+y|^2=(|x|+|y|)^2?, x^2+2xy+y^2=x^2+2|xy|+y^2\)? is derived. If you delete \(x^2 y^2\) from the both equations, 2xy=2|xy|?, xy=|xy|? is derived, which becomes xy≥0?. Then, in a case of 1), it is yes and sufficient.

Answer: A


So, does |x+y|^2 is same as (X+Y)^2 , going by the expanded form as explained above


Yes, \((|a|)^2 = a^2\) for any a.
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Re: Is |x+y|=|x|+|y|? &nbs [#permalink] 02 Apr 2018, 07:50
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