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# |x| + |y| > |x + z|

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Founder
Joined: 18 Apr 2015
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|x| + |y| > |x + z| [#permalink]  09 Aug 2018, 03:46
1
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Expert's post
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Question Stats:

75% (00:46) correct 24% (00:49) wrong based on 117 sessions
$$|x| + |y| > |x + z|$$

 Quantity A Quantity B y z

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.

Kudos for R.A.E
[Reveal] Spoiler: OA

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Manager
Joined: 06 Jun 2018
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Kudos [?]: 80 [1] , given: 0

Re: |x| + |y| > |x + z| [#permalink]  09 Aug 2018, 15:34
1
KUDOS
Carcass wrote:
$$|x| + |y| > |x + z|$$

 Quantity A Quantity B y z

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.

Kudos for R.A.E

General formula : $$|a| + |b| \geq|a+b|$$

In this case we don't know anything about z. Given datum is not sufficient.

Intern
Joined: 10 Oct 2017
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Kudos [?]: 4 [0], given: 0

Re: |x| + |y| > |x + z| [#permalink]  24 Sep 2018, 03:05
General formula : |a|+|b|≥|a+b|
is this a formula for every value we put in? thanks
Intern
Joined: 20 Feb 2020
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Re: |x| + |y| > |x + z| [#permalink]  24 Feb 2020, 09:59
fixzion wrote:
General formula : |a|+|b|≥|a+b|
is this a formula for every value we put in? thanks

Yes, and the two sides are equal only if a and b are both non negatives, Otherwise, if ab<0 then |a|+|b|>|a+b|
Intern
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Re: |x| + |y| > |x + z| [#permalink]  18 Sep 2020, 02:11
In case someone is not aware of the property, they can do this:

Take x = 0,

Then you have |y| > |z|

Now its clearly seen, y can be lesser and greater than z, since only the absolute of y is greater than z.
Re: |x| + |y| > |x + z|   [#permalink] 18 Sep 2020, 02:11
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