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Is |x - y| > |x| - |y|? (1) y < x (2) xy < 0

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nick1816
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Re: Is |x - y| > |x| - |y|? (1) y < x (2) xy < 0 [#permalink] New post   13 Mar 2020, 14:57
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|x - y| > |x| - |y|

Above inequality will be true when xy<0. As in LHS, absolute values of x and y will add up, while in RHS absolute values of x and y will get subtracted.

Also,inequality will be true, when xy>0 and |x|<|y|, As LHS will be positive, but RHS will be negative.

Statement 1- y<x

if x<0 and y<0, |y|>|x| (inequality holds)
if x>0 and y>0, |y|<|x| (inequality won't hold)

Statement 2- xy<0
Inequality holds (As explained above)


study wrote:
Is |x - y| > |x| - |y|?

(1) y < x
(2) xy < 0


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3_DS_Absolute_B.JPG
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anwesharath
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Re: Is |x - y| > |x| - |y|? (1) y < x (2) xy < 0 [#permalink] New post   19 Jul 2021, 18:46
Can anybody suggest what should be the method of solving absolute value inequalities? I seem to be struggling with such kind of questions.
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Bunuel
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Re: Is |x - y| > |x| - |y|? (1) y < x (2) xy < 0 [#permalink] New post   20 Jul 2021, 00:46
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anwesharath wrote:
Can anybody suggest what should be the method of solving absolute value inequalities? I seem to be struggling with such kind of questions.


10. Absolute Value



For more check Ultimate GMAT Quantitative Megathread



Hope it helps.
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Re: Is |x - y| > |x| - |y|? (1) y < x (2) xy < 0 [#permalink] New post   20 Jul 2021, 00:54
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Bunuel wrote:
anwesharath wrote:
Can anybody suggest what should be the method of solving absolute value inequalities? I seem to be struggling with such kind of questions.


10. Absolute Value



For more check Ultimate GMAT Quantitative Megathread



Hope it helps.


This is extremely helpful! Thank you so much :)
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Re: Is |x - y| > |x| - |y|? (1) y < x (2) xy < 0 [#permalink] New post   06 Nov 2021, 23:54
I think this approach is wrong. Reasons
1) What is the reason behind assuming |x| > |y| please ? This ssumption will only
remove a scenario in which |y| can be greater than |x|. How can that be accounted for in this method please ?
2) How would a student know to make this (incorrect) under the 2 minute time pressure that GMAT Quant imposes ?




MathRevolution wrote:
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Is |x - y| > |x| - |y|?

(1) y < x
(2) xy < 0

If we modify the original condition,
if |x|>=|y|,
|x-y|>|x|-|y|>=0, so we can square both sides, which gives us (|x-y|)^2>(|x|-|y|)^2, and (x-y)^2>(|x|-|y|)^2
This becomes x^2+y^2-2xy>x^2+y^2-2|xy|, and if we simplify the inequality, -2xy>-2|xy|, and we ultimately want to know whether xy<0. This makes condition 2 sufficient.
if |x|<|y|, then |x|-|y|<0,
so |x-y|>|x|-|y| always work. Hence we do not need to deal with this, so the answer becomes (B).

Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.
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Re: Is |x - y| > |x| - |y|? (1) y < x (2) xy < 0 [#permalink] New post   18 Nov 2021, 04:40
|x-y|^2 > {|x|-|y|}^2
x2 + y2 - 2xy > x2 + y2 - 2 |x||y|
=> xy < |x||y|

Only case when xy < |x||y| is when x is -ve and y is +ve or x is +ve and y is -ve

Hence, xy < 0

Also, y < x cant be deduced from xy < |x||y|

Can anyone please tell me whether this approach is correct or not?
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Re: Is |x - y| > |x| - |y|? (1) y < x (2) xy < 0 [#permalink] New post   14 Dec 2021, 05:46
GMATGuruNY wrote:
Quote:
Is |x-y| > |x| - |y| ?
1) y < x
2) xy < 0


|x|= the distance between x and 0 = the RED segment on the number lines below.
|y| = the distance between y and 0 = the BLUE segment on the number lines below.
|x-y| = the distance BETWEEN X AND Y.

Statement 1: y < x
Case 1:
[edq435/absolute_number_line_1.jpg[/img][/url]
|x| - |y| = RED - BLUE.
|x-y| = RED - BLUE.
Thus, |x-y| = |x| - |y|.

Case 2:
[mber_line_2.jpg[/img][/url]
|x| - |y| = RED - BLUE.
|x-y| = RED + BLUE.
Thus, |x-y| > |x| - |y|.
INSUFFICIENT.

Statement 2: xy < 0
Since x and y have different signs, they are on OPPOSITE SIDES OF 0.e_3.jpg[/img][/url]
In each case:
|x| - |y| = RED - BLUE.
|x-y| = RED + BLUE.
Thus, |x-y| > |x| - |y|.
SUFFICIENT.

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kudos for this perfect graphic solution. Exact way the asian teachers taught us at school.
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Re: Is |x - y| > |x| - |y|? (1) y < x (2) xy < 0 [#permalink] New post   21 May 2022, 11:03
GMATNinja, could you please advice what standard method is worthwhile to remember to solve this type of question? What should be the first step to solve this type of questions?
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Re: Is |x - y| > |x| - |y|? (1) y < x (2) xy < 0 [#permalink] New post   25 May 2023, 01:30
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Re: Is |x - y| > |x| - |y|? (1) y < x (2) xy < 0 [#permalink]
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