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# Is |x+y|>|x+z|?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8011
GMAT 1: 760 Q51 V42
GPA: 3.82

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21 Mar 2018, 02:50
00:00

Difficulty:

55% (hard)

Question Stats:

52% (01:34) correct 48% (01:27) wrong based on 72 sessions

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[GMAT math practice question]

Is $$|x+y|>|x+z|?$$

$$1) y>z$$
$$2) x>0$$

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Current Student Joined: 07 Jan 2016 Posts: 1088 Location: India GMAT 1: 710 Q49 V36 Re: Is |x+y|>|x+z|? [#permalink] ### Show Tags 21 Mar 2018, 03:18 2 MathRevolution wrote: [GMAT math practice question] Is $$|x+y|>|x+z|?$$ $$1) y>z$$ $$2) x>0$$ 1) y>z we know nothing about x - insufficient 2) we know nothing about y and z - insufficient combining 1 and 2 if y and z are both positive the statement holds true if y and z are negatve the statement isn't true a clear (E) Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8011 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Is |x+y|>|x+z|? [#permalink] ### Show Tags 23 Mar 2018, 00:20 1 => Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. Since we have $$3$$ variables ($$x$$ and $$y$$) and $$0$$ equations, E is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first. Conditions 1) & 2) together: If $$x =1, y = 2$$, and $$z = 3$$, the answer is ‘yes’. If $$x = 1, y = -2$$, and $$z = -3$$, the answer is ‘no’. Since we don’t have a unique solution, both conditions together are not sufficient. Therefore, the answer is E. Answer: E In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Joined: 05 Dec 2016
Posts: 236
Concentration: Strategy, Finance
GMAT 1: 620 Q46 V29

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23 Mar 2018, 02:28
The fastest way would be to test the numbers:

(1) y>z
case 1:
x= 1
y= 2
z=-17

substituing we get:
3<16 so inequality doesn't hold true,

case 2:
x= 1
y= 15
z=2
substituting, we get:
16>3 now the inequality holds true

(2) x>0
same example as in (1) works well, so Insufficient

(1)+(2) Again, applying above example shows that it is still Insufficient

Re: Is |x+y|>|x+z|?   [#permalink] 23 Mar 2018, 02:28
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