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# Is x = |y - z|?

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Director
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Is x = |y - z|?  [#permalink]

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21 Sep 2010, 07:23
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55% (01:08) correct 45% (01:16) wrong based on 324 sessions

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Is x = |y - z|?

(1) x = y - z
(2) y > z

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Joined: 02 Sep 2009
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Is x = |y - z|?  [#permalink]

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21 Sep 2010, 07:36
rxs0005 wrote:
is x = | y - z | ?

x = y - z

y > z

Is $$x=|y-z|$$?

If $$y-z\geq{0}$$ then the question becomes is $$x=y-z$$?
If $$y-z\leq{0}$$ then the question becomes is $$x=-(y-z)$$?

Basically the question asks whether the distance between $$y$$ and $$z$$ on the number line equals to $$x$$. Note that $$x$$ as it's equal to the distance (or to the absolute value) cannot be negative.

(1) $$x=y-z$$, not sufficient, because we don't know whether $$y-z>\geq{0}$$.
(2) $$y-z>0$$ --> $$|y-z|=y-z$$, but still not sufficient as no info about $$x$$.

(1)+(2) From (1) $$x=y-z$$ and from (2) $$|y-z|=y-z$$ --> $$x=|y-z|=y-z$$. Sufficient.

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21 Sep 2010, 10:39
rxs0005 wrote:
is x = | y - z | ?

x = y - z

y > z

Since absolute value can't be negative, for x to be equal to |y - z|, x must be greater than or equal to 0.

(1) If y > z, then x is positive and x = |y - z| = y - z. However, if y < z, then x is negative and cannot be equal to the absolute value. Insufficient.

(2) This tells you nothing about x. Insufficient.

Together: Since y > z, we know that y - z > 0. Therefore |y - z| = y - z, and we know that x = y - z. Sufficient. (C).
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Is x = |y - z|?  [#permalink]

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05 Jul 2013, 10:27
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Re: Is x = |y - z|?  [#permalink]

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05 Jul 2013, 10:35
Hi,

So what you are saying is that the stem asks whether positive x (because its set to an absolute value) is = to y-z or z-y but #1 could allow for x to be a negative value? Thus making it insufficient?
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Re: Is x = |y - z|?  [#permalink]

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06 Jul 2013, 01:47
WholeLottaLove wrote:
Hi,

So what you are saying is that the stem asks whether positive x (because its set to an absolute value) is = to y-z or z-y but #1 could allow for x to be a negative value? Thus making it insufficient?

Yes. For (1) x could be negative (when y - z is negative). Now if x is negative it cannot equal to absolute value.

Hope it's clear.
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Re: Is x = |y - z|?  [#permalink]

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21 Nov 2015, 10:22
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 - z|?

(1) x = y - z
(2) y > z

|a|=a when a>=0,

There are 3 variables (x,y,z) but only 2 equations are given by the 2 conditions, so there is high chance (E) will be our answer.
If we combine the 2 equations,
from y-z>0, x=|y-z|? --> x=y-z?
this is always 'yes' so this is sufficient and the answer becomes (C).

For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.
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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Board of Directors Joined: 17 Jul 2014 Posts: 2653 Location: United States (IL) Concentration: Finance, Economics GMAT 1: 650 Q49 V30 GPA: 3.92 WE: General Management (Transportation) Re: Is x = |y - z|? [#permalink] ### Show Tags 28 Jan 2016, 20:32 y-z can be negative, in this case, x is not equal to |y-z|. 1 insufficient. 2 alone - insufficient, as nothing is specified about z. 1+2 -> we know that y-z is positive, and this is the same as |y-z|, thus both are sufficient. C Intern Joined: 23 Oct 2014 Posts: 11 Re: Is x = |y - z|? [#permalink] ### Show Tags 24 May 2016, 00:25 Hello Experts, I interpreted the question as "Is X = positive " since the abs value is always positive. Considering the above understanding I concluded that Option 1 is insufficient since we don't know the signs of z or y but I chose Option 2 (B) because it's given y>z. I substituted all combinations of positive and negative values for y and z and found that we can answer the question if X is positive. (eg: y=-1,z=-2 or y=2,z=-5 or y=3,z=2 --- for all of these I got X as positive) Kindly help me understand where is my reasoning incorrect. Thanks & Regards, Nab Math Expert Joined: 02 Sep 2009 Posts: 49968 Re: Is x = |y - z|? [#permalink] ### Show Tags 24 May 2016, 03:54 1 Nab77 wrote: Hello Experts, I interpreted the question as "Is X = positive " since the abs value is always positive. Considering the above understanding I concluded that Option 1 is insufficient since we don't know the signs of z or y but I chose Option 2 (B) because it's given y>z. I substituted all combinations of positive and negative values for y and z and found that we can answer the question if X is positive. (eg: y=-1,z=-2 or y=2,z=-5 or y=3,z=2 --- for all of these I got X as positive) Kindly help me understand where is my reasoning incorrect. Thanks & Regards, Nab The question cannot be translated as "is x positive". The question asks whether the distance between y and z on the number line equals to x. Check complete solutions above. _________________ Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6375 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Is x = |y - z|? [#permalink] ### Show Tags 25 May 2016, 03:59 There are 3 variables in the original condition (x, y, and z). In order to match the number of variables to the number of equations, we need 3 equations. Since the condition 1) and the condition 2) each has 1 equation, we lack 1 equation. There is high chance that E is the correct answer. Using both the condition 1) and the condition 2), from y-z>0, we get |y-z|=y-z. Then, the question becomes x=|y-z|?, x=y-z?. The answer is always yes and the conditions are sufficient. Therefore, the correct answer is C. Attachments variable approach's answer probability.jpg [ 219.74 KiB | Viewed 1302 times ] _________________ 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$99 for 3 month Online Course"
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Re: Is x = |y - z|?  [#permalink]

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30 Aug 2016, 02:27
Is x = |y - z|?

(1) x = y - z
(2) y > z

X has to be positive. for Is x = |y - z|?

1> we don't know if y>z or not. not sufficient.

2> we know relation between y and z but no info about X.
combined. yes
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Re: Is x = |y - z|?  [#permalink]

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