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Re: Is |x| = y - z ? (1) x + y = z (2) x < 0 [#permalink]

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13 Dec 2015, 11:39

DenisSh wrote:

Is |x| = y - z ?

(1) x + y = z (2) x < 0

Question: x=y-z (when x is +ve) or x=z-y (when x is -ve) (1) x=z-y, we don't know the sign of x (2) clearly not sufficient (1) + (2) from (2) we know that x<0 --> in this case |x| = y - z is equal to x=z-y and (1) gives us this expression Answer C
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Re: Is |x| = y - z ? (1) x + y = z (2) x < 0 [#permalink]

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19 Dec 2015, 13:39

Hi Bunnel- It might sound lame, but why do we need to consider 2 cases for statement 1? Why can we not simply consider x= z-y which means z>y while we are testing for whether y>equal to Z and hence statement 1 is sufficient.

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Is |x| = y - z ? (1) x + y = z (2) x < 0 [#permalink]

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20 Oct 2016, 11:29

1

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yashrakhiani wrote:

IS |x| = y -z??

1)x+ y = z

2)x<0

Answer is C.

From the question, if x>0, x = y-z if x<0, x = -(y-z) = z-y

Let's start with the easy statement - Statement 2.

(2): Insufficient x<0 doesn't give us any information about y and z. Eliminate B and D

(1): Insufficient Statement 1 says that x = z - y If x<0 , then the answer is yes since |x| will be equal to y-z if x>0, then the answer is no since |x| = z-y We have a Yes and a No. Eliminate A.

(1) and (2) together: Sufficient We have x<0 and x = z - y. hence, |x| = y-z

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I have a doubt here. if we see, if x is +ve then x=y-z and if x is -ve x+y = z.

st 1 says x+y = z , so why cant A be suff

(1) says that -x = y - z. For this case, |x| = y - z would be true ONLY IF x is negative but if x is positive, then |x| = y - z would not be true.
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Re: Is |x| = y - z ? (1) x + y = z (2) x < 0 [#permalink]

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29 Oct 2016, 01:04

per st 1, when x + y = z, this will happen when x<=0, so this st is sufficient. as when x<=0, then |x|=y-z where am i going wrong or am confusing some concept

Re: Is |x| = y - z ? (1) x + y = z (2) x < 0 [#permalink]

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08 Feb 2017, 20:52

EvaJager wrote:

sayak636 wrote:

Is |X|= Y- Z?

1. X+Y= Z 2. X< 0

(1) Can be rewritten as X = -Y + Z, so |X| = |-Y + Z|, which would be equal to Y - Z, if and only if \(-Y+Z\leq0\). Obviously, we don't know that, so (1) insufficient. (2) Cannot be sufficient, it doesn't say anything about Y and Z. (1) and (2) together: X = -Y + Z < 0, therefore |X| = Y - Z, sufficient.

Answer: C

Hello Eva,

Can you please explain how do you reach to below conclusion :

"(1) and (2) together: X = -Y + Z < 0, therefore |X| = Y - Z, sufficient."
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Re: Is |x| = y - z ? (1) x + y = z (2) x < 0 [#permalink]

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29 Jul 2017, 18:06

Bunuel wrote:

Is \(|x|=y-z\)?

Note that \(y-z\) must be \(\geq{0}\), because absolute value (in our case \(|x|\)) can not be negative.

Generally question asks whether \(y-z\geq{0}\) and whether the difference between them equals to \(|x|\).

(1) \(-x=y-z\) if \(x>0\) --> \(y-z\) is negative --> no good for us; if \(x\leq{0}\) --> \(y-z\) is positive --> good. Two possible answers not sufficient;

(2) \(x<0\) Not sufficient (we need to know value of y-z is equal or not to |x|)

(1)+(2) Sufficient.

Answer: C.

Just to make this good answer a little clearer. An absolute value cannot equal a negative value. Therefore -x=y-z. as shown in expression 1. If X>0 then we have -5 (because there is a neg sign in front so X = positive 5 but the expression is -5) = y-z. But if Y-z = -5 that means |x| = -5 which is not possible! As said above an absolute value has to equal a positive number. So if X<0 then X could be -5 and - * -5 is positive 5. So y-z = 5 and therefore together we can say that X=Y-Z

Re: Is |x| = y - z ? (1) x + y = z (2) x < 0 [#permalink]

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13 Aug 2017, 18:30

So absolute value we have x = y-z or –x = y-z . That's how you rewrite the ABS value equation. You write one equation with positive X and one with negative to cover both sides.

1) Tells us X+Y=z . It can be arranged into –x=Y-z which matches one of our absolute value formulas. However, if X is positive y-z would be negative and then Y-Z couldn’t equal the absolute value since the ABS value has to equal a non negative numbers.

2) X<0 but we know nothing about Y or Z

3) Combined now we know –(negative number) is positive therefore Y-Z must be positive = Therefore we know |x| = y - z ?

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