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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) 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
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PhD in Applied Mathematics Love GMAT Quant questions and running.

take x=1, z=2, y=1 1=1-2 (no) take x=-1, z=2, y=3 |x|=y-z? |-1|=3-2=1 YES

so what solving for |x|=-x meant was that x MUST be negative for the equation to be true, if it is positive then it is not true (since in that case, |x| would not equal -x).

The question poses as x being the centerpiece variable but Bunuel turns it on its face and makes y-z the main subject. Which makes all the difference with data pt 1 when u look at it as y-z=-x. You immediately see that the right side has to be -ve for the LEft side to be +ve. Brilliant approach.

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|)

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.

Bunuel, I was wondering if we can square the sides and then evaluate:

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

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20 Oct 2016, 11:29

1

This post received KUDOS

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

-- Need 3 Kudos
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If you find this post hepful, please press +1 Kudos

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.

Bunuel, thanks for your explanation. However, I tried solving this testing cases and I feel like i proved found a case where st1&2 don't hold. Can someone help me out please?

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

Let's say x=-4, y=3, z=1

-4 +3=1

l-4l does not equal 3-1 (i.e. lxl does not equal y-z.

However, if you use -2,5,&3 then it does work. Hence, shouldn't it be E?

x=-4, y=3, z=1 does not satisfy the first statement.
_________________

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.

Hi bunuel, I am not able to understand the solution for this problem. Can you kindly explain the highlighted areas. 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.

Waiting for reply.
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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.

Hi bunuel, I am not able to understand the solution for this problem. Can you kindly explain the highlighted areas. 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.

Waiting for reply.

Look at \(|x|=y-z\): the left hand side is absolute value (|x|), which cannot be negative, hence the right hand side (y-z) also cannot be negative. Therefore must be true that \(y-z\geq{0}\).

Next, for (1) given that \(-x=y-z\). Now, if \(x>0\), or if \(x\) is positive, then we'll have that \(-positive =y-z\) --> \(negative=y-z\). But as we concluded above \(y-z\) cannot be negative, hence this scenario is not good.

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