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Is |x| = y - z ? (1) x + y = z (2) x < 0

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Re: Is |x| = y - z ? (1) x + y = z (2) x < 0 [#permalink]
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Bunuel wrote:
y-z=|x|? --> y-z must be >=0...

Brilliant, thank you! :^)
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Re: Is |x| = y - z ? (1) x + y = z (2) x < 0 [#permalink]
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is |x|=y-z?

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

solving (1) first:

y=z-x
|x|=(z-x)-z
|x|=-x

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).

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

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

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

(1)+(2) Sufficient.

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.

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

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

(1)+(2) Sufficient.

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.

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.

Hope it's clear.
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Re: Is |x| = y - z ? (1) x + y = z (2) x < 0 [#permalink]
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yashrakhiani wrote:
IS |x| = y -z??

1)x+ y = z

2)x<0

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

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

St 1: x + y = z ==> Not sufficient since we do not know the signs

St 2: x<0 ==> Not sufficient since we are not told anything about z and y

Sts 1 and 2 together ==> From St 1 we see that x= z-y and from St 2 x<0 ==> z-y<0 ==> z<y ==> sufficient since it answers the question. Therefore the answer is C
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Re: Is |x| = y - z ? (1) x + y = z (2) x < 0 [#permalink]
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|x| is always positive so the question asks us is the (y-z) a positive magnitude of X.
1. Now with stm-1 y-z=-x , this could be positive value of x or negative value of x depending on the value of x. Yes and No, so Not sufficient.
2. Stm -2 X< 0, what about the remaining terms - not sufficient.

1+2, X<0 so -X>0, so (y-z)= positive x = |x|, which is always positive.

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

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

(1)+(2) Sufficient.

Bunuel KarishmaB
I solved it this way. Let me know if there are any conceptual gaps in this method:
Qs: |x| = y-z
Thus qs is : Is -x=z-y or x=y-z

St 1:
x+y=z
x=z-y
This is neither of the equations: -x=z-y or x=y-z
Not sufficient

St 2:
Clearly Insufficient

St: 1+2
x is negative. Substituting x=-x in x=z-y
-x=z-y
One of the derived question equations
Thus sufficient

I am a bit unsure about the substitution. Looking forward to your response for more clarity.
Thanks!
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Re: Is |x| = y - z ? (1) x + y = z (2) x < 0 [#permalink]
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RenB wrote:
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.

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

(1)+(2) Sufficient.

Bunuel KarishmaB
I solved it this way. Let me know if there are any conceptual gaps in this method:
Qs: |x| = y-z
Thus qs is : Is -x=z-y or x=y-z

Not Correct.
Question: Is |x| = y - z
means
Is x = y - z if x is positive or is -x = y - z if x is negative.

We use the definition of absolute values to replace |x| by some expression in x. There is no multiplication by -1 on both sides.
I suggest you to check out the absolute values section of some test prep company content.
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Re: Is |x| = y - z ? (1) x + y = z (2) x < 0 [#permalink]
We have :
Is |x| = y - z ?

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

if x >0 then inequality will be x= y-z ; if x < 0 then inequality will be x= z-y
1. x= z-y we can not say for sure if the condition hold
2. x <0 then again we can not sure for sure
combining both x < 0 then x = z-y which is what we are getting above in the inequality.
Hence C is the correct option.
Re: Is |x| = y - z ? (1) x + y = z (2) x < 0 [#permalink]
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