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Re: Inequality Problem [#permalink]
01 Aug 2010, 13:15

1

This post received KUDOS

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).

(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 _________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

Re: Abs equation from GMATPrep [#permalink]
05 Oct 2012, 04:44

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.

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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Re: Abs equation from GMATPrep [#permalink]
05 Oct 2012, 05:12

Expert's post

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. 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.

Re: Abs equation from GMATPrep [#permalink]
25 Nov 2012, 17:17

1

This post received KUDOS

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|)