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# modulus gmat prep

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modulus gmat prep [#permalink]

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13 Sep 2008, 01:07
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why is the ans wrong??
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Re: modulus gmat prep [#permalink]

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13 Sep 2008, 07:30
i think its b...

if y is postive, x and z are both negative. but x>z
so let's say x=-1 and z=-4

l -1-(-5)l + l-1l= lzl
l4l + l-1l= l-5l
4+1=5
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Re: modulus gmat prep [#permalink]

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13 Sep 2008, 10:17
arjtryarjtry wrote:
why is the ans wrong??

why YOUR ans is wrong??

because statement 2 states that y < 0, which must mean that x and z must be negative, and x is closer to zero on the number line. The statement 2 is enough to answer the question.
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Re: modulus gmat prep [#permalink]

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14 Sep 2008, 00:27
Youngd8 wrote:
i think its b...

if y is postive, x and z are both negative. but x>z
so let's say x=-1 and z=-4

l -1-(-5)l + l-1l= lzl
l4l + l-1l= l-5l
4+1=5

(1) x>z means x can be +ve or -ve or z can be +ve or -ve or y can be +ve or -ve hence cannot answer

(2) y>0 says x>z and x<0,z<0 hence answers SUFFI
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Re: modulus gmat prep [#permalink]

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14 Sep 2008, 01:42
zy <xy<0 ==> y(z-x)<0
1. insuff.
2. y>0 ==> z-x<0 ==> z<x<0
|z-x| +|x| =|z| <==> x-z -x =-z <==> x-z=x-z SUFF
Answer should be B.
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Re: modulus gmat prep [#permalink]

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14 Sep 2008, 22:55
For modulus related questions, number line helps me answer.

In stmt 2, y > 0. and zy < xy < 0. that means both z and x are negative and z < x. The number line will look like
Z---------X-------0------Y

Now, the question really asks if the sum of positive distance between Z and X as well as between X and 0 is equal to the positive distance between Z and 0......and stmt 2 helps answer this.
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Re: modulus gmat prep [#permalink]

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25 Mar 2009, 05:26
The basic condition for the equation |x-z| + |x| = |z| to be true is that
|z| > |x|

The inequality zy < xy < 0
further implies that |z| > |x| where the y value could be both +/ - respectively to maintain the inequality. (I hope I don't need to elaborate this part)

So considering the answers:

1. z < x (if it is considered with the inequality both z and x are negative and that y is positive.) so proves |z| > |x|, hence true.
2. y < 0 (when fit into the inequality proves that again |z| > |x|) so true.

Answer most definitely is D.

Please feel free to discuss this!
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Re: modulus gmat prep [#permalink]

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25 Mar 2009, 07:33
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This is one of the strangest questions in GMATPrep, since you don't need either of the statements to answer the question. That's not supposed to happen on a GMAT DS question, which makes me wonder whether there was an error in the question design. In any case, we're given:

zy < xy < 0

Rewrite this as three inequalities:

(1) xy < 0
(2) zy < 0
(3) zy < xy

From (1), we have two possibilities:

(A) x is positive, and y is negative. Then, from (2), z is positive, and from (3), dividing by y and reversing the inequality because y is negative, we have x < z. So it may be that y < 0 < x < z .

(B) x is negative and y is positive. Then, from (2), z is negative, and from (3), dividing by y, we have z < x. So it may be that z < x < 0 < y .

Those are the only two possibilities here. Draw the number line in each case:

(A)

--------y-------0--------x--------z----------

(B)

-z--------x-----0---------y------------------

In either case, we can see that the distance from z to zero is equal to the sum of the distance from x to zero and the distance from x to z. That is, in either case, |z| = |x| + |x - z|. So we don't need any additional information to be sure that the answer to the question is yes - neither of the statements is required here.

I suppose that makes the answer 'D', though it's the only question I know of in any official GMAT material (and I've seen pretty much every question) where the statements aren't needed to answer the question given.
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Re: modulus gmat prep [#permalink]

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30 May 2009, 11:07
The answer is D

From I we get -----> Z<X AND ALSO ZY< YX<0 THAT IS Y(Z-X)< 0 SINCE Z<X , Z-X<0 SO Y > 0

THAT MEANS THAT MOD X < MOD Z SO WE CAN ANSWER .HENCE I IS SUFFICIENT

II IS NOTHING BUT I SO II IS ALSO SUFFICIENT

HENCE ANS = D
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Re: modulus gmat prep [#permalink]

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18 Dec 2009, 15:45
D for me

The question stem says that -
zy and xy are less than 0
xy is greater than zy

Therefore either y is +ve and x and y are negative or y is negative and x and z are positive

Statement 1 ---------SUFFICIENT

X>Z. therefore y is positive
now plug in some values in the given absolute function
Let x = -2, z = -6
You will get LHS = RHS (Try this for more values and you will get same answer)

Statement 2--------SUFFICIENT

If y>0 then xy can be greater than zy only if x>z and both x and z are negative

same situation as statement 1
hence sufficient
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Re: modulus gmat prep [#permalink]

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18 Dec 2009, 16:54
As it was pointed out by Ian Stewart neither of statements is required to answer the question.

Similar question was discussed at: gmatprep-modulus-q-44909.html
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Re: modulus gmat prep   [#permalink] 18 Dec 2009, 16:54
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# modulus gmat prep

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