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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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New post 31 Aug 2017, 08:59
Bunuel wrote:
brandon7 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.


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.



You're right, I am idiot. I was just about to delete. thank you for responding though, appreciate it.
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Re: Is |x| = y - z ? (1) x + y = z (2) x < 0  [#permalink]

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New post 16 Jun 2019, 12:50
anairamitch1804 wrote:
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."

anairamitch1804
Here you go for the highlighted part, please.
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Re: Is |x| = y - z ? (1) x + y = z (2) x < 0   [#permalink] 16 Jun 2019, 12:50

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