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

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Intern
Joined: 09 Mar 2017
Posts: 37

Kudos [?]: 2 [0], given: 23

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

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31 Aug 2017, 08:54
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.

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?

Kudos [?]: 2 [0], given: 23

Math Expert
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 129018 [1], given: 12187

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

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31 Aug 2017, 08:57
1
KUDOS
Expert's post
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.

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.
_________________

Kudos [?]: 129018 [1], given: 12187

Intern
Joined: 09 Mar 2017
Posts: 37

Kudos [?]: 2 [0], given: 23

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

### Show Tags

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.

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.

Kudos [?]: 2 [0], given: 23

Re: Is |x| = y - z ? (1) x + y = z (2) x < 0   [#permalink] 31 Aug 2017, 08:59

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

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