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

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

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19 Dec 2015, 12:39
Hi Bunnel- It might sound lame, but why do we need to consider 2 cases for statement 1? Why can we not simply consider x= z-y which means z>y while we are testing for whether y>equal to Z and hence statement 1 is sufficient.
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Is |x| = y - z ? (1) x + y = z (2) x < 0  [#permalink]

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20 Oct 2016, 10:29
1
1
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

Let's start with the easy statement - Statement 2.

(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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28 Oct 2016, 22:19
I have a doubt here.
if we see,
if x is +ve then x=y-z and if x is -ve x+y = z.

st 1 says x+y = z , so why cant A be suff
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Re: Is |x| = y - z ? (1) x + y = z (2) x < 0  [#permalink]

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28 Oct 2016, 23:41
vsvikas wrote:
I have a doubt here.
if we see,
if x is +ve then x=y-z and if x is -ve x+y = z.

st 1 says x+y = z , so why cant A be suff

(1) says that -x = y - z. For this case, |x| = y - z would be true ONLY IF x is negative but if x is positive, then |x| = y - z would not be true.
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Re: Is |x| = y - z ? (1) x + y = z (2) x < 0  [#permalink]

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29 Oct 2016, 00:04
per st 1, when x + y = z, this will happen when x<=0, so this st is sufficient. as when x<=0, then |x|=y-z
where am i going wrong or am confusing some concept
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Re: Is |x| = y - z ? (1) x + y = z (2) x < 0  [#permalink]

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01 Nov 2016, 07:02
Bunuel : Is mod x = y-z

I interpreted the question as " Is x = +(y-z) or x= -(y -z)?"

And hence, since the first option mentions x = -y+z, i chose A. Am i missing something?
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Re: Is |x| = y - z ? (1) x + y = z (2) x < 0  [#permalink]

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01 Nov 2016, 11:36
Tricky, but do-able:

(1) x+y = z

Ex 1: -2+3=1 --> 3-1=2 --> works *

Ex 2: 3+(-2)=1 = --> -2-1=-3 --> fail (we don't get absolute value)

Ex 3: 3+5=8 --> 5-8=-3 --> fail

We can see a pattern from Ex 2 and 3 that x must be negative in order for this to work.

NOT SUFFICIENT

(2) x<0 --> NOT SUFFICIENT by itself

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

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08 Feb 2017, 19:52
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.

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."
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Is |x| = y - z?  [#permalink]

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06 Mar 2017, 18:19
sitagupta385 wrote:
Is |x| = y - z?

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

is
x= y-z && x= z-y ??

(1) x= z-y ...but we dont know whether x= y-z..
insuff

(2) x<0
so x= z-y but we dont know x= y-z or not..
insuff

combining we know x= y-z (from 1) && x= y-z(from2)
thus |x| = y - z
suff

Ans C
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Re: Is |x| = y - z?  [#permalink]

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06 Mar 2017, 19:21
1. X+Y=Z
-x=y-z
|x|=y-z
Ans a.

Hit kudos if i this solution is ryt.

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

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07 Mar 2017, 21:56
Bunuel , i have one doubt in this question. i have gone through the explanations in chain, still not clear.

suppose we have been asked in question ...
is |x|=1 ? according to explanations it says x=-1 && x=1 ?
A) x=1 .... so this must be insufficient.

please correct me if I am missing anything.
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Re: Is |x| = y - z ? (1) x + y = z (2) x < 0  [#permalink]

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07 Mar 2017, 23:21
1
mbaprep2016 wrote:
Bunuel , i have one doubt in this question. i have gone through the explanations in chain, still not clear.

suppose we have been asked in question ...
is |x|=1 ? according to explanations it says x=-1 && x=1 ?
A) x=1 .... so this must be insufficient.

please correct me if I am missing anything.

So, the question is:

Does |x| = 1?

(1) x = 1. This would be sufficient because |1| = 1 and we would have a definite YES answer to the question.

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

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08 Mar 2017, 04:17
St 1: y-z = -x. if x is positive |x| = z-y. if x is negative, |x| = y-z. INSUFFICIENT
St 2: x is negative. no idea about y and z. INSUFFICIENT

St 1 & St 2: y-z = -x. x is negative. hence |x| = y-z. ANSWER

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

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08 Mar 2017, 11:26
1
Bunuel wrote:
mbaprep2016 wrote:
Bunuel , i have one doubt in this question. i have gone through the explanations in chain, still not clear.

suppose we have been asked in question ...
is |x|=1 ? according to explanations it says x=-1 && x=1 ?
A) x=1 .... so this must be insufficient.

please correct me if I am missing anything.

So, the question is:

Does |x| = 1?

(1) x = 1. This would be sufficient because |1| = 1 and we would have a definite YES answer to the question.

Hope it helps.

I am sorry for asking same question again and again but with similar logic
Question : Is |x| = y - z?

when x > 0 x= y-z && when x<0 x= z-y ??

we have to choose between two values

Now A says x= z-y... this clearly indicates x<0 ...hence sufficient
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Re: Is |x| = y - z ? (1) x + y = z (2) x < 0  [#permalink]

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08 Mar 2017, 23:04
mbaprep2016 wrote:
Bunuel wrote:
mbaprep2016 wrote:
Bunuel , i have one doubt in this question. i have gone through the explanations in chain, still not clear.

suppose we have been asked in question ...
is |x|=1 ? according to explanations it says x=-1 && x=1 ?
A) x=1 .... so this must be insufficient.

please correct me if I am missing anything.

So, the question is:

Does |x| = 1?

(1) x = 1. This would be sufficient because |1| = 1 and we would have a definite YES answer to the question.

Hope it helps.

I am sorry for asking same question again and again but with similar logic
Question : Is |x| = y - z?

when x > 0 x= y-z && when x<0 x= z-y ??

we have to choose between two values

Now A says x= z-y... this clearly indicates x<0 ...hence sufficient

OK. Let me demonstrate with number plugging. For (1) if x = 1, and y =2 and z=3, |x| does not equal to y - z.
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Re: Is |x| = y - z ? (1) x + y = z (2) x < 0  [#permalink]

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25 Apr 2017, 22:09
Hi Bunuel, Please point out the error in my approach.

|x|= y - z.
So, when x<0, -x=y-z => x = z - y------(1)
x>0, x = y - z

Statement 1. x = z - y, which is same as (1). So is A not the answer ?
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Re: Is |x| = y - z ? (1) x + y = z (2) x < 0  [#permalink]

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29 Jul 2017, 17:06
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.

Just to make this good answer a little clearer. An absolute value cannot equal a negative value. Therefore -x=y-z. as shown in expression 1. If X>0 then we have -5 (because there is a neg sign in front so X = positive 5 but the expression is -5) = y-z. But if Y-z = -5 that means |x| = -5 which is not possible! As said above an absolute value has to equal a positive number. So if X<0 then X could be -5 and - * -5 is positive 5. So y-z = 5 and therefore together we can say that X=Y-Z
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Re: Is |x| = y - z ? (1) x + y = z (2) x < 0  [#permalink]

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13 Aug 2017, 17:30
So absolute value we have x = y-z or –x = y-z . That's how you rewrite the ABS value equation. You write one equation with positive X and one with negative to cover both sides.

1) Tells us X+Y=z . It can be arranged into –x=Y-z which matches one of our absolute value formulas. However, if X is positive y-z would be negative and then Y-Z couldn’t equal the absolute value since the ABS value has to equal a non negative numbers.

2) X<0 but we know nothing about Y or Z

3) Combined now we know –(negative number) is positive therefore Y-Z must be positive = Therefore we know |x| = y - z ?
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Re: Is |x| = y - z ? (1) x + y = z (2) x < 0  [#permalink]

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31 Aug 2017, 07:54
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?
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Re: Is |x| = y - z ? (1) x + y = z (2) x < 0  [#permalink]

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31 Aug 2017, 07:57
1
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.
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Re: Is |x| = y - z ? (1) x + y = z (2) x < 0 &nbs [#permalink] 31 Aug 2017, 07:57

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