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Is |x| = y + z?

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Is |x| = y + z? [#permalink]

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New post 05 Jun 2012, 16:38
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Is |x| = y + z?

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

[Reveal] Spoiler:
I know how to solve this by plugging in numbers and could arrive at the right answer. I want to learn how to solve this using algebra. When I tried with algebra I get answer as A. Can some please verify my steps and explain me what I am missing? Thank you.

1. -x = y +z ==> x+y=z (This is 1. and satisfies the question with different values of y and z for a negative x)
x=y+z ==> is not the same as given equation.
So A is sufficient.

2. Clearly insufficient.
[Reveal] Spoiler: OA

Last edited by Bunuel on 28 Nov 2013, 10:24, edited 1 time in total.
Edited the OA.

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Re: Inequalities [#permalink]

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New post 05 Jun 2012, 18:00
pgmat wrote:
Is |x| = y + z?
1. x + y = z
2. x < 0

I know how to solve this by plugging in numbers and could arrive at the right answer. I want to learn how to solve this using algebra. When I tried with algebra I get answer as A. Can some please verify my steps and explain me what I am missing? Thank you.

1. -x = y +z ==> x+y=z (This is 1. and satisfies the question with different values of y and z for a negative x)
x=y+z ==> is not the same as given equation.
So A is sufficient.

2. Clearly insufficient.


|x| = y + x

(A) x = y + z AND/IF x > 0
(B) x = - ( y + z ) AND/IF x <0

I don't get Statement (1)

Shouldn't it be x = - y - z ??

But this is insufficient because we have to have the condition that x > 0

Statement (2)

x < 0 <-- insufficient (this is the condition we are looking for in statement (1))

Clearly, Statement (1) and Statement (2) = (C)
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Re: Inequalities [#permalink]

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New post 05 Jun 2012, 20:19
gmatsaga wrote:
pgmat wrote:
Is |x| = y + z?
1. x + y = z
2. x < 0

I know how to solve this by plugging in numbers and could arrive at the right answer. I want to learn how to solve this using algebra. When I tried with algebra I get answer as A. Can some please verify my steps and explain me what I am missing? Thank you.

1. -x = y +z ==> x+y=z (This is 1. and satisfies the question with different values of y and z for a negative x)
x=y+z ==> is not the same as given equation.
So A is sufficient.

2. Clearly insufficient.


|x| = y + x

(A) x = y + z AND/IF x > 0
(B) x = - ( y + z ) AND/IF x <0

I don't get Statement (1)

Shouldn't it be x = - y - z ??

But this is insufficient because we have to have the condition that x > 0

Statement (2)

x < 0 <-- insufficient (this is the condition we are looking for in statement (1))

Clearly, Statement (1) and Statement (2) = (C)

Statement 1, x=-y-z is same as -x=y+z. and this implies x<0 and hence the statement should be sufficient. This is where I got lost.

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Re: Inequalities [#permalink]

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New post 05 Jun 2012, 20:33
pgmat wrote:
gmatsaga wrote:
pgmat wrote:
Is |x| = y + z?
1. x + y = z
2. x < 0

I know how to solve this by plugging in numbers and could arrive at the right answer. I want to learn how to solve this using algebra. When I tried with algebra I get answer as A. Can some please verify my steps and explain me what I am missing? Thank you.

1. -x = y +z ==> x+y=z (This is 1. and satisfies the question with different values of y and z for a negative x)
x=y+z ==> is not the same as given equation.
So A is sufficient.

2. Clearly insufficient.


|x| = y + x

(A) x = y + z AND/IF x > 0
(B) x = - ( y + z ) AND/IF x <0

I don't get Statement (1)

Shouldn't it be x = - y - z ??

But this is insufficient because we have to have the condition that x > 0

Statement (2)

x < 0 <-- insufficient (this is the condition we are looking for in statement (1))

Clearly, Statement (1) and Statement (2) = (C)

Statement 1, x=-y-z is same as -x=y+z. and this implies x<0 and hence the statement should be sufficient. This is where I got lost.


Yeah I also got this wrong the first time because I thought Statement (1) was already sufficient. However, we need Statement (2).
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Re: Inequalities [#permalink]

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New post 06 Jun 2012, 13:14
pgmat wrote:
Is |x| = y + z?
1. x + y = z
2. x < 0

I know how to solve this by plugging in numbers and could arrive at the right answer. I want to learn how to solve this using algebra. When I tried with algebra I get answer as A. Can some please verify my steps and explain me what I am missing? Thank you.

1. -x = y +z ==> x+y=z (This is 1. and satisfies the question with different values of y and z for a negative x)
x=y+z ==> is not the same as given equation.
So A is sufficient.

2. Clearly insufficient.

Did you copy this problem down correctly? -x=y+z =/=> x+y=z.

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Re: Inequalities [#permalink]

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New post 06 Jun 2012, 13:17
pgmat wrote:
gmatsaga wrote:
pgmat wrote:
Is |x| = y + z?
1. x + y = z
2. x < 0

I know how to solve this by plugging in numbers and could arrive at the right answer. I want to learn how to solve this using algebra. When I tried with algebra I get answer as A. Can some please verify my steps and explain me what I am missing? Thank you.

1. -x = y +z ==> x+y=z (This is 1. and satisfies the question with different values of y and z for a negative x)
x=y+z ==> is not the same as given equation.
So A is sufficient.

2. Clearly insufficient.


|x| = y + x

(A) x = y + z AND/IF x > 0
(B) x = - ( y + z ) AND/IF x <0

I don't get Statement (1)

Shouldn't it be x = - y - z ??

But this is insufficient because we have to have the condition that x > 0

Statement (2)

x < 0 <-- insufficient (this is the condition we are looking for in statement (1))

Clearly, Statement (1) and Statement (2) = (C)

Statement 1, x=-y-z is same as -x=y+z. and this implies x<0 and hence the statement should be sufficient. This is where I got lost.

This is where you're incorrect. -x=y+z alone does not imply that x<0 without the condition that y+z >0.

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

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New post 09 Jun 2012, 14:13
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pgmat wrote:
Is |x| = y + z?

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

I know how to solve this by plugging in numbers and could arrive at the right answer. I want to learn how to solve this using algebra. When I tried with algebra I get answer as A. Can some please verify my steps and explain me what I am missing? Thank you.

1. -x = y +z ==> x+y=z (This is 1. and satisfies the question with different values of y and z for a negative x)
x=y+z ==> is not the same as given equation.
So A is sufficient.

2. Clearly insufficient.


The answer to this question is E, not C.

Consider below 2 cases:
\(x=-1\), \(y=1\) and \(z=0\) --> \(|x|=1\) and \(y+z=1\) --> answer YES;
\(x=-1\), \(y=2\) and \(z=1\) --> \(|x|=1\) and \(y+z=3\) --> answer NO.

I think you refer to the following question:

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 --> \(-x=y-z\)
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.

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

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New post 17 Aug 2012, 23:08
Bunuel wrote:
pgmat wrote:
Is |x| = y + z?

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

I know how to solve this by plugging in numbers and could arrive at the right answer. I want to learn how to solve this using algebra. When I tried with algebra I get answer as A. Can some please verify my steps and explain me what I am missing? Thank you.

1. -x = y +z ==> x+y=z (This is 1. and satisfies the question with different values of y and z for a negative x)
x=y+z ==> is not the same as given equation.
So A is sufficient.

2. Clearly insufficient.


The answer to this question is E, not C.

Consider below 2 cases:
\(x=-1\), \(y=1\) and \(z=0\) --> \(|x|=1\) and \(y+z=1\) --> answer YES;
\(x=-1\), \(y=2\) and \(z=1\) --> \(|x|=1\) and \(y+z=3\) --> answer NO.

I think you refer to the following question:

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 --> \(-x=y-z\)
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.

Hope it's clear.



Hi ,

Though it looks reasonable , I am not sure on what is wrong with this logic.



1. -x = y +z ==> x+y=z (This is 1. and satisfies the question with different values of y and z for a negative x)
x=y+z ==> is not the same as given equation.
So A is sufficient.

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

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New post 18 Aug 2012, 01:00
pgmat wrote:
Is |x| = y + z?

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

I know how to solve this by plugging in numbers and could arrive at the right answer. I want to learn how to solve this using algebra. When I tried with algebra I get answer as A. Can some please verify my steps and explain me what I am missing? Thank you.

1. -x = y +z ==> x+y=z (This is 1. and satisfies the question with different values of y and z for a negative x)
x=y+z ==> is not the same as given equation.
So A is sufficient.

2. Clearly insufficient.


given that x = y+z or -x=Y+z

so 1. x+Y = z..... not sufficient
2. it does not tell everything either... so not sufficient..

together.... -x+y = z

-x = -y+z, hence not same as given in the question, hence the answer to the main question is NO and with C option we are answering it.
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Re: Is |x| = y + z? (1) x + y = z (2) x < 0 [#permalink]

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pgmat wrote:
Is |x| = y + z?

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

I know how to solve this by plugging in numbers and could arrive at the right answer. I want to learn how to solve this using algebra. When I tried with algebra I get answer as A. Can some please verify my steps and explain me what I am missing? Thank you.

1. -x = y +z ==> x+y=z (This is 1. and satisfies the question with different values of y and z for a negative x)
x=y+z ==> is not the same as given equation.
So A is sufficient.

2. Clearly insufficient.



(1) \(x = y-z\). Then \(|x|=|y-z|\) which is either \(y-z\) or \(z-y.\)
In order to have \(y+z=y-z\), necessarily \(z=0\) and also \(y\geq0.\)
In order to have \(y+z=z-y\), necessarily \(y=0\) and also \(z\geq0.\)
Obviously not sufficient.

(2) Clearly not sufficient.

(1) and (2)
We are in the case \(x=y-z<0\) so \(|x|=z-y\). For \(|x|=y+z\) as seen above we need \(y=0\) and \(z\geq0.\) Neither condition is guaranteed.
Not sufficient.

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

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New post 22 Aug 2012, 13:59
Answer is E. Plugged in a bunch of numbers.

1) x=3, y=4, z=7 gives us the answer no, but x= -5, y=3, z=2 gives us yes. Insufficient

2) x<0 insufficient since y and z are unknown

Put them together, x=-5, y=3, z=2 gives us yes, but x=-5, y=-7, z=-12 gives us no. Insufficient.

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Re: Is |x| = y + z? [#permalink]

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New post 29 Nov 2013, 05:40
Hi Bunuel!
I have a doubt.
|x|= y+z gives us two equations..
X= y+ z or -x= y+z
Statement one says x+y=z .. It is not possible to get the above mentioned statements with this equation.
Statement two says x<0 ..this should be sufficient to answer right?

Similarly. In the question |x|= y-z.
We can x= y-z and -x= y-z
Statement one by substituting we get -x= y-z so this should be suffice to right?

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Re: Is |x| = y + z? [#permalink]

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New post 29 Nov 2013, 06:05
anujpadia wrote:
Hi Bunuel!
I have a doubt.
|x|= y+z gives us two equations..
X= y+ z or -x= y+z
Statement one says x+y=z .. It is not possible to get the above mentioned statements with this equation.
Statement two says x<0 ..this should be sufficient to answer right?

Similarly. In the question |x|= y-z.
We can x= y-z and -x= y-z
Statement one by substituting we get -x= y-z so this should be suffice to right?


Not sure I understand your logic there...

Number plugging proving that E is the answer: is-x-y-z-133977.html#p1094912
Algebraic approach proving the same: is-x-y-z-133977.html#p1114409

Hope this helps.
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Re: Is |x| = y + z? [#permalink]

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New post 29 Nov 2013, 12:30
In the question |x|= y-z.
We get two equations I.e.(removing the modulus . x= y-z and -x= y-z
Statement one says x+z =y
Therefore by substituting we get -x= y-z. so this should be suffice to answer right?
As the question stem also has the same equation.

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Re: Is |x| = y + z? [#permalink]

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New post 29 Nov 2013, 12:46
anujpadia wrote:
In the question |x|= y-z.
We get two equations I.e.(removing the modulus . x= y-z and -x= y-z
Statement one says x+z =y
Therefore by substituting we get -x= y-z. so this should be suffice to answer right?
As the question stem also has the same equation.

Posted from my mobile device


Since the correct answer is E, then this is obviously not right.

If \(x\geq{0}\), the questions asks: is \(x=y+z\)?
If \(x<{0}\), the questions asks: is \(-x=y+z\)?

When we combine the statements, since it's given that x<0, the questions becomes: is \(-x=y+z\). From (1) we have that \(-x=y-z\), which is not sufficient to get whether \(-x=y+z\).

Consider the examples given here: http://gmatclub.com/forum/is-x-y-z-133977.html#p1094912
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Is |x| = y + z? [#permalink]

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New post 25 Apr 2017, 12:38
pgmat wrote:
Is |x| = y + z?

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

[Reveal] Spoiler:
I know how to solve this by plugging in numbers and could arrive at the right answer. I want to learn how to solve this using algebra. When I tried with algebra I get answer as A. Can some please verify my steps and explain me what I am missing? Thank you.

1. -x = y +z ==> x+y=z (This is 1. and satisfies the question with different values of y and z for a negative x)
x=y+z ==> is not the same as given equation.
So A is sufficient.

2. Clearly insufficient.

(I think the question could have been better stated.)

My answer is 'E'.

statement-1: Insufficient.
rewrite x+y=z as x=z-y.
If (z=0 and y=0, thus z+y=0 and x=z-y=0) then |x|=z+y. But, if (z=2 and y=1, thus z+y=3 and x=z-y=1) then |x|\(\neq\)z+y.

statement-2: Insufficient as it doesn't give any info on y and z. Example, x=-3, z=-1, y=-2, thus |x|\(\neq\)z+y OR x=-3, z=1, y=2, thus |x|=z+y.

1+2: Insufficient.
Here, we know that, x=z-y and x<0,
when z=1 and y=2 then x = z-y=-1, and |x|\(\neq\)=y+z
but when z=0, y=1 then x=z-y=-1, and |x| = y+z

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Re: Is |x| = y + z? [#permalink]

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New post 30 Apr 2017, 06:33
The way I approached this question was this:

since abs(x)>=0, the question is asking is y+z>=0

Statement 1 says that Y=Z-X. This means that Y+Z=2Z-X. We don't have specific values for Z or X so not sufficient

Statement 2 says x>0. This alone means nothing. Insufficient.

Together x>0 and the question is whether 2Z-X>0. We have no indication of the direction of Z, so insufficient together.

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Re: Is |x| = y + z? [#permalink]

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New post 25 Jul 2017, 15:36
For statement (1) we derive that

x+y = z

-x = y - z

When x is negative, y-z>0 and when x is positive, y-z<0 .. Knowing that y-z would be greater or less than 0 is insufficient to give us a similar indication for y+z ..

My question is whether this is a correct understanding of the information and can it be universally applied for two variables getting subtracted and added?

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Re: Is |x| = y + z? [#permalink]

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New post 28 Jul 2017, 00:46
TheMastermind wrote:
For statement (1) we derive that

x+y = z

-x = y - z

When x is negative, y-z>0 and when x is positive, y-z<0 .. Knowing that y-z would be greater or less than 0 is insufficient to give us a similar indication for y+z ..

My question is whether this is a correct understanding of the information and can it be universally applied for two variables getting subtracted and added?


Hi TheMastermind ,

Yeah, this is another way to approach such questions.

Since you don't have any information about the sign of (y-z), you cannot conclude anything for y+z.

This is universally accepted concept and is not specific to this question.
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Re: Is |x| = y + z?   [#permalink] 28 Jul 2017, 00:46
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