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Is |x| = y + z?

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Is |x| = y + z? [#permalink] New post 05 Jun 2012, 15:38
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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, 09:24, edited 1 time in total.
Edited the OA.
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Re: Inequalities [#permalink] New post 05 Jun 2012, 17:00
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] New post 05 Jun 2012, 19:19
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] New post 05 Jun 2012, 19:33
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] New post 06 Jun 2012, 12:14
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] New post 06 Jun 2012, 12:17
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] New post 09 Jun 2012, 13:13
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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] New post 17 Aug 2012, 22:08
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] New post 18 Aug 2012, 00:00
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] New post 20 Aug 2012, 12:33
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] New post 22 Aug 2012, 12:59
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? (1) x + y = z (2) x < 0 [#permalink] New post 28 Nov 2013, 09:13
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Re: Is |x| = y + z? (1) x + y = z (2) x < 0 [#permalink] New post 28 Nov 2013, 09:25
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Re: Is |x| = y + z? [#permalink] New post 29 Nov 2013, 04:40
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] New post 29 Nov 2013, 05:05
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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] New post 29 Nov 2013, 11:30
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] New post 29 Nov 2013, 11:46
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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.

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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: is-x-y-z-133977.html#p1094912
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COLLECTION OF QUESTIONS:
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Re: Is |x| = y + z?   [#permalink] 29 Nov 2013, 11:46
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