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

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Is |x| = y + z? (1) x + y = z (2) x < 0 [#permalink]  05 Jun 2012, 16:38
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24% (01:39) correct 76% (01:01) wrong based on 1 sessions
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.
[Reveal] Spoiler: OA
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Re: Inequalities [#permalink]  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]  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]  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]  06 Jun 2012, 11:51
I am getting answer C , when i plug -in numbers. Please post OA along with the question.
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Re: Inequalities [#permalink]  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]  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]  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.

(2) x<0
Not sufficient (we need to know value of y-z is equal or not to |x|)

(1)+(2) Sufficient.

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

(2) x<0
Not sufficient (we need to know value of y-z is equal or not to |x|)

(1)+(2) Sufficient.

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]  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]  20 Aug 2012, 13:33
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.

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Re: Is |x| = y + z? (1) x + y = z (2) x < 0 [#permalink]  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.
Re: Is |x| = y + z? (1) x + y = z (2) x < 0   [#permalink] 22 Aug 2012, 13:59
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