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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.

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) _________________

Far better is it to dare mighty things, to win glorious triumphs, even though checkered by failure... than to rank with those poor spirits who neither enjoy nor suffer much, because they live in a gray twilight that knows not victory nor defeat. - T. Roosevelt

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.

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). _________________

Far better is it to dare mighty things, to win glorious triumphs, even though checkered by failure... than to rank with those poor spirits who neither enjoy nor suffer much, because they live in a gray twilight that knows not victory nor defeat. - T. Roosevelt

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.

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.

Re: Is |x| = y + z? (1) x + y = z (2) x < 0 [#permalink]
09 Jun 2012, 13:13

Expert's post

2

This post was BOOKMARKED

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|)

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

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

Regards, Harsha

Note: Give me kudos if my approach is right , else help me understand where i am missing.. I want to bell the GMAT Cat

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

PhD in Applied Mathematics Love GMAT Quant questions and running.

Re: Is |x| = y + z? [#permalink]
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?

Re: Is |x| = y + z? [#permalink]
29 Nov 2013, 05:05

Expert's post

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?

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

Re: Is |x| = y + z? [#permalink]
29 Nov 2013, 11:46

Expert's post

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 \(-x=y+z\).

Re: Is |x| = y + z? [#permalink]
20 Jan 2015, 14:07

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