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Is |x| = y + z? (1) x + y = z (2) x < 0 [#permalink]
 05 Jun 2012, 16:38
Question Stats:
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.
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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. |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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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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Manager
Status: Rising GMAT Star
Joined: 05 Jun 2012
Posts: 133
Location: Philippines
Concentration: General Management, Finance
GMAT 1: 660 Q V
GPA: 3.22
WE: Corporate Finance (Consulting)
Followers: 5
Kudos [?]:
5
[0], given: 16
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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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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
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Senior Manager
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I am getting answer C , when i plug -in numbers. Please post OA along with the question.
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Intern
Joined: 30 May 2012
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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. Did you copy this problem down correctly? -x=y+z =/=> x+y=z.
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Intern
Joined: 30 May 2012
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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. Two possible answers not sufficient; (2) x<0Not 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]
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<0Not 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]
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. Answer E
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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.
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Re: Is |x| = y + z? (1) x + y = z (2) x < 0
[#permalink]
22 Aug 2012, 13:59
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