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a^2+b^2=6, a+b=? 1. b-a=2 2. a=-b

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a^2+b^2=6, a+b=? 1. b-a=2 2. a=-b [#permalink] New post 06 Nov 2010, 23:56
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a^2+b^2=6, a+b=?

1. b-a=2
2. a=-b
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Re: a^2+b^2=6 [#permalink] New post 07 Nov 2010, 00:17
(a+b)^2 + (b-a)^2 = a^2 + b^2 +2ab + b^2 + a^2 -2ab = 2(a^2 + b^)
=> (a+b)^2 + 2^2 = 2 x 6 = 12
=> (a+b)^2 = 8
=> a+b = 2 x (2)^(1/2) -- 2 x square root of 2

if a = -b, then a+b = 0


Therefore, (1) and (2) alone are sufficient
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Re: a^2+b^2=6 [#permalink] New post 07 Nov 2010, 00:24
srjaidev wrote:
(a+b)^2 + (b-a)^2 = a^2 + b^2 +2ab + b^2 + a^2 -2ab = 2(a^2 + b^)
=> (a+b)^2 + 2^2 = 2 x 6 = 12
=> (a+b)^2 = 8
=> a+b = 2 x (2)^(1/2) -- 2 x square root of 2

if a = -b, then a+b = 0


Therefore, (1) and (2) alone are sufficient


Since \((a+b)^2 = 8\), a+b should equal to \(+-\sqrt{8}\)? Am I missing something?
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Re: a^2+b^2=6 [#permalink] New post 07 Nov 2010, 05:29
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Creeper300 wrote:
a^2+b^2=6, a+b=?

1. b-a=2
2. a=-b


What is the source of this question? The question is certainly not GMAT specific.
From statement II, you get a = -b, so a + b = 0
While from statement I, you get \((a + b) = \sqrt{8} or -\sqrt{8}\)

Both statements need to give at least one same value of a + b. It isn't possible that (a + b) is both 0 and \(\sqrt{8} or -\sqrt{8}\)

Data Sufficiency questions are like puzzles.
I have an equation on a paper and I ask you, what is the sum of a and b? (Question Stem)
You say that you do not know.
I give you a hint - b - a = 2. (Statement I)
You analyze the hint and say a + b is either root 8 or - root 8.
I decide to give you another hint to solve the puzzle. b - a = 0. (Statement II)
This is incorrect, isn't it? It is the same equation I am asking about. How can a + b be both 0 and either root 8 or - root 8.
Since it is the same puzzle, my hints (i.e. the two statements) cannot contradict each other.
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Re: a^2+b^2=6 [#permalink] New post 07 Nov 2010, 05:35
VeritasPrepKarishma wrote:
Creeper300 wrote:
a^2+b^2=6, a+b=?

1. b-a=2
2. a=-b


What is the source of this question? The question is certainly not GMAT specific.
From statement II, you get a = -b, so a + b = 0
While from statement I, you get \((a + b) = \sqrt{8} or -\sqrt{8}\)

Both statements need to give at least one same value of a + b. It isn't possible that (a + b) is both 0 and \(\sqrt{8} or -\sqrt{8}\)

Data Sufficiency questions are like puzzles.
I have an equation on a paper and I ask you, what is the sum of a and b? (Question Stem)
You say that you do not know.
I give you a hint - b - a = 2. (Statement I)
You analyze the hint and say a + b is either root 8 or - root 8.
I decide to give you another hint to solve the puzzle. b - a = 0. (Statement II)
This is incorrect, isn't it? It is the same equation I am asking about. How can a + b be both 0 and either root 8 or - root 8.
Since it is the same puzzle, my hints (i.e. the two statements) cannot contradict each other.



WOW! Interesting point, Karishma!
I never thought about that when I was preparing for GMAT. So you are saying that ultimately the answer to the question (a+b) =? should have the same answer from the 2 hints and if the 2 hints give different answers then it doesn't make sense.

If I had figured that out, I would have saved sometime in the test!

+1 for the tip!
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Re: a^2+b^2=6 [#permalink] New post 07 Nov 2010, 06:14
Expert's post
srjaidev wrote:
VeritasPrepKarishma wrote:
Creeper300 wrote:
So you are saying that ultimately the answer to the question (a+b) =? should have the same answer from the 2 hints and if the 2 hints give different answers then it doesn't make sense.

If I had figured that out, I would have saved sometime in the test!

+1 for the tip!


Yes, for it to be a valid GMAT question, if the two statements are giving you one possible solution each, they have to be the same. If you are getting multiple solutions from both the statements, at least one solution has to be common.
e.g.
Stmnt 1 could give you x = root 8 or - root 8

Stmnt 2 could give you x = root 8 or root 6
Answer would then be (C) since using both together you can say that x = root 8 (the only common solution).

Had stmnt 2 given you that x = root 8 or root -8 or root 6, then of course, even using both statements together, you couldn't get the answer since x could be root 8 or - root 8.

BTW, even if you had figured it out, you couldn't have obtained more than 51 in Quant!
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Re: a^2+b^2=6   [#permalink] 07 Nov 2010, 06:14
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a^2+b^2=6, a+b=? 1. b-a=2 2. a=-b

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