a^2+b^2=6, a+b=? 1. b-a=2 2. a=-b : GMAT Data Sufficiency (DS)
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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]

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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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Joined: 25 Jul 2010
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Location: India
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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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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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07 Nov 2010, 05:29
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Expert's post
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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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Senior Manager Joined: 25 Jul 2010 Posts: 300 Location: India Concentration: Strategy, Technology GMAT 1: 770 Q51 V46 GPA: 3.2 WE: Engineering (Computer Software) Followers: 20 Kudos [?]: 34 [0], given: 20 Re: a^2+b^2=6 [#permalink] ### Show Tags 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! Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7121 Location: Pune, India Followers: 2133 Kudos [?]: 13638 [0], given: 222 Re: a^2+b^2=6 [#permalink] ### Show Tags 07 Nov 2010, 06:14 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! _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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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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