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What is the value of x^2 + y^2 ?
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Updated on: 09 Aug 2017, 05:46
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What is the value of x^2 + y^2 ? (1) x^2 + y^2 = 2xy + 1 (2) x^2 + y^2 = 4 2xy Source: GMAThacks 1800
OA is E, wanted to get some feedback as to whether I am missing something or this is a bad question.
Each alone is insufficient, but I feel as if:
x^2 + y^2 = 2xy + 1 & x^2 + y^2 = 4 2xy
So:
2xy + 1 = 4 2xy xy = 3/4
Therefore:
x^2 + y^2 = 2(3/4) + 1 x^2 + y^2 = 2.5
Can someone tell me where I am going wrong here? Thanks!
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Originally posted by grassmonkey on 04 Aug 2017, 20:01.
Last edited by Bunuel on 09 Aug 2017, 05:46, edited 1 time in total.
Edited the OA.



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Re: What is the value of x^2 + y^2 ?
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05 Aug 2017, 09:07
Why not answer choice c?



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Re: What is the value of x^2 + y^2 ?
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06 Aug 2017, 20:13
Bunuel can you help out? Thanks!



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Re: What is the value of x^2 + y^2 ?
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06 Aug 2017, 23:48
I think the reason it could be E is As you have right pointed out, xy=3/4. We need the value of the expression x^2 + y^2. Case 1: x=1, y=3/4. x^2 + y^2 = 25/4 Case 2: x=3, y=1/4. x^2 + y^2 = 145/4
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Re: What is the value of x^2 + y^2 ?
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07 Aug 2017, 23:40
pushpitkc wrote: I think the reason it could be E is
As you have right pointed out, xy=3/4. We need the value of the expression x^2 + y^2.
Case 1: x=1, y=3/4. x^2 + y^2 = 25/4 Case 2: x=3, y=1/4. x^2 + y^2 = 145/4 I do agree that xy=3/4 . Though when you do combine the statements we do get the solution for x^2 + y^2 as 2.5 Could you please elaborate on why combining the 2 statements in the way I did is wrong as opposed to the way you did?



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Re: What is the value of x^2 + y^2 ?
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09 Aug 2017, 05:41
pushpitkc wrote: I think the reason it could be E is
As you have right pointed out, xy=3/4. We need the value of the expression x^2 + y^2.
Case 1: x=1, y=3/4. x^2 + y^2 = 25/4 Case 2: x=3, y=1/4. x^2 + y^2 = 145/4 Since we have already established that xy=3/4 Why don't we directly put the value of xy into the individual equations. For instance, from (1) x^2 + y^2 = 2(3/4) +1 = 5/2 ly, from (2) x^2 +y^2 = 42(3/4) = 5/2 Please change the OA to C.
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Re: What is the value of x^2 + y^2 ?
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09 Aug 2017, 10:26
grassmonkey wrote: What is the value of x^2 + y^2 ? (1) x^2 + y^2 = 2xy + 1 (2) x^2 + y^2 = 4 2xy Source: GMAThacks 1800
OA is E, wanted to get some feedback as to whether I am missing something or this is a bad question.
Each alone is insufficient, but I feel as if:
x^2 + y^2 = 2xy + 1 & x^2 + y^2 = 4 2xy
So:
2xy + 1 = 4 2xy xy = 3/4
Therefore:
x^2 + y^2 = 2(3/4) + 1 x^2 + y^2 = 2.5
Can someone tell me where I am going wrong here? Thanks! 1. \(x^2 + y^2  2xy = 1\) \((xy)^2 =1\) \(xy = 1\) Insufficient 2. \(x^2 +y^2 +2xy = 4\) \((x+y)^2 = 2^2\) \(x+y = 2\) Insufficient 1 + 2 2 variables, 2 equations  can be solved Sufficient (choice C)



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Re: What is the value of x^2 + y^2 ?
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09 Aug 2017, 13:00
Ok thanks for the help everyone, seems like the OA is wrong and the answer here should be (C) and not (E).



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Re: What is the value of x^2 + y^2 ?
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09 Aug 2017, 15:38
grassmonkey wrote: Ok thanks for the help everyone, seems like the OA is wrong and the answer here should be (C) and not (E). I spent 5 pages trying to see how the answer could be E but it didn’t make much sense. I always got C. Btw.. do you have the official explanation for this question? It’s good to know why the prep company thought the answer is E. Sent from my iPhone using GMAT Club Forum mobile app
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Re: What is the value of x^2 + y^2 ?
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09 Aug 2017, 15:58
Ans will be E. Let me explain Rewriting the first eq: (x  y)^2 = 1 => (x  y) = (+) 1. (NOT +1) ie x  y = 1,+1 Rewriting the second eq: (x + y)^2 = 4 => (x + y) = + 2. ( NOT +2) ie x + y = 2,+2 By Solving both equations we will get more than one value for x and y. Hence no specific answer. Therefore option E. Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app



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What is the value of x^2 + y^2 ?
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25 Aug 2017, 06:17
roadrunner wrote: grassmonkey wrote: What is the value of x^2 + y^2 ? (1) x^2 + y^2 = 2xy + 1 (2) x^2 + y^2 = 4 2xy Source: GMAThacks 1800
OA is E, wanted to get some feedback as to whether I am missing something or this is a bad question.
Each alone is insufficient, but I feel as if:
x^2 + y^2 = 2xy + 1 & x^2 + y^2 = 4 2xy
So:
2xy + 1 = 4 2xy xy = 3/4
Therefore:
x^2 + y^2 = 2(3/4) + 1 x^2 + y^2 = 2.5
Can someone tell me where I am going wrong here? Thanks! 1. \(x^2 + y^2  2xy = 1\) \((xy)^2 =1\) \(xy = 1\) Insufficient 2. \(x^2 +y^2 +2xy = 4\) \((x+y)^2 = 2^2\) \(x+y = 2\) Insufficient 1 + 2 2 variables, 2 equations  can be solved Sufficient (choice C) You ignore the fact that xy could be = 1 in statement 1 and x + y could be = 2 in statement 2 But then, after solving all the possibility, the results of x^2 and y^2 are still the same so C is right.



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Re: What is the value of x^2 + y^2 ?
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25 Aug 2017, 09:41
grassmonkey wrote: What is the value of x^2 + y^2 ? (1) x^2 + y^2 = 2xy + 1 (2) x^2 + y^2 = 4 2xy Source: GMAThacks 1800
OA is E, wanted to get some feedback as to whether I am missing something or this is a bad question.
Each alone is insufficient, but I feel as if:
x^2 + y^2 = 2xy + 1 & x^2 + y^2 = 4 2xy
So:
2xy + 1 = 4 2xy xy = 3/4
Therefore:
x^2 + y^2 = 2(3/4) + 1 x^2 + y^2 = 2.5
Can someone tell me where I am going wrong here? Thanks! 1 is insufficient 2 is insufficient now taking both together if we add 1 and 2 the 2xy get cancelled and we can easily get the needed value hence, OAC
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