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What is the value of x^2 + y^2 ? [#permalink ]

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04 Aug 2017, 20:01
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54% (01:20) wrong

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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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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 ? [#permalink ]

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05 Aug 2017, 09:07

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Why not answer choice c?

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Re: What is the value of x^2 + y^2 ? [#permalink ]

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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 ? [#permalink ]

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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 ? [#permalink ]

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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 ? [#permalink ]

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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 = 4-2(3/4)

= 5/2

Please change the OA to C.

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Re: What is the value of x^2 + y^2 ? [#permalink ]

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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. \(x^2 + y^2 - 2xy = 1\)

\((x-y)^2 =1\)

\(x-y = 1\)

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 ? [#permalink ]

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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 ? [#permalink ]

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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.

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Re: What is the value of x^2 + y^2 ? [#permalink ]

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09 Aug 2017, 15:58

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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.

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What is the value of x^2 + y^2 ? [#permalink ]

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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. \(x^2 + y^2 - 2xy = 1\)

\((x-y)^2 =1\)

\(x-y = 1\)

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 x-y 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 ? [#permalink ]

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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, OA-C

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Re: What is the value of x^2 + y^2 ?
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25 Aug 2017, 09:41