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What is the value of x^2 + y^2 ?

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

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Updated on: 09 Aug 2017, 05:46
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Difficulty:

85% (hard)

Question Stats:

59% (01:36) correct 41% (01:38) wrong based on 140 sessions

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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!

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 ?  [#permalink]

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05 Aug 2017, 09:07
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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
1
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
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 ?   [#permalink] 25 Aug 2017, 09:41
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