77. What is the value of x^2 + y^2 ?
(1) x^2 + y^2 = 2xy + 1
(2) x^2 + y^2 = 4 - 2xy
[spoiler]
OA:E[/spoiler]
Source: Jeff Seckman
DS question
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- hemant_rajput
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IMO it should be C
ST1: x^2 + y^2 = 2xy + 1
we cannot find 3 variables from 1 eqaution
Hence Insufficient
St2: x^2 + y^2 = 4 - 2xy
we cannot find 3 variables from 1 eqaution
Hence Insufficient
Together: Adding the 2 equations we get 2(x^2 + y^2) = 1 + 4 (xy terms cancel out)
Hence x^2 + y^2 = 5/2
Hence Sufficient
ST1: x^2 + y^2 = 2xy + 1
we cannot find 3 variables from 1 eqaution
Hence Insufficient
St2: x^2 + y^2 = 4 - 2xy
we cannot find 3 variables from 1 eqaution
Hence Insufficient
Together: Adding the 2 equations we get 2(x^2 + y^2) = 1 + 4 (xy terms cancel out)
Hence x^2 + y^2 = 5/2
Hence Sufficient
- hemant_rajput
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Here is my approachsrcc25anu wrote:IMO it should be C
ST1: x^2 + y^2 = 2xy + 1
we cannot find 3 variables from 1 equation
Hence Insufficient
St2: x^2 + y^2 = 4 - 2xy
we cannot find 3 variables from 1 equation
Hence Insufficient
Together: Adding the 2 equations we get 2(x^2 + y^2) = 1 + 4 (xy terms cancel out)
Hence x^2 + y^2 = 5/2
Hence Sufficient
1 and 2 are definitely not sufficient alone.
now from 1 and 2 :-
2xy + 1 = 4 - 2xy
4xy = 3
xy = 3/4
now substituting value of xy in 1 and 2
1 x^2 + y^2 = 2 * 3/4 + 1 = 5/2
2 x^2 + y^2 = 4 - 2 * 3/4 = 4 - 3/2 = 5/2
I guess OA is wrong unless someone has some other method to prove OA is right.
I'm no expert, just trying to work on my skills. If I've made any mistakes please bear with me.
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77. What is the value of x^2 + y^2 ?
(1) x^2 + y^2 = 2xy + 1
(2) x^2 + y^2 = 4 - 2xy
I think the answer is correct.
From 1) (x-y)^2 = 1 So x-y = plus minus 1. Their can be many solutions:
Just for +1 : (1,0)(2,1),(3,2).....(a,a-1)
Similiarly for -1 : their can be infinite solns.
From 2)
(x+y) ^ 2 = plus minus 2.
If you think about it every set of the form (2,0),...(a,a-2) will satisfy this for plus 2. Similarly for -2.
Even if you combine the results of 1 and 2 . You don't get anything because their is no overlap. Hence E is the answer.
(1) x^2 + y^2 = 2xy + 1
(2) x^2 + y^2 = 4 - 2xy
I think the answer is correct.
From 1) (x-y)^2 = 1 So x-y = plus minus 1. Their can be many solutions:
Just for +1 : (1,0)(2,1),(3,2).....(a,a-1)
Similiarly for -1 : their can be infinite solns.
From 2)
(x+y) ^ 2 = plus minus 2.
If you think about it every set of the form (2,0),...(a,a-2) will satisfy this for plus 2. Similarly for -2.
Even if you combine the results of 1 and 2 . You don't get anything because their is no overlap. Hence E is the answer.
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Statement 1:hemant_rajput wrote:77. What is the value of x^2 + y^2 ?
(1) x^2 + y^2 = 2xy + 1
(2) x^2 + y^2 = 4 - 2xy
x² - 2xy + y² = 1.
(x-y)² = 1.
Thus, x-y = 1 or x-y = -1.
No way to determine the value of x² + y².
INSUFFICIENT.
Statement 2:
x² + 2xy + y² = 4.
(x+y)² = 4.
Thus, x+y = 2 or x+y = -2.
No way to determine the value of x² + y².
INSUFFICIENT.
Statements combined:
Adding x² - 2xy + y² = 1 to x² + 2xy + y² = 4, we get:
(x² - 2xy + y²) + (x² + 2xy + y²) = 1+4
2x² + 2y² = 5
x² + y² = 5/2.
SUFFICIENT.
The correct answer is C.
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I do agree with you but hemant_rajput says OA is E
Thanks
Thanks
GMATGuruNY wrote:Statement 1:hemant_rajput wrote:77. What is the value of x^2 + y^2 ?
(1) x^2 + y^2 = 2xy + 1
(2) x^2 + y^2 = 4 - 2xy
x² - 2xy + y² = 1.
(x-y)² = 1.
Thus, x-y = 1 or x-y = -1.
No way to determine the value of x² + y².
INSUFFICIENT.
Statement 2:
x² + 2xy + y² = 4.
(x+y)² = 4.
Thus, x+y = 2 or x+y = -2.
No way to determine the value of x² + y².
INSUFFICIENT.
Statements combined:
Adding x² - 2xy + y² = 1 to x² + 2xy + y² = 4, we get:
(x² - 2xy + y²) + (x² + 2xy + y²) = 1+4
2x² + 2y² = 5
x² + y² = 5/2.
SUFFICIENT.
The correct answer is C.
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The OA is incorrect.iamniladri wrote:I do agree with you but hemant_rajput says OA is E
Thanks
The correct answer is C.
The two statements combined imply the following cases:
Case 1: x-y = 1 and x+y = 2
Here, x=3/2 and y=1/2, with the result that x² + y² = 5/2.
Case 2: x-y = 1 and x+y = -2
Here, x=-1/2 and y=-3/2, with the result that x² + y² = 5/2.
Case 3: x-y = -1 and x+y = 2
Here, x=1/2 and y=3/2, with the result that x² + y² = 5/2.
Case 4: x-y = -1 and x+y = -2
Here, x=-3/2 and y=-1/2, with the result that x² + y² = 5/2.
In each case, x² + y² = 5/2.
SUFFICIENT.
The correct answer is C.
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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
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