What is the value of (x + y)^2 : GMAT Data Sufficiency (DS)
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# What is the value of (x + y)^2

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

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26 Dec 2012, 10:04
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What is the value of (x + y)^2

(1) x^2 + xy = 3
(2) y^2 + yx = 5
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Re: What is the value of (x + y)^2 [#permalink]

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26 Dec 2012, 10:16
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(x+y)^2= x^2 +xy+y^2 +xy

Using the above two statements add both the values which gives the answer 5+3=8

Hope that helps!!!!
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Re: What is the value of (x + y)^2 [#permalink]

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22 Jul 2014, 00:59
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Re: What is the value of (x + y)^2 [#permalink]

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24 Oct 2015, 09:36
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Re: What is the value of (x + y)^2 [#permalink]

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30 Oct 2015, 20:30
What is the value of (x + y)^2

(1) x^2 + xy = 3
(2) y^2 + yx = 5

(1) x^2 + xy = 3

(1) x( x + y) = 3
therefore either x = 3 or x+y = 3

not sufficient

(2) y^2 + yx = 5
y( y + x ) = 5

therefore either y = 5 or x+y = 5
not sufficient

together
x+y = have different value that is from st 1 --> x + y = 3 and st 2 --> x+y = 5

so we have x = 3 and y = 5
x +y = 8

hence C ans .

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

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01 Nov 2015, 08:55
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

What is the value of (x + y)^2

(1) x^2 + xy = 3
(2) y^2 + yx = 5

There are 2 variable (x,y) and 2 equations from the question and the conditions; there is high chance (D) will be our answer.
If we look at the 2 conditions together,
we get x^2+xy+y^2+yx=x^2+2xy+y^2=8, (x+y)^2=8 when we add them together.
The conditions are sufficient, and the answer becomes (C).

For cases where we need 2 more equation, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
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Re: What is the value of (x + y)^2 [#permalink]

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01 Nov 2015, 09:20
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x+y = have different value that is from st 1 --> x + y = 3 and st 2 --> x+y = 5

so we have x = 3 and y = 5
x +y = 8

hence C ans .
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Re: What is the value of (x + y)^2 [#permalink]

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11 May 2016, 22:42
jsphcal wrote:
What is the value of (x + y)^2

(1) x^2 + xy = 3
(2) y^2 + yx = 5

From statement 1, (x+y) = 3 or x=3, and from statement 2, (x+y) = 5 or y=5. From any of them we can figure out the value of (x+y)^2
Instead we're adding the statements to derive at the formula (x+y)^2. Could someone please clarify why we're doing this?

Thank you.
Regards.
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Re: What is the value of (x + y)^2 [#permalink]

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11 May 2016, 22:54
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Expert's post
jsphcal wrote:
What is the value of (x + y)^2

(1) x^2 + xy = 3
(2) y^2 + yx = 5

From statement 1, (x+y) = 3 or x=3, and from statement 2, (x+y) = 5 or y=5. From any of them we can figure out the value of (x+y)^2
Instead we're adding the statements to derive at the formula (x+y)^2. Could someone please clarify why we're doing this?

Thank you.
Regards.

hi,
(1) x^2 + xy = 3....... x(x+y) = 3............
this does not mean (x+y) = 3 or x=3..........
It ONLY means x\neq{0} and x+y will depend on x
and there can be lot of combinations..
x= 1/3 and x+y = 9
if x= 3, x+y = 1..
x=1, x+y = 3..
so different values..

(2) y^2 + yx = 5
similarly you can find many combinations for x and y..
we are not told if x and y are + or - or integer or fraction
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Re: What is the value of (x + y)^2   [#permalink] 11 May 2016, 22:54
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