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# If x + 2y = 2 and (x + y)^2 = 9, which of the following is a possible

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Math Expert
Joined: 02 Sep 2009
Posts: 58117
If x + 2y = 2 and (x + y)^2 = 9, which of the following is a possible  [#permalink]

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06 Feb 2019, 03:43
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Difficulty:

45% (medium)

Question Stats:

69% (01:57) correct 31% (02:33) wrong based on 67 sessions

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If x + 2y = 2 and (x + y)^2 = 9, which of the following is a possible value of y ?

A. -8
B. -5
C. -3/2
D. 3/2
E. 5

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Posts: 1456
Concentration: Accounting, Finance
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Re: If x + 2y = 2 and (x + y)^2 = 9, which of the following is a possible  [#permalink]

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06 Feb 2019, 03:49
Bunuel wrote:
If x + 2y = 2 and (x + y)^2 = 9, which of the following is a possible value of y ?

A. -8
B. -5
C. -3/2
D. 3/2
E. 5

nice question.

x + 2y = 2

(x + y)^2 = 9

x + y = 3 or -3.

...........

x + 2y = 2
x + y = -3
..................................deduct second from the first.
y = 5.

**** anyone can form equation considering x + y =3. but we are looking for possible value . need to consider both aspects.
Director
Joined: 09 Mar 2018
Posts: 999
Location: India
If x + 2y = 2 and (x + y)^2 = 9, which of the following is a possible  [#permalink]

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06 Feb 2019, 22:53
Bunuel wrote:
If x + 2y = 2 and (x + y)^2 = 9, which of the following is a possible value of y ?

A. -8
B. -5
C. -3/2
D. 3/2
E. 5

Out of the 3 ways which i thought of solving this question, inline is the easiest

(x + y)^2 = 9, can be written as x+ y = 3 or x+y =-3

(a)
x+2y = 2
x+y = 3

(b)
x+2y = 2
x+y =-3

b when solved gives us answer as E.
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Joined: 12 Sep 2017
Posts: 301
If x + 2y = 2 and (x + y)^2 = 9, which of the following is a possible  [#permalink]

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Updated on: 22 Feb 2019, 14:08
Hello KanishkM !

Can someone please give me some advice on how to improve the "way" to approach this kind of exercises?

In the end, I made it correct but I was stuck several minutes doing it in the wrong way, I was expanding the term:

(x + y)^2 = 9 and x + 2y = 2

x^2 + 2xy + y^2 = 9

x2 + y (2x + y) = 9

At this point, I thought I was going well but I couldn't get further and then the time went against me and I got stressed and stopped thinking.

Thank you so much in advance!

Thank you KanishkM narendran1990 !

Originally posted by jfranciscocuencag on 21 Feb 2019, 21:16.
Last edited by jfranciscocuencag on 22 Feb 2019, 14:08, edited 2 times in total.
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Re: If x + 2y = 2 and (x + y)^2 = 9, which of the following is a possible  [#permalink]

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21 Feb 2019, 22:09
Hello Jfrancis,

I solved the question in the same way you have done, though it doesn't yield a quick solution, it's solvable:

Taking from your last step - x^2 + y^2 + 2y.x = 9

x^2 + y^2+(2-x).x=9 [x+2y=2, rewritten as 2y=2-x)

Upon expansion, x^2 cancels out giving the equation, 2x+y^2=9

2(2-2y)+y^2=9

4-4y+y^2 = 9

y^2-4y = 5 , taking y as common , y(y-4)=5, hence y can be 5 or 9. Only 5 is in the answer choice.
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Joined: 09 Mar 2018
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Location: India
Re: If x + 2y = 2 and (x + y)^2 = 9, which of the following is a possible  [#permalink]

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22 Feb 2019, 05:14
jfranciscocuencag wrote:
Hello KanishkM !

Can someone please give me some advice on how to improve the "way" to approach this kind of exercises?

In the end, I made it correct but I was stuck several minutes doing it in the wrong way, I was expanding the term:

(x + y)^2 = 9 and x + 2y = 2

x^2 + 2xy + y^2 = 9

x2 + y (2x + y) = 9

At this point, I thought I was going well but I couldn't get further and then the time went against me and I got stressed and stopped thinking.

Thank you so much in advance!

jfranciscocuencag

So i believe you got the response on how this question could have been solved by using your approach.

Whenever you get such equations with two vairables, try to reduce the question in simplest form. If after substitution you are able to get an easy expression, you are on right track, if not, then you missed out on something.

Eg : just for illustration
2x -3y = 6, find x

y = (2x-6) /3

Whenever you think you are taking time to solve the question, you assumed something, in turn made the question complicated.

Posted from my mobile device
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.
Re: If x + 2y = 2 and (x + y)^2 = 9, which of the following is a possible   [#permalink] 22 Feb 2019, 05:14
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