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Quadratic Question (Hard difficulty) Data Sufficienct

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NinjaScout
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Quadratic Question (Hard difficulty) Data Sufficienct [#permalink] New post   06 Feb 2024, 10:45
Hi can someone help me understand this solition a bit.

what is the value of X

1) x2 - y2  = 54  
2) x - y = 9 

Solution provided:

Statement #1
x2 - y2  = 54
(x-y)(x+y) = 54
Not sufficient

Statement #2
 x - y = 9 
Not sufficient

Together
Plug  x - y = 9  into x2 - y2  = 54
(x-y)(x+y) = 54 --> 9(x+y) = 54
Reduce: 1(x+y) = 6

You have two equations now:
x - y = 9 and x + y = 6 --> add them

x - y = 9
x + y = 6
2x + 0 = 15
x = 15/2 
Sufficient 

Question:
After plugging equation 1 into 2 you have already used both equations. Ive never seen anyone add the equations after substitution...unless I'm totally blanking. Wouldnt that create redundency? Is that allowed?
 ­
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Faqihshinoda
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Quadratic Question (Hard difficulty) Data Sufficienct [#permalink] New post   06 Feb 2024, 10:56
Yes it is allowed. It is called elimination.

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HarshaBujji
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Re: Quadratic Question (Hard difficulty) Data Sufficienct [#permalink] New post   08 Feb 2024, 17:36
NinjaScout wrote:
Hi can someone help me understand this solition a bit.

what is the value of X

1) x2 - y2  = 54  
2) x - y = 9 

Solution provided:

Statement #1
x2 - y2  = 54
(x-y)(x+y) = 54
Not sufficient

Statement #2
 x - y = 9 
Not sufficient

Together
Plug  x - y = 9  into x2 - y2  = 54
(x-y)(x+y) = 54 --> 9(x+y) = 54
Reduce: 1(x+y) = 6

You have two equations now:
x - y = 9 and x + y = 6 --> add them

x - y = 9
x + y = 6
2x + 0 = 15
x = 15/2 
Sufficient 

Question:
After plugging equation 1 into 2 you have already used both equations. Ive never seen anyone add the equations after substitution...unless I'm totally blanking. Wouldnt that create redundency? Is that allowed?
 ­

­Here there are 2 equations & 2 variables hence it's possible to get the solns.. 
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KarishmaB
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Re: Quadratic Question (Hard difficulty) Data Sufficienct [#permalink] New post   16 Apr 2024, 22:26
Expert Reply
NinjaScout wrote:
Hi can someone help me understand this solition a bit.

what is the value of X

1) x2 - y2  = 54  
2) x - y = 9 

Solution provided:

Statement #1
x2 - y2  = 54
(x-y)(x+y) = 54
Not sufficient

Statement #2
 x - y = 9 
Not sufficient

Together
Plug  x - y = 9  into x2 - y2  = 54
(x-y)(x+y) = 54 --> 9(x+y) = 54
Reduce: 1(x+y) = 6

You have two equations now:
x - y = 9 and x + y = 6 --> add them

x - y = 9
x + y = 6
2x + 0 = 15
x = 15/2 
Sufficient 

Question:
After plugging equation 1 into 2 you have already used both equations. Ive never seen anyone add the equations after substitution...unless I'm totally blanking. Wouldnt that create redundency? Is that allowed?
 ­

­You can use the given data as many times as you wish and in as many different forms as you wish. 
Consider this - here you are using statement 2 to elicit a particular information (x+y) from statement 1. Then you are using both that information and statement 2 together to get the answer. Nothing wrong in it. 
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gmatclubot
Re: Quadratic Question (Hard difficulty) Data Sufficienct [#permalink]
16 Apr 2024, 22:26
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Johnson, CBS, and McDonough Moderator
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