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# x^2-y^2 = 28 and x - y = 8 then what is the average of x and y?

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Senior RC Moderator
Joined: 02 Nov 2016
Posts: 4908
GPA: 3.39
x^2-y^2 = 28 and x - y = 8 then what is the average of x and y?  [#permalink]

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11 Dec 2019, 10:58
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25% (medium)

Question Stats:

77% (01:00) correct 23% (01:18) wrong based on 26 sessions

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If $$x^2-y^2 = 28$$ and $$x - y = 8$$ then what is the average of $$x$$ and $$y$$?

A. 3.5

B. 1.75

C. 7

D. 8

E. 5

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Senior Manager
Joined: 16 Feb 2015
Posts: 264
Location: United States
Concentration: Finance, Operations
Re: x^2-y^2 = 28 and x - y = 8 then what is the average of x and y?  [#permalink]

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11 Dec 2019, 11:04
2
$$x^2-y^2 = 28$$ and $$x - y = 8$$ then what is the average of $$x$$ and $$y$$?

A. 3.5

B. 1.75

C. 7

D. 8

E. 5

Explanation:
Given: x-y=8
x^2-y^2 = 28
(x+y)(x-y)=28
Putting value of x-y =8
x+y=28/8
x+y=3.5----1

As we know averge of x&y = (x+y)/2
from 1,
3.5/2= 1.75

IMO-B

Please Give Kudos, If you find my explanation Good Enough
Intern
Joined: 07 Nov 2019
Posts: 3
Re: x^2-y^2 = 28 and x - y = 8 then what is the average of x and y?  [#permalink]

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11 Dec 2019, 13:09
The answer can be 7 here
7/2/2/1 = 7/2*2/1 = 7

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Intern
Joined: 13 Apr 2018
Posts: 13
Re: x^2-y^2 = 28 and x - y = 8 then what is the average of x and y?  [#permalink]

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11 Dec 2019, 13:50
X^2 - y^2 = 28
(x+y)(x-y) = 28
(x+y)×8 = 28
(x+y) = 28/8
(x+y)/2 = 28/16
(x+y)/2 = 1.75

Posted from my mobile device
Intern
Joined: 03 Jan 2019
Posts: 10
Re: x^2-y^2 = 28 and x - y = 8 then what is the average of x and y?  [#permalink]

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11 Dec 2019, 14:02
If $$x^2-y^2 = 28$$ and $$x - y = 8$$ then what is the average of $$x$$ and $$y$$?

A. 3.5

B. 1.75

C. 7

D. 8

E. 5

from the information we know that:
x^2 - y^2 = 28;
x - y = 8; and
x^2 - y^2 is a simplified form of (x+y)(x-y); thus

(x+y)(x-y) = 28
(x+y)(8) = 28
(x+y) = 28/8

since we are asked the average of x and y or (x+y)/2, thus
(28/8) / 2 = 1.75 (B)
Senior Manager
Joined: 16 Feb 2015
Posts: 264
Location: United States
Concentration: Finance, Operations
Re: x^2-y^2 = 28 and x - y = 8 then what is the average of x and y?  [#permalink]

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11 Dec 2019, 20:13
bhvya324 wrote:
The answer can be 7 here
7/2/2/1 = 7/2*2/1 = 7

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Dear bhvya324 ,

How u have solved to get 7 as the answer. Please explain. So we can find the mistake.

Regards,
Rajat Chopra
Intern
Joined: 07 Nov 2019
Posts: 3
Re: x^2-y^2 = 28 and x - y = 8 then what is the average of x and y?  [#permalink]

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12 Dec 2019, 01:09
Sure,

(X+y) 8 = 28 = 28/8 = 7/2

Posted from my mobile device
Senior Manager
Joined: 16 Feb 2015
Posts: 264
Location: United States
Concentration: Finance, Operations
x^2-y^2 = 28 and x - y = 8 then what is the average of x and y?  [#permalink]

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12 Dec 2019, 01:21
bhvya324 wrote:
Sure,

(X+y) 8 = 28 = 28/8 = 7/2

Posted from my mobile device

bhvya324
Till Above You are right.
After this Question has asked for Average of x+y.
So we need to divide it by 2.

So, u got the value of x+y = 7/2
For Average, divide it by 2.
Therefore, 7/4 =1.75

I hope U will understand it. Pls do PM, if you didn't get it.

Regards,
Rajat Chopra
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9143
Location: United States (CA)
Re: x^2-y^2 = 28 and x - y = 8 then what is the average of x and y?  [#permalink]

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12 Dec 2019, 19:48
If $$x^2-y^2 = 28$$ and $$x - y = 8$$ then what is the average of $$x$$ and $$y$$?

A. 3.5

B. 1.75

C. 7

D. 8

E. 5

Using the difference of squares, the first equation becomes:

(x + y)(x - y) = 28

Substituting, we have:

(x + y) * 8 = 28

x + y = 28/8 = 7/2 = 3.5

Thus, the average of x and y is (x + y)/2 = 3.5/2 = 1.75.

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Re: x^2-y^2 = 28 and x - y = 8 then what is the average of x and y?   [#permalink] 12 Dec 2019, 19:48
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