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# What is the value of x given that |x-y| = |x-z| (1) y is not

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Manager
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What is the value of x given that |x-y| = |x-z| (1) y is not [#permalink]  02 Jul 2006, 13:45
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What is the value of x given that |x-y| = |x-z|

(1) y is not equal to z

(2) the sum of y and z is 10
Director
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Re: DS: value of x [#permalink]  02 Jul 2006, 14:34
consultinghokie wrote:
What is the value of x given that |x-y| = |x-z|

(1) y is not equal to z

(2) the sum of y and z is 10

(1) is INSUFF, does not tell us anything about x, then look for B,C or E

(2) y+z = 10

case 1 : x-y = x-z =>y=z

case 2: y-x = z-x =>y=z , y+z = 10 and y = z => y = z = 5, but this does not tell us what X is, x can, in fact, be any number.

(E)
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Manager
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I thinks its B

the given equation is |x-y| = |x-z| which when squared gives

=> x^2+y^2-2xy = x^2+z^2-2xz
=> y^2 - z^2 + 2xz - 2xy = 0
=> (y-z)[(y+z)-2x] = 0
=> (y+z)-2x = 0
From statement 2 it is
10 - 2x = 0 => x = 5

Let me know if mised something

Last edited by humans on 02 Jul 2006, 18:44, edited 1 time in total.
Director
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humans wrote:
I thinks its B

the given equation is |x-y| = |x-z| which when squared gives

=> x^2+y^2-2xy = x^2+z^2-2zy
=> y^2 - z^2 + 2zy - 2xy = 0
=> (y-z)[(y+z)-2x] = 0
=> (y+z)-2x = 0
From statement 2 it is
10 - 2x = 0 => x = 5

Let me know if mised something

humans - what I'm not sure is, in a condition where y = z so that y = z = 5, we have infinite solutions for the equation (x is any integer). How can it be B then? (your solution seems OK, so I can't make out what I'm missing)
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Re: DS: value of x [#permalink]  02 Jul 2006, 16:41
consultinghokie wrote:
What is the value of x given that |x-y| = |x-z|

(1) y is not equal to z
(2) the sum of y and z is 10

1. x-y = x-z or -x +z
if x-y = x-z
y = z which is incorrect cuz it is given in st 1 that y is not equal to z.

if x-y = -x +z
x = (y+z)/2 but we donot know the value.

2. same repets but x = (y+z)/2 = 10/2 = 5
So B.
Senior Manager
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(C)

I. Insufficient.

II. gives us anyvalue of x when y =z, and x = 5, given y + z = 10
Insufficient.

Combining,
(C)
Director
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Re: DS: value of x [#permalink]  03 Jul 2006, 06:11
consultinghokie wrote:
What is the value of x given that |x-y| = |x-z|

(1) y is not equal to z

(2) the sum of y and z is 10

stmt 1,

you can have 4 situations here

both +ve, both -ve , LHS +ve - RHS -ve and vice versa -- it doesnt tell you anything about x

stmt 2,

the only equation which satisfies is (x-y)= -(x-z) , therefore x=(y+z)/2=5. Hence B.
Intern
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C

I. insufficient, could result in any value for X

II. insufficient; if y and z are not 5, then x=5; however if y and z are equal to 5 then x can be any value. Thus, I and II combined allows you to solve for x.
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Re: DS: value of x [#permalink]  03 Jul 2006, 15:27
consultinghokie wrote:
What is the value of x given that |x-y| = |x-z|

(1) y is not equal to z

(2) the sum of y and z is 10

C

Squaring both sides and then solving we get

(y-z)(y+z-2x) = 0

St1: In above equation we get y+z-2x = 0: Multiple Solutions: INSUFF

St2: if y+z = 10 then from above eq we get (y-z)(10-2x) = 0 : Multiple Solutions: INSUFF

Combined: From above equation we have 10-2x = 0 i.e x = 5: SUFF
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Re: DS: value of x   [#permalink] 03 Jul 2006, 15:27
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