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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, 14:45
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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
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Director
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Re: DS: value of x [#permalink]
02 Jul 2006, 15:34
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
AD-BCE
(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, 19:44, edited 1 time in total.
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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, 17:41
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.
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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)
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Re: DS: value of x [#permalink]
03 Jul 2006, 07:11
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.
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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, 16:27
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, 16:27
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