What is the value of x given that |x - y| = |x - z| ?

Question

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

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nkme2007 · Answer

Given that |x-y| = |x-z|

=> x-y=x-z or x-y=-(x-z)
=> y=z or 2x=y+z

From Statement 1, y is not equal to z.
Hence, 2x=y+z only remains.
But, we don't know the value of y and z and hence, we don't know what x is.

So, INSUFFICIENT.

From Statement 2, y+z = 10
Hence, 2x=10
=>x=5
But, when y and z are equal, x can be any value.
So, INSUFFICIENT

Combining both

Hence, y+z = 10
Hence, 2x=10
=>x=5

OA = C

RaghavKhanna · Answer

|x - y| = |x - z|

Squaring both sides:
(x - y)^2 = (x - z)^2
(x - y)^2 - (x - z)^2 = 0
(2x - y - z)(z - y) = 0
 Either: x = (y+z)/2 or y = z

Statement 1:  
y ! = z
=> x = (y + z)/2
But no information about values of x and y
=>  Statement 1 is insufficient

Statement 2:  
y + z = 10
=> 2x = 10
=> x = 5

but, if y = z
x can be anything

Statement 2 is insufficient

Statement 1 and Statement 2 together imply x = 5
 Answer: C

Lipun · Answer

|x - y| = |x - z|
=> x = (y+z)/2 
 or y = z (x can be anything)

Statement 1:
y != z
=> x = (y + z)/2
y and z are unknowns

Insufficient

Statement 2:
y + z = 10
case 1: if y = z = 5, then x can be anything
case 2: if y != z, then x = 5

Insufficient

Statement 1 and Statement 2 together:

y != z and y+z = 10 => x = 5

Answer: C

KaramveerBakshi · Answer

Given |x-y|=|x-z|

Using mod function, this means either x-y=x-z (A) or x-y= -(x-z) (B)

(A) gives us y=z and (B) gives us x= (y+z)/10

Statements : 
(1) y is not equal to z. This means that x=(y+z)/10. But we don't know either y or z.
 Insufficient 
(2) Sum of y and z is 10. But we don't know which of (A) or (B) is true.
 Insufficient

Combining, statements (1) and (2) we get y+z = 10 and y not equal to z.
 Sufficient

Answer (C)

daniformic · Answer

|x-y|=|x-z|
x-y=-x+z -> 2x=y+z

S1: y is not equal to z.
We don't know the exact value of y and z -> NS

S2: y+z = 10
If we know that 2x=y+z -> x=5 -> Sufficient

Answer -> B

minustark · Answer

1) x can assume many values.

2) When y = 0, z = 10, x =5. Again when, y = z =5, x can assume any value. Not sufficient.

Both statements together, y = -2, z = 12. x = 5. y =0, z =10. Again x = 5. y = -10, z =20, x will still be 5. Sufficient.

C is the answer.

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What is the value of x given that |x - y| = |x - z| ?

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