Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

If both sides are squared then absolute value sign is eliminated and stem is 2XZ-2XY=Z^2-Y^2 => 2X*(Z-Y)=(Z-Y)*(Z+Y)or 2X=Y+Z
now A) is useless IMO
B) IS SUFF X=5

B looks appealing but has one fault.
Say y and z both be 5 that satisfies B y+z = 10
The equation becomes.......
|x-5| = |x-5|
With this x can be any number.
hence we cannot get the answer with B.
But if we know that y not= z
we will get eh answer

Re: DS: Absolute values [#permalink]
10 Jun 2006, 17:32

Professor 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.

|x - y| = |x - z| means
x-y=+/-(x-z)
If x-y=x-z then y=z, and x can be anything
If x-y=-(x-z) then 2x=y+z

(1) y<>z we know then 2x=y+z. However we don't know the value of y+z therefore value of x is not determinable.
(2) y+z=10, we don't know if x-y=x-z or -(x-z) so the value of x is indeterminable.

Combined it's obvious x=5. Therefore C.

Something that is worth of notice is that we often have what's given in (1) in mind when checking (2) and thought that (2) itself is sufficient without realizing that we are actually assuming (1). I've made this mistake before. Be careful with this when you do your test. _________________

Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.

No OA for this one too. C looks good as explained by Honghu and others.

but honghu whats wrong with the approach used by BG.

BG wrote:

If both sides are squared then absolute value sign is eliminated and stem is 2XZ-2XY=Z^2-Y^2 => 2X*(Z-Y)=(Z-Y)*(Z+Y)or 2X=Y+Z

now A) is useless IMO

B) IS SUFF X=5

Prof,

In BG's approach, Z-Y cannot be cancelled from both sides unless we know that Z-Y <> 0. If Z-Y = 0, the expression becomes 0/0 or indeterminate one.
2XZ-2XY=Z^2-Y^2
=> 2X*(Z-Y)=(Z-Y)*(Z+Y)
=> (Z-Y) (2X-Z-Y) =0
=> Z-Y = 0 or X = (Z+Y)/2
1. Z <> Y, but we don't know the value of Z+Y
2. Z+Y = 10, but we don't know if Z<>Y

Combine. SUFF to say X = 10/2 = 5. _________________

"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."

1. My favorite football team to infinity and beyond, the Dallas Cowboys, currently have the best record in the NFL and I’m literally riding on cloud 9 because...

I couldn’t help myself but stay impressed. young leader who can now basically speak Chinese and handle things alone (I’m Korean Canadian by the way, so...