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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

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:

71% (01:52) correct
29% (01:04) wrong based on 147 sessions

Is |x-z| = |y-z|?

1) x=y 2) |x|-z = |y|-z

Here is my problem. I solved this two ways and got two different answers. The first method was to square both sides and simplify and in doing so I got the right answer. The other way was to take the positive and negative cases of the stem in which case I got two separate solutions and the incorrect answer, i.e.

(x-z) = (y-z) OR (x-z) = (z-y)

Can someone tell me why the second method wouldn't be used in this case?

Re: Is |x-z| = |y-z|? [#permalink]
05 Jul 2013, 11:02

1

This post received KUDOS

1

This post was BOOKMARKED

WholeLottaLove wrote:

Here is my problem. I solved this two ways and got two different answers. The first method was to square both sides and simplify and in doing so I got the right answer. The other way was to take the positive and negative cases of the stem in which case I got two separate solutions and the incorrect answer, i.e.

(x-z) = (y-z) OR (x-z) = (z-y)

Can someone tell me why the second method wouldn't be used in this case?

2) |x|-z = |y|-z So \(|x|=|y|\) this could mean \(y=x\) (as above) or \(y=-x\). In the case y=x the answer is YES, in the other case (x=-y) you get \(|-y-z| = |y-z|\) and the answer could be NO, consider z=1 and y=2 for example; or YES (all zeros). Not sufficient

I am sorry but I did not get what you did for the second statement... and there is no need t square the terms here. This could be solved more easily _________________

It is beyond a doubt that all our knowledge that begins with experience.

Re: Is |x-z| = |y-z|? [#permalink]
07 Jul 2013, 17:10

Sorry, I did a poor job explaining what I did wrong.

Is |x-z| = |y-z|?

1) x=y

|x-z| = |y-z|

So, I did this one of two ways:

The first way: squaring both sides: |x-z| = |y-z| (x-z)*(x-z) = (y-z)*(y-z) x^2-2xz+z^2 = y^2-2yz+z^2 x^2-2xz=y^2-2yz x(x-2z)=y(y-2z) x=y y(y-2z)=y(y-2z)

Sufficient

The second way was to take the positive and negative cases of |x-z| = |y-z| i.e.

x-z = y-z x=y y-z=y-z OR x-z=z-y x=y y-z=z-y

See my problem?

Zarrolou wrote:

WholeLottaLove wrote:

Here is my problem. I solved this two ways and got two different answers. The first method was to square both sides and simplify and in doing so I got the right answer. The other way was to take the positive and negative cases of the stem in which case I got two separate solutions and the incorrect answer, i.e.

(x-z) = (y-z) OR (x-z) = (z-y)

Can someone tell me why the second method wouldn't be used in this case?

2) |x|-z = |y|-z So \(|x|=|y|\) this could mean \(y=x\) (as above) or \(y=-x\). In the case y=x the answer is YES, in the other case (x=-y) you get \(|-y-z| = |y-z|\) and the answer could be NO, consider z=1 and y=2 for example; or YES (all zeros). Not sufficient

I am sorry but I did not get what you did for the second statement... and there is no need t square the terms here. This could be solved more easily

Re: Is |x-z| = |y-z|? [#permalink]
07 Jul 2013, 21:09

1

This post received KUDOS

Your mistake was that you solved the absolutes first and the variables inside it later. You should've solved the variables first as you already know that x=y, for both the positive and the negative values of either of the two variables. Thus the difference between x and z will be the same as is between y and z.

Re: Is |x-z| = |y-z|? [#permalink]
07 Jul 2013, 22:19

1

This post received KUDOS

WholeLottaLove wrote:

The second way was to take the positive and negative cases of |x-z| = |y-z| i.e.

x-z = y-z x=y y-z=y-z OR x-z=z-y x=y y-z=z-y

See my problem?

2) |x|-z = |y|-z

You do NOT know that y=x from statement 2. In your method you substitute x=y, but this is not what 2 says

\(y=+-x\)<== this is what is says, so

\(x-z = y-z\) if \(y=x\) \(y-z=y-z\) true but if \(y=-x\) you get \(x-z=-x-z\) that could be true or not. Same thing for the other case \(x-z=z-y\). Hope it's clear _________________

It is beyond a doubt that all our knowledge that begins with experience.

Re: Is |x-z| = |y-z|? [#permalink]
08 Jul 2013, 15:06

Hmmm...I think you misunderstood me (or maybe I misunderstood you?) I wasn't refering to 2) above. I was saying that for 1) I solved two different ways. One way was to square |x-z|=|y-z| and the other way was to take the positive and negative case of |x-z|=|y-z| i.e. (x-z)=(y-z) OR (x-z)= -(y-z).

Zarrolou wrote:

WholeLottaLove wrote:

The second way was to take the positive and negative cases of |x-z| = |y-z| i.e.

x-z = y-z x=y y-z=y-z OR x-z=z-y x=y y-z=z-y

See my problem?

2) |x|-z = |y|-z

You do NOT know that y=x from statement 2. In your method you substitute x=y, but this is not what 2 says

\(y=+-x\)<== this is what is says, so

\(x-z = y-z\) if \(y=x\) \(y-z=y-z\) true but if \(y=-x\) you get \(x-z=-x-z\) that could be true or not. Same thing for the other case \(x-z=z-y\). Hope it's clear

Re: Is |x-z| = |y-z|? [#permalink]
08 Jul 2013, 22:05

1

This post received KUDOS

WholeLottaLove wrote:

The second way was to take the positive and negative cases of |x-z| = |y-z| i.e.

x-z = y-z x=y y-z=y-z OR x-z=z-y x=y y-z=z-y

See my problem?

Ok, now I got it.

So the first case you get \(y-z=y-z\) which is fine.

Then you analyze the case in which \(|x-z|=x-z\) so \(x>z\) in this scenario \(|y-z|=z-y\) so \(y<z\) in this scenario

So \(x\) is a number greater than \(z\), and \(y\) is a number lesser than \(z\) => they cannot be equal (\(x\neq{y}\)). This is not a valid scenario to substitute \(x=y\).

The only case in which \(y-z=z-y\) is true is when the terms are all zeros (as I stated in a previous post).

Hope it's clear. _________________

It is beyond a doubt that all our knowledge that begins with experience.

Re: Is |x-z| = |y-z|? [#permalink]
11 Jul 2013, 10:35

RnH wrote:

Your mistake was that you solved the absolutes first and the variables inside it later. You should've solved the variables first as you already know that x=y, for both the positive and the negative values of either of the two variables. Thus the difference between x and z will be the same as is between y and z.

This is a great Plug-in question btw.

Interesting. It's always been my understanding that we solve out the stem as much as possible before we move on to the two statements?

Re: Is |x-z| = |y-z|? [#permalink]
11 Jul 2013, 10:38

1

This post received KUDOS

Expert's post

WholeLottaLove wrote:

RnH wrote:

Your mistake was that you solved the absolutes first and the variables inside it later. You should've solved the variables first as you already know that x=y, for both the positive and the negative values of either of the two variables. Thus the difference between x and z will be the same as is between y and z.

This is a great Plug-in question btw.

Interesting. It's always been my understanding that we solve out the stem as much as possible before we move on to the two statements?

That's not always correct way of solving. Consider this question, for example. _________________

Re: Is |x-z| = |y-z|? [#permalink]
11 Jul 2013, 10:50

1

This post received KUDOS

WholeLottaLove wrote:

Is |x-z| = |y-z|?

2) |x|-z = |y|-z |x|=|y| x=y OR x=-y

Positive |x-z| = |y-z| x-z = (y-z) x-z = y-z

y-z = y-z OR -y=z = y-z

Negative |x-z| = |y-z| (x-z) = -(x-z) x-z = z-x

y-z = z-y OR -y-z = z+y

Is that why it is insufficient?

I think you are over complicating it. Refer here: is-x-z-y-z-155459.html#p1243251 and tell me if everything is clear There is no need to consider all possible cases _________________

It is beyond a doubt that all our knowledge that begins with experience.

Re: Is |x-z| = |y-z|? [#permalink]
11 Jul 2013, 12:17

I see what you are saying and I understand the solution. You are right, I am over complicating it...I am just trying to figure out how to go about this problem and when to use what methods for what problems.

Thanks!!!

Zarrolou wrote:

WholeLottaLove wrote:

Is |x-z| = |y-z|?

2) |x|-z = |y|-z |x|=|y| x=y OR x=-y

Positive |x-z| = |y-z| x-z = (y-z) x-z = y-z

y-z = y-z OR -y=z = y-z

Negative |x-z| = |y-z| (x-z) = -(x-z) x-z = z-x

y-z = z-y OR -y-z = z+y

Is that why it is insufficient?

I think you are over complicating it. Refer here: is-x-z-y-z-155459.html#p1243251 and tell me if everything is clear There is no need to consider all possible cases

Re: Is |x-z| = |y-z|? [#permalink]
03 Apr 2014, 10:28

Is |x-z| = |y-z|?

1) x=y 2) |x|-z = |y|-z

I am weak in DS so trying to approach the question to solve them faster

Is |x-z| = |y-z|?

In English : Is the distance between x and z equal to the distance between y and z ?

Statement 1: Says x = y in other words x and y are essentially the same point . So for the stem question distance would be the same and hence information here is sufficient .

Statement 2: Simplifying |x|-z = |y|-z

|x| = |y| which would mean y = x or y = -x ?

Hence distances for x and z and y and z are same if y = x . They differ for x and z and y and z if y = -x .

gmatclubot

Re: Is |x-z| = |y-z|?
[#permalink]
03 Apr 2014, 10:28

Hey, everyone. After a hectic orientation and a weeklong course, Managing Groups and Teams, I have finally settled into the core curriculum for Fall 1, and have thus found...

MBA Acceptance Rate by Country Most top American business schools brag about how internationally diverse they are. Although American business schools try to make sure they have students from...

For the past couple of weeks I’ve been winding down my affairs in New York by working on consulting projects, trying every exotic sandwich there is and then intensely...