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:

Re: If A<Y<Z<B, is /Y-A/< /Y-B/? [#permalink]
18 Aug 2009, 19:26

3

This post received KUDOS

yezz wrote:

If A<Y<Z<B, is /Y-A/< /Y-B/?

1) /Z-A/ < /Z-B/

2) /Y-A/ < /Z-B/

Consider A,Y,Z,B lying on the straight line

Given that A<Y<Z<B

1) statement 1 talks nothing about Y but however it clearly brings out the fact that the distance between B&Z is greater than the distance between A&Z. Now we know that since Y<Z, Y lies closer to A than Z and farther from B than Z. hence answers our question

2) Statement 2 : it says distance between Y&A is less than the distance between Z&B. As already stated Y lies closer to A than Z and farther to B than Z, hence this answers the question as well

Re: If A<Y<Z<B, is /Y-A/< /Y-B/? [#permalink]
28 Oct 2009, 19:41

D

I drew a number line for this which helped me conceptualize the problem (4 points A, Y, Z and B). (A) Given distance between Z and B is greater than Z and A is sufficient as Y lies between A and Z. (B) Similar approach as A. Sufficient.

Re: If A<Y<Z<B, is |Y-A|< |Y-B|? [#permalink]
09 Aug 2012, 00:26

16

This post received KUDOS

Expert's post

7

This post was BOOKMARKED

If A<Y<Z<B, is |Y-A|< |Y-B|?

Since given that \(A<Y\) (\(Y-A>0\)), then \(|Y-A|=Y-A\); Since given that \(Y<B\) (\(Y-B<0\)), then \(|Y-B|=B-Y\);

So, the question becomes: is \(Y-A<B-Y\)? --> is \(2Y<A+B\)?

(1) |Z-A| < |Z-B|. The same way as above: Since given that \(A<Z\) (\(Z-A>0\)), then \(|Z-A|=Z-A\); Since given that \(Z<B\) (\(Z-B<0\)), then \(|Z-B|=B-Z\);

So, we have that: \(Z-A<B-Z\) --> \(2Z<A+B\). Now, since \(Y<Z\), then \(2Y<2Z\), so \(2Y<2Z<A+B\). Sufficient.

(2) |Y-A| < |Z-B|. The same way as above: Since given that \(A<Y\) (\(Y-A>0\)), then \(|Y-A|=Y-A\); Since given that \(Z<B\) (\(Z-B<0\)), then \(|Z-B|=B-Z\);

So, we have that: \(Y-A<B-Z\) --> \(Y+Z<A+B\). Now, since \(Y<Z\), then \(2Y<Y+Z\) (\(2Y=Y+Y<Y+Z\) ), so \(2Y<Y+Z<A+B\). Sufficient.

Re: If A<Y<Z<B, is |Y-A|< |Y-B|? [#permalink]
09 Aug 2012, 09:54

yezz wrote:

If A<Y<Z<B, is |Y-A|< |Y-B|?

(1) |Z-A| < |Z-B|

(2) |Y-A| < |Z-B|

Use the meaning of the absolute value: distance between two points. Rephrasing the question: we are given 4 distinct points on the number line, A, Y, Z, B, from left to right (in increasing order). The question is: is the distance between A and Y smaller than the distance between Y and B?

(1) A---Y--Z------B would visualize a typical situation, distance between A and Z less than the distance between Z and B. Since Y is between A and Z, the answer to the question "is the distance between A and Y smaller than the distance between Y and B" is definitely YES. Sufficient.

(2) A---Y-Z----B this would be a typical situation, distance between A and Y, less than the distance between Z and B. Now Z is between Y and B, so again, the distance between A and Y is smaller than the distance between Y and B. Sufficient.

Answer D _________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

Re: If A<Y<Z<B, is /Y-A/< /Y-B/? [#permalink]
09 Aug 2012, 10:31

gmattokyo wrote:

D

I drew a number line for this which helped me conceptualize the problem (4 points A, Y, Z and B). (A) Given distance between Z and B is greater than Z and A is sufficient as Y lies between A and Z. (B) Similar approach as A. Sufficient.

Please correct this if wrong.

You are absolutely right. Sorry, I missed your post and I have just presented a similar solution. _________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

Re: If A<Y<Z<B, is |Y-A|< |Y-B|? [#permalink]
18 Oct 2012, 04:21

Bunuel,

For statement 1, everything works until z-a<b-z = 2z<a+b. y<z so 2y<2z ok but this does not mean 2z<a+b. we know that a<y<z<b. Now if we plug in values say 3<4<5<6 then 2(5) is not < 3+6 i.e 2z<a+b.

What could I be doing wrong here Bunuel? Could you please help me with that. Thanks in advance!

Re: If A<Y<Z<B, is |Y-A|< |Y-B|? [#permalink]
23 Oct 2012, 05:52

2

This post received KUDOS

Expert's post

liarish wrote:

Bunuel,

For statement 1, everything works until z-a<b-z = 2z<a+b. y<z so 2y<2z ok but this does not mean 2z<a+b. we know that a<y<z<b. Now if we plug in values say 3<4<5<6 then 2(5) is not < 3+6 i.e 2z<a+b.

What could I be doing wrong here Bunuel? Could you please help me with that. Thanks in advance!

You derived yourself that \(2Z<A+B\) and later you are negating that (blue parts).

We know from (1) that \(2Z<A+B\) (i) . We also know that \(Y<Z\), so \(2Y<2Z\) (ii).

Now, combine (i) and (ii): 2Z is less than A+B and 2Y is less than 2Z, thus 2Y is less than A+B (\(2Y<2Z<A+B\)).

Also, numbers you chose does not satisfy \(2Z<A+B\).

Re: If A<Y<Z<B, is /Y-A/< /Y-B/? [#permalink]
06 Apr 2013, 09:56

alwynjoseph wrote:

yezz wrote:

If A<Y<Z<B, is /Y-A/< /Y-B/?

1) /Z-A/ < /Z-B/

2) /Y-A/ < /Z-B/

Consider A,Y,Z,B lying on the straight line

Given that A<Y<Z<B

1) statement 1 talks nothing about Y but however it clearly brings out the fact that the distance between B&Z is greater than the distance between A&Z. Now we know that since Y<Z, Y lies closer to A than Z and farther from B than Z. hence answers our question

2) Statement 2 : it says distance between Y&A is less than the distance between Z&B. As already stated Y lies closer to A than Z and farther to B than Z, hence this answers the question as well

So choice is Either statement alone is sufficient

I've struggled with this question for 10 min., then I looked at first sentence and the light bulb turned on. It becomes quite, quite a simple task the minute you draw a straight line... thank you! _________________

A<Y<Z<B. So, Z is greater than Y. if 2Z < B+A then 2Y (Y being less than Z) must also be less than B+A SUFFICIENT

(2) |Y-A| < |Z-B| (Y-A) < -(Z-B) Y-A < -Z + B Y + Z < B + A

A<Y<Z<B. Y + Z is less than B + A. If Y + Z is less than B + A then 2Y must be less than B + A. 2Y is Y + Y but Y + Z is Y + a number greater than Y. If Y + a Number greater than Y is less than B + A then Y + Y must be less than Y.

I noticed it is a bit different from the way others have solved this problem. Is my way correct?

Re: If A<Y<Z<B, is |Y-A|< |Y-B|? [#permalink]
06 Feb 2015, 04:56

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Type of Visa: You will be applying for a Non-Immigrant F-1 (Student) US Visa. Applying for a Visa: Create an account on: https://cgifederal.secure.force.com/?language=Englishcountry=India Complete...