GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 21 Oct 2019, 13:27 GMAT Club Daily Prep

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

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.  If x, y and z are real numbers, is y – z < x – z?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 58396
If x, y and z are real numbers, is y – z < x – z?  [#permalink]

Show Tags 00:00

Difficulty:   35% (medium)

Question Stats: 68% (01:41) correct 32% (01:43) wrong based on 98 sessions

HideShow timer Statistics

If x, y and z are real numbers, is y – z < x – z?

(1) y lies between x and z.
(2) z < x < 0

_________________
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4015
If x, y and z are real numbers, is y – z < x – z?  [#permalink]

Show Tags

1
Top Contributor
Bunuel wrote:
If x, y and z are real numbers, is y – z < x – z?

(1) y lies between x and z.
(2) z < x < 0

Target question: Is y – z < x – z?
This is a good candidate for rephrasing the target question.
Take y – z < x – z and add z to both sides to get: y < x.
So,......
REPHRASED target question: Is y < x?

Statement 1: y lies between x and z.
BE CAREFUL, we cannot conclude that x < y < z, because it could also be the case that z < y < x
In both cases, y lies between x and z on the number line. These two possible scenarios yield different answers to the REPHRASED target question.
Case a: if x < y < z, then we can see that x < y.
Case b: if z < y < x, then we can see that y < x.
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: z < x < 0
There's no information about y.
So, there's no way to determine whether or not y < x
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that EITHER x < y < z OR z < y < x
Statement 2 tells us that z < x, which RULES OUT the possibility that x < y < z
So, it MUST be the case that z < y < x, which means y < x
So, the answer to the REPHRASED target question is "YES. It is definitely the case that y < x"
Since we can answer the REPHRASED target question with certainty, the combined statements are SUFFICIENT

RELATED VIDEOS FROM OUR COURSE

_________________

Originally posted by GMATPrepNow on 26 Feb 2017, 10:45.
Last edited by GMATPrepNow on 19 Oct 2017, 16:03, edited 1 time in total.
CEO  D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2978
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: If x, y and z are real numbers, is y – z < x – z?  [#permalink]

Show Tags

Bunuel wrote:
If x, y and z are real numbers, is y – z < x – z?

(1) y lies between x and z.
(2) z < x < 0

Question: Is y – z < x – z?
Question: Is y < x ?

Statement 1: y lies between x and z.
But y may be greater than or smaller than x
NOT SUFFICIENT

Statement 2: z < x < 0
No mention of y hence
NOT SUFFICIENT

Combining the two statements
z < x < 0 and
y lies between x and z
i.e. y must be smaller than x hence
SUFFICIENT

_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Intern  B
Joined: 12 Aug 2016
Posts: 7
Re: If x, y and z are real numbers, is y – z < x – z?  [#permalink]

Show Tags

1
GMATPrepNow wrote:
Bunuel wrote:
If x, y and z are real numbers, is y – z < x – z?

(1) y lies between x and z.
(2) z < x < 0

Target question: Is y – z < x – z?
This is a good candidate for rephrasing the target question.
Take y – z < x – z and add z to both sides to get: y < x.
So,......
REPHRASED target question: Is y < x?

Statement 1: y lies between x and z.
BE CAREFUL, we cannot conclude that x < y < z, because it could also be the case that z < y < x
In both cases, y lies between x and z on the number line. These two possible scenarios yield different answers to the REPHRASED target question.
Case a: if x < y < z, then we can see that x < y.
Case b: if z < y < x, then we can see that y < x.
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: z < x < 0
There's no information about y.
So, there's no way to determine whether or not y < x
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that EITHER x < y < z OR z < y < x
Statement 2 tells us that z < x, which RULES OUT the possibility that x < y < z
So, it MUST be the case that x < y < z, which means x < y

So, the answer to the REPHRASED target question is "NO. It is definitely NOT the case that y < x"
Since we can answer the REPHRASED target question with certainty, the combined statements are SUFFICIENT

RELATED VIDEOS FROM OUR COURSE

Hi Brent,

Nice solution! I do think you've made a mistake in the highlighted part though. I believe you meant to say:

Statement 2 tells us that z < x, which RULES OUT the possibility that x < y < z
So, it MUST be the case that z < y < x, which means y < x

So, the answer to the REPHRASED target question is "YES. It is DEFINITELY the case that y < x"
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4015
Re: If x, y and z are real numbers, is y – z < x – z?  [#permalink]

Show Tags

Top Contributor
Thanks BalysLTU!!

I have edited my answer accordingly.

Cheers,
Brent
_________________
Non-Human User Joined: 09 Sep 2013
Posts: 13383
Re: If x, y and z are real numbers, is y – z < x – z?  [#permalink]

Show Tags

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.
_________________ Re: If x, y and z are real numbers, is y – z < x – z?   [#permalink] 22 Sep 2019, 07:19
Display posts from previous: Sort by

If x, y and z are real numbers, is y – z < x – z?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  