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

It is currently 17 Oct 2018, 06:01

Close

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
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.

Close

Request Expert Reply

Confirm Cancel

Is s between r and t

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

Hide Tags

Intern
Intern
avatar
Joined: 29 Jul 2012
Posts: 13
Is s between r and t  [#permalink]

Show Tags

New post Updated on: 03 Sep 2012, 04:08
1
4
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

78% (01:44) correct 22% (01:16) wrong based on 156 sessions

HideShow timer Statistics

Is s between r and t

(1) |r-s| < |r-t|
(2) |r-s| < |s-t|

Official answer E


Is s between r and t

(1) |r-t| > |r-s|
(2) |r-t| > |t-s|

Official answer C

Originally posted by pnf619 on 02 Sep 2012, 08:03.
Last edited by Bunuel on 03 Sep 2012, 04:08, edited 1 time in total.
Renamed and edited the topic.
Intern
Intern
avatar
Joined: 28 Aug 2012
Posts: 44
Location: Austria
GMAT 1: 770 Q51 V42
Re: DS inequalities and Modulus  [#permalink]

Show Tags

New post 02 Sep 2012, 08:38
1
First question:
Statement (1) + (2) together: r=1, s=2, t=4 OR s=1, r=2, t=4 Both satisfy both statements.
So we do not know, whether s is between r and t. --> not sufficient

Second question:
Statement (1) + (2) together: If s<t<r, then |r-s|>|r-t| violating statement (1).
If s<r<t, then |t-s|>|r-t| violating statement (2).
If r<t<s, then |r-s|>|r-t| violating statement (1).
If t<r<s, then |t-s|>|r-t| violating statement (2).
Therefore, s must be between r and t to satisfy both statements at once. --> sufficient

Or with other words:
In the first question, we know that |r-s| is the smallest of the three possible differences (|r-s|, |r-t|, and |s-t|).
But that's not sufficient, as shown above. r and s can switch, while t remains the same, simply being far away from r and s.

In the second question, we know that |r-t| is the greatest of the three possible diffences.
So we know that r and t are the extreme values, being minimum and maximum.
The only place left for s is in the middle.
Director
Director
User avatar
Joined: 22 Mar 2011
Posts: 601
WE: Science (Education)
Re: Is s between r and t  [#permalink]

Show Tags

New post 03 Sep 2012, 14:39
1
pnf619 wrote:
Is s between r and t

(1) |r-s| < |r-t|
(2) |r-s| < |s-t|


Is s between r and t

(1) |r-t| > |r-s|
(2) |r-t| > |t-s|




Official answer C



Use the property of absolute value, \(|a - b|\) is the distance between \(a\) and \(b,\) and visualization on the number line.

Q1:
(1) t- - - - s - - r - - s - - - - t
\(s\) and \(t\) can be on either side of \(r.\)
Not sufficient.
(2) t - - r - - - s - - - r - - t
Now \(r\) and \(t\) can be on either side of \(s.\)
Not sufficient.
(1) and (2): Still not sufficient, as one can see from the above situation for (1).

Answer E


Q2:
(1) t - - - s - - r - - s - - - t
\(s\) and \(t\) can be on either side of \(r.\)
Not sufficient.
(2) r - - s - - - t - - - s - - r
Now \(r\) and \(s\) can be on either side of \(t.\)
Not sufficient.
(1) and (2): Sufficient, because in (1) now \(s\) must be between \(r\) and \(t.\)

Answer C
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Intern
Intern
avatar
Joined: 01 Jun 2012
Posts: 19
Location: United States
Concentration: Nonprofit
GMAT 1: 720 Q48 V43
GPA: 3.83
Re: Is s between r and t  [#permalink]

Show Tags

New post 07 Oct 2012, 16:36
For Q2, I just plugged in numbers and came up with the following:

r = 3, s= 5

a) |3 -5| > |3 - s| = 2 > |3 - s| -> therefore, s can equal 2, 3, or 4 to make the expression true. Only 4 is between t and r, but we can't be sure that is the answer. No sufficient.

b) |3 - 5| > |5 - s| = 2 > |5 - s| -> therefore, s can equal 4, 5, or 6 to make the expression true. Only 4 is between t and r, but we can't be sure that is the answer. Not sufficient.

Taking both together, 4 is the only answer that both statements have in common so that must be the solution to the problem. Since, 4 is between t and r, both statements together is sufficient. Answer is C.

Is this the right way to go about solving it?
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8386
Location: Pune, India
Re: Is s between r and t  [#permalink]

Show Tags

New post 07 Oct 2012, 22:18
egiles wrote:
For Q2, I just plugged in numbers and came up with the following:

r = 3, s= 5

a) |3 -5| > |3 - s| = 2 > |3 - s| -> therefore, s can equal 2, 3, or 4 to make the expression true. Only 4 is between t and r, but we can't be sure that is the answer. No sufficient.

b) |3 - 5| > |5 - s| = 2 > |5 - s| -> therefore, s can equal 4, 5, or 6 to make the expression true. Only 4 is between t and r, but we can't be sure that is the answer. Not sufficient.

Taking both together, 4 is the only answer that both statements have in common so that must be the solution to the problem. Since, 4 is between t and r, both statements together is sufficient. Answer is C.

Is this the right way to go about solving it?


Not entirely though the logic is fine.

"a) |3 -5| > |3 - s| = 2 > |3 - s| -> therefore, s can equal 2, 3, or 4 to make the expression true. Only 4 is between t and r, but we can't be sure that is the answer. No sufficient."

Actually s can take any value in this range 1 < s < 5 (since it needn't be an integer)
Some values will lie between 3 and 5 and some will not. Not sufficient.

"b) |3 - 5| > |5 - s| = 2 > |5 - s| -> therefore, s can equal 4, 5, or 6 to make the expression true. Only 4 is between t and r, but we can't be sure that is the answer. Not sufficient."

s can take any value in this range 3 < s < 7
Some values will lie between 3 and 5 and some will not. Not sufficient.

The overlap in the two cases is only of 3 < s < 5 and that lies between 3 and 5. So sufficient.

But generally speaking, taking numbers is not a good idea especially in DS questions. You don't know whether you have considered all relevant cases or not.

The same questions have been put up here and I have discussed how to solve them using number line:
ds-inequalities-and-modulus-138237.html#p1119436
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Intern
Intern
avatar
Joined: 01 Jun 2012
Posts: 19
Location: United States
Concentration: Nonprofit
GMAT 1: 720 Q48 V43
GPA: 3.83
Re: Is s between r and t  [#permalink]

Show Tags

New post 08 Oct 2012, 05:20
You rock. Thank you so much for the help!

VeritasPrepKarishma wrote:
egiles wrote:
For Q2, I just plugged in numbers and came up with the following:

r = 3, s= 5

a) |3 -5| > |3 - s| = 2 > |3 - s| -> therefore, s can equal 2, 3, or 4 to make the expression true. Only 4 is between t and r, but we can't be sure that is the answer. No sufficient.

b) |3 - 5| > |5 - s| = 2 > |5 - s| -> therefore, s can equal 4, 5, or 6 to make the expression true. Only 4 is between t and r, but we can't be sure that is the answer. Not sufficient.

Taking both together, 4 is the only answer that both statements have in common so that must be the solution to the problem. Since, 4 is between t and r, both statements together is sufficient. Answer is C.

Is this the right way to go about solving it?


Not entirely though the logic is fine.

"a) |3 -5| > |3 - s| = 2 > |3 - s| -> therefore, s can equal 2, 3, or 4 to make the expression true. Only 4 is between t and r, but we can't be sure that is the answer. No sufficient."

Actually s can take any value in this range 1 < s < 5 (since it needn't be an integer)
Some values will lie between 3 and 5 and some will not. Not sufficient.

"b) |3 - 5| > |5 - s| = 2 > |5 - s| -> therefore, s can equal 4, 5, or 6 to make the expression true. Only 4 is between t and r, but we can't be sure that is the answer. Not sufficient."

s can take any value in this range 3 < s < 7
Some values will lie between 3 and 5 and some will not. Not sufficient.

The overlap in the two cases is only of 3 < s < 5 and that lies between 3 and 5. So sufficient.

But generally speaking, taking numbers is not a good idea especially in DS questions. You don't know whether you have considered all relevant cases or not.

The same questions have been put up here and I have discussed how to solve them using number line:
ds-inequalities-and-modulus-138237.html#p1119436
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8432
Premium Member
Re: Is s between r and t  [#permalink]

Show Tags

New post 28 Sep 2018, 20:15
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: Is s between r and t &nbs [#permalink] 28 Sep 2018, 20:15
Display posts from previous: Sort by

Is s between r and t

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.