BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Help - GMATPrep DS Number Line Question

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 47
Joined: Sun Feb 05, 2012 7:56 pm
Followed by:3 members

Help - GMATPrep DS Number Line Question

by queenisabella » Sun Mar 11, 2012 1:20 pm
this is the 2nd time i've seen this question and i'm still struggling with it. can someone please help explain to me the rationale, and the fastest way to solve this?

DATA SUFFICIENCY:

On the number line shown, is zero halfway between r and s?
(1) s is to the right of zero.
(2) The distance between t and r is the same as the distance between t and -s.

OA is C
Attachments
a.jpg
Top
Source: — Data Sufficiency |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 768
Joined: Wed Dec 28, 2011 4:18 pm
Location: Berkeley, CA
Thanked: 387 times
Followed by:140 members

by Mike@Magoosh » Sun Mar 11, 2012 3:52 pm
Hi, there. I'm happy to help with this. :)

So, from the diagram, we know r < s < t. That's it.

Prompt: On the number line shown, is zero halfway between r and s?


In other words, |r| = |s|, or r = -s. That is the question.

Statement #1: s is to the right of zero.

From this, we know only that s is positive, but nothing else. This gives us almost no information, so by itself, it's not sufficient.

Statement #2: The distance between t and r is the same as the distance between t and -s.

This one is tricky, because it opens a several possibilities.
a) t > 0, s > 0, r < 0 ----> t = 3, s = 2, r = -2, answer to prompt = YES
b) t < 0, s < 0, r < 0 ---> t = -1, s = -3, r = -5, answer to prompt = NO

Two different configurations consistent with this statement lead to two different answers. Therefore, Statement #1, by itself, is not sufficient.

Combined Statements #1 & #2:

Now, we know we must have t > 0 and s > 0. Therefore, -s will be a negative number. We also know now that -s and r are both to the left of t, so if they are both the same distance from t, they must be in the same place ---- i.e. -s = r. This leads to a definitive YES answer to the prompt. Combined, the statements are sufficient.

Answer = E

Does this make sense? Please let me know if you have any questions on what I've said here.

Mike :-)
Last edited by Mike@Magoosh on Mon Mar 12, 2012 7:42 am, edited 1 time in total.
Magoosh GMAT Instructor
https://gmat.magoosh.com/
Top
Junior | Next Rank: 30 Posts
Posts: 26
Joined: Sat Aug 27, 2011 8:50 pm

by [email protected] » Sun Mar 11, 2012 4:44 pm
Hi Mike,

Can you please explain the below ?

b) t > 0, s < 0, r < 0 ---> t = 1, s = -2, r = -4, answer to prompt = NO

As per statement 2, distance between t & r is same as distance between t & -s.
In b) distance between t & r is 5 units but distance between t & -s is 1 unit.
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 768
Joined: Wed Dec 28, 2011 4:18 pm
Location: Berkeley, CA
Thanked: 387 times
Followed by:140 members

by Mike@Magoosh » Mon Mar 12, 2012 7:45 am
Dear [email protected]

Very sorry about that --- apparently, I made some arithmetic mistake when I first typed that. I correct it in the original post, and here's the corrected line:

b) t < 0, s < 0, r < 0 ---> t = -1, s = -3, r = -5, answer to prompt = NO

Distance from t = -1 and r = -5 is 4.
Distance from t = -1 and -s = 3 is 4.

Thank you for pointing that out, and please let me know if you have any other questions.

Mike :)
Magoosh GMAT Instructor
https://gmat.magoosh.com/
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Fri Mar 23, 2012 11:00 am
For an alternate approach, check my solution to a very similar problem here:

https://www.beatthegmat.com/best-approac ... 67985.html
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Post new topic Post Reply
• Page 1 of 1