It is currently 16 Oct 2017, 19:12

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If m and r are two numbers on a number line, what is the

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

### Hide Tags

Manager
Joined: 07 May 2013
Posts: 108

Kudos [?]: 30 [0], given: 1

Re: If m and r are two numbers on a number line, what is the [#permalink]

### Show Tags

04 Jun 2014, 20:16
Buneul, I did not understand why you took the case r=-3m.

Kudos [?]: 30 [0], given: 1

Math Expert
Joined: 02 Sep 2009
Posts: 41875

Kudos [?]: 128459 [1], given: 12173

Re: If m and r are two numbers on a number line, what is the [#permalink]

### Show Tags

05 Jun 2014, 01:30
1
KUDOS
Expert's post
Buneul, I did not understand why you took the case r=-3m.

Please rad the post just above yours: if-m-and-r-are-two-numbers-on-a-number-line-what-is-the-89018.html#p1359757

Hope it helps.
_________________

Kudos [?]: 128459 [1], given: 12173

Intern
Joined: 07 Mar 2016
Posts: 4

Kudos [?]: 2 [1], given: 30

Re: If m and r are two numbers on a number line, what is the [#permalink]

### Show Tags

07 Mar 2016, 12:21
1
KUDOS
1) m=6; r=18
2) m=-12; r=36

Not sufficient,

E

Kudos [?]: 2 [1], given: 30

Intern
Joined: 31 Jan 2016
Posts: 26

Kudos [?]: 2 [0], given: 6

Schools: Rotman '19 (A)
Re: If m and r are two numbers on a number line, what is the [#permalink]

### Show Tags

13 Nov 2016, 18:54
Bunuel wrote:
TooLong150 wrote:
Bunuel wrote:
TIP:
On the GMAT we can often see such statement: $$k$$ is halfway between $$m$$ and $$n$$ on the number line. Remember this statement can ALWAYS be expressed as:

$$\frac{m+n}{2}=k$$.

Also on the GMAT when we see the distance between x and y, this can be expressed as $$|x-y|$$.

Back to the question:
If m and r are two numbers on a number line, what is the value of r?

(1) The distance between r and zero is 3 times the distance between m and zero --> $$|r-0|=3|m-0|$$ --> $$|r|=3|m|$$ --> $$r=3m$$ OR $$r=-3m$$. Clearly insufficient.

(2) 12 is halfway between m and r --> $$\frac{r+m}{2}=12$$ --> $$r+m=24$$. Clearly insufficient.

(1)+(2) $$r=3m$$ OR $$r=-3m$$ and $$r+m=24$$.

$$r=3m$$ --> $$r+m=3m+m=24$$ --> $$m=6$$ and $$r=18$$
OR
$$r=-3m$$ --> $$r+m=-3m+m=24$$ --> $$m=-12$$ and $$r=36$$

Two different values for $$r$$. Not sufficient.

Bunuel, can you explain how $$|r|=3|m|$$ --> $$r=3m$$ OR $$r=-3m$$?

$$|r|=3|m|$$ means that the distance from r to 0 is thrice the distance from m to 0:

-----0--m-----r------
r-----m--0--------------

--m--0--------r------
r--------0--m------------

If r and m have the same sign (cases A and B), then r=3m but if r and m have different signs (cases C and D), then r=-3m.

Hope it's clear.

Hi Buenel,

I looked into your solution and noticed many are saying there is only 2 solutions hence insufficient. But just to fully understand this problem, isn't there more than 2 solutions?

For instance:

r could be - or +, m could be the opposite sign of r (- or +), or they both can be negative. Therefore multiple solutions? Or, am I missing something. I understand you wrote |r| = 3|m| -> r = 3m or r=-3m, however, could we also have -r = 3m?

Thank you

Kudos [?]: 2 [0], given: 6

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16795

Kudos [?]: 273 [0], given: 0

Re: If m and r are two numbers on a number line, what is the [#permalink]

### Show Tags

07 Oct 2017, 22:43
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.
_________________

Kudos [?]: 273 [0], given: 0

Re: If m and r are two numbers on a number line, what is the   [#permalink] 07 Oct 2017, 22:43

Go to page   Previous    1   2   [ 25 posts ]

Display posts from previous: Sort by

# If m and r are two numbers on a number line, what is the

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

 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®.