It is currently 23 Feb 2018, 00:41

### 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 two numbers on a number line, what is the value

Author Message
SVP
Joined: 21 Jul 2006
Posts: 1508
If m and r two numbers on a number line, what is the value [#permalink]

### Show Tags

25 Jul 2008, 07:31
1
This post was
BOOKMARKED
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

### HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

If m and r two numbers on a number line, what is the value or r?

(1) The distance between r and 0 is 3 times the distance between m and 0.

(2) 12 is halfway between m and r.

According to the explanation, for statement 2, it treated 12 as a possibility to be either positive or negative. How on earth can we consider these 2 possibilities for 12? It clearly says in statement 2 that 12 is halfway. It's not like it says that the difference of 12 is halfway between m and r, you know?? How can we know whether the 12 mentioned in statement 2 is the actual value on the number line or just just the difference? I honestly don't like the wording in statement 2....what do you think?
thanks
Current Student
Joined: 12 Jun 2008
Posts: 287
Schools: INSEAD Class of July '10

### Show Tags

25 Jul 2008, 07:58
*** (1) r can be either 3m or -3m : two possibilities ==> (1) is insufficient

If we want an equation it would be (r-3m)(r+3m)=0

*** (2) r=12+(12-m)=24-m : since we don't know m, we don't know r either ==> (2) is insufficient

*** (1) & (2) : plug r=24-m into (r-3m)(r+3m)=0:

(24-4m)(24+2m)=0 i.e. (12-2m)(12+m)=0 ==> m=6 (and r=18) or m=-12 (and m=36)

Insufficient too

Last edited by Oski on 25 Jul 2008, 08:54, edited 2 times in total.
GMAT Tutor
Joined: 24 Jun 2008
Posts: 1346

### Show Tags

25 Jul 2008, 08:24
1
KUDOS
Expert's post
Just answered this on another forum- will paste here:

I assume it's clear that neither statement is sufficient on its own. You could do the problem algebraically:

From (2) 12-m = r-12

From (1) |r| = 3|m|
Thus either r = 3m (if they are on the same side of zero) OR r = -3m (if they are on opposite sides of zero)

In each case, you'll get two equations/two unknowns- if you solve, in the first case you'll find m = 6, r = 18; in the second case you'll find m = -12, r = 36.

Or you could do the problem 'pictorially'. From 1), we don't know if m and r are on the same side of zero, or on opposite sides. Using 1)+2), we know that m and r cannot both be negative- but they could both be positive, or we could have that r > 0, m < 0. So we should get two different solutions, even using both statements. You can confirm that both cases are possible- you should be able to see that there will be one solution where m is negative and r is a positive number quite far to the right of 12, and another solution where both m and r are positive, and are closer together than in the first case.

No matter how you look at it, E.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Manager
Joined: 27 Apr 2008
Posts: 110

### Show Tags

08 Nov 2008, 04:39
E

1 tells us that r=3|m|, if r is +ve, or that r=-3|m|, if r is -ve --> gives us 4 equeations:

r<0 --> r=-3|m| --> (1) m>0 --> r=-3m
(2) m<0 --> r=3m
r>0 --> r=3|m| --> (3) m>0 --> r=3m
(4) m<0 --> r=-3m

ins because we dont know the signs of m and r

2 tells us that 12 is between r and m, thus r+m=24 --> ins

together,
if r is -ve --> (1) -2m=24 --> m=-2 --> X, in 1 m>0
(2) 4m=24 --> m=6 --> X in 2 M<0
if r is +ve --> (3) 4m=24 --> m=6 --> OK, in 3 m>0 --> x=18
(2) -2m=24 --> m=-12 --> ok, in 4 M<0 --> x=36

we get 2 possibilities, so together is ins as well

VP
Joined: 05 Jul 2008
Posts: 1401

### Show Tags

08 Nov 2008, 10:58
tarek99 wrote:
If m and r two numbers on a number line, what is the value or r?

(1) The distance between r and 0 is 3 times the distance between m and 0.

(2) 12 is halfway between m and r.

According to the explanation, for statement 2, it treated 12 as a possibility to be either positive or negative. How on earth can we consider these 2 possibilities for 12? It clearly says in statement 2 that 12 is halfway. It's not like it says that the difference of 12 is halfway between m and r, you know?? How can we know whether the 12 mentioned in statement 2 is the actual value on the number line or just just the difference? I honestly don't like the wording in statement 2....what do you think?
thanks

I am not sure what's wrong with the second statement. To me, it's just saying (m+r) / 2 = 12 -> m + r = 24

(1) is saying |r|= 3|m| -> r = 3m or r = -3m

We get r =36 or 18. Hence E
Re: DS: Number line   [#permalink] 08 Nov 2008, 10:58
Display posts from previous: Sort by