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If m and r are two numbers on a number line, what is the value of r?  [#permalink]

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Question Stats: 44% (02:11) correct 56% (01:58) wrong based on 974 sessions

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If m and r are two numbers on a number line, what is the value of 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.

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

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28
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.

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Math Expert V
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Re: If m and r are two numbers on a number line, what is the value of r?  [#permalink]

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xcusemeplz2009 wrote:
bth the statments are not suff...

s1) let m-0=x, then r-0=3x ( x can be 1,2,3,4,......anything)...not suff
s2) m-12=12-r or r-12=12-m....(can have any value)...not suff

s1)+s2)if m-12=1,2,3,4,5.... then 12-r=3,6,9,12,15...any thing
same for r-12...hence
from bth also we are not getting any particular value
so E

The answer is correct, but there is some problems in solution:

(1) When you write: m=x and r=3x, it's not right: if m=x, then r=3x OR r=-3x, as |r|=3|m|.

(2) You wrote: m-12=12-r or r-12=12-m. If you look at it you'll see that these two equations are the same and derived from $$\frac{m+r}{2}=12$$.

Again:
Statement: distance between r and x, is three times the distance between m and x can be expressed as $$|r-x|=3|m-x|$$.

Statement: $$k$$ is halfway between $$m$$ and $$r$$ on the number line can be expressed as:

$$\frac{m+r}{2}=k$$.
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Re: If m and r are two numbers on a number line, what is the value of r?  [#permalink]

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Bunuel wrote:
xcusemeplz2009 wrote:
bth the statments are not suff...

s1) let m-0=x, then r-0=3x ( x can be 1,2,3,4,......anything)...not suff
s2) m-12=12-r or r-12=12-m....(can have any value)...not suff

s1)+s2)if m-12=1,2,3,4,5.... then 12-r=3,6,9,12,15...any thing
same for r-12...hence
from bth also we are not getting any particular value
so E

The answer is correct, but there is some problems in solution:

(1) When you write: m=x and r=3x, it's not right: if m=x, then r=3x OR r=-3x, as |r|=3|m|.

(2) You wrote: m-12=12-r or r-12=12-m. If you look at it you'll see that these two equations are the same and derived from $$\frac{m+r}{2}=12$$.

Again:
Statement: distance between r and x, is three times the distance between m and x can be expressed as $$|r-x|=3|m-x|$$.

Statement: $$k$$ is halfway between $$m$$ and $$r$$ on the number line can be expressed as:

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

thanks bunuel
i cud not express it in a correct manner , but my intention was same since i tried on no. line and i got it in a easier way ,however cudn't express that in my post(appologies for that), on a no. line it was clear that the position of m and r is not fix with bth the given information hence insuff....
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Re: If m and r are two numbers on a number line, what is the value of r?  [#permalink]

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IMO ... E..

Question: wat is r?

ST1: The distance between r and 0 is 3 times the distance between m and 0
Since the statement has the term 'distance' in it, it signifies that we are not consider the -ve or +ve possibility of the number position.
Hence ST1 can be written algebrically as:
|r-0| = 3|m-0| ---> |r| = 3|m|
Clearly NOT SUFF as m could be anything and even if m is constant, r could be -3m or 3m

ST2: 12 is halfway between m & r is clearly NOT SUFF as the same is true for (m=11,r = 13) , (m=10,r = 14)....

Both ST1 and ST2 together would give us:
m = 6 and r = 18, m=-12 & r = 36 ...etc..Hence NOT SUFF....

OA as D.... ... Not sure.. _________________
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Re: If m and r are two numbers on a number line, what is the value of r?  [#permalink]

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nikhilsrl wrote:
If m and r are two numbers on a number line, what is the value of 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.

OA is provided.

I though D is possible.

I somehow remembered the answer for this question.

Try m=6 and r=18. |r|=3|m| and 12 is midway
OR
m=-12 and r=36; |r|=3*|m| and 12 is midway

I don't remember any algebraic solution for this, but it would be great.

Ans: "E"
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Re: If m and r are two numbers on a number line, what is the value of r?  [#permalink]

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nikhilsrl wrote:
If m and r are two numbers on a number line, what is the value of 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.

I used the number line and tested two cases.

Case 1. Assume m is negative and r is positive, each dashed segments ----- is 1x

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

m = -x
r = 3x (3 times the distance between m and 0)

If 12 is the midpoint, the graph becomes:

m ----- 0 ----- 12 ----- ----- r

That means x = 12 and m = -12 and r = 36

Case 2. Assume both m and r are positive

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

m = x
r = 3x

Add 12 as the mid point:

0 ----- m ----- 12 ----- r

Therefore m = 6 and r = 18

This shows that even if you combine the 2 statements, you still can't get a unique answer. Therefore the answer should be E.
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Re: If m and r are two numbers on a number line, what is the value of r?  [#permalink]

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1
Another DS good example

If m and r are two numbers on number line, what is the value of 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

*Edited the question. It should be r instead of n.

Stmnt 1 alone: Too many values possible. Say r = 3, m = 1 OR r= 6, m = 2 etc
Stmnt 2 alone: Again too many values possible. Think 12 is in the middle. m and r are equidistant from it so m = 11, r = 13 OR m = 10, r = 14 etc

Both together:
Focus on the logic behind it. You don't need to do any calculations.
We are looking for two values equidistant from 12. Let's say both m and r are at 12 initially. Their distance from 0 is the same i.e. 12 at this point. As they both start moving away from 12 simultaneously, the distance of m from 0 is reducing and that of r from 0 is increasing. There will be point when the distance of m from 0 will be a third of the distance of r from 0. This will be our first pair (shown in blue).
Let's say they keep moving. m will finally reach 0 when its distance from 0 is 0 while r will be at 24. Then m will move in the negative range and its distance from 0 will start increasing. Distance of r from 0 is continuing to increase. There will be a point again when distance of m from 0 is a third of the distance of r from 0 (shown in red).
Attachment: Ques4.jpg [ 7.07 KiB | Viewed 8174 times ]

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

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VeritasPrepKarishma wrote:
Another DS good example

If m and r are two numbers on number line, what is the value of 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

*Edited the question. It should be r instead of n.

$$|a-b|=c$$ ---> Distance of $$a$$ from $$b$$ equals $$c$$

Question: r=?

Statement 1:

$$|r-0|=3*|m-0|$$ ---> $$r=3*m$$ or $$r=-3*m$$,

$$r$$ depends on $$m$$, and since we don't know $$m$$, Insufficient.

Statement 2:

Number line is like a set with consecutive numbers. Since this set is an evenly spaced set we know that median=average.

Because 12 is halfway of $$m$$ and $$r$$ :

$$12=\frac{m+r}{2}$$ ---> $$m+r=24$$, Insufficient.

Statement 1+2:

$$r=3*m$$ ---> $$r=3*(24-r)$$ ---> $$r=18$$
$$r=-3*m$$ ---> $$r=-3*(24-r)$$ ---> $$r=36$$

Therefore Insufficient and the correct answer is E.
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Re: If m and r are two numbers on a number line, what is the value of r?  [#permalink]

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Janealams wrote:
Can somebody explain this to me please.

stmnt1:

let m = 4 then r = 12
let m = 6 then r = 18

Hence insuff

stmnt2:
We can have different combinations for this as well

m= 10 and r = 14
m = 6 and r = 18

Hence insuff

taking together when m = 6 then r = 18 and 12 is halfway between m and r

also for m = -12 r = +36, 12 is halfway of m and r and r = 3 times the distance from 0 and m (distance is +ve value)
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GMAT 1: 750 Q50 V41 Re: If m and r are two numbers on a number line, what is the value of r?  [#permalink]

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Algebraically this can be solved as a system of two equations

|r| = 3|m|

$$\frac{m+r}{2}=12$$

1) m=6; r=18
2) m=-12; r=36

Not sufficient, so the answer is E
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Re: If m and r are two numbers on a number line, what is the value of r?  [#permalink]

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arjtryarjtry wrote:
If m and r are two numbers on a number line, what is the value of 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

STAT1.
Firstly, we dont know the value of m. So r being 3times m will not help.Also, r can be positive or negative so we are not sure about the value of r.
So, INSUFFICIENT

STAT2.
12 is halfway between m and r.
Now. There are four cases.
1. Both m and r are positive.
2. Both m and r are negative
3. m is positive and r is negative
4. m is negative and r is positive
So, NOT SUFFICIENT

Taking both together:--
Still all the four cases mentioned in statement 2 are possible. So NOT SUFFICIENT.

Hope it helps!
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Re: If m and r are two numbers on a number line, what is the value of r?  [#permalink]

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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.

tnx lot for this
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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 $$r=-3m$$?
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Re: If m and r are two numbers on a number line, what is the value of r?  [#permalink]

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

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1) m=6; r=18
2) m=-12; r=36

Not sufficient,

E
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