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

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

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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

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Re: DS: Number line [#permalink]

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New post 25 Jul 2008, 08:58
*** (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

==> Answer is (E)

Last edited by Oski on 25 Jul 2008, 09:54, edited 2 times in total.

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Re: DS: Number line [#permalink]

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New post 25 Jul 2008, 09:24
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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.
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Re: DS: Number line [#permalink]

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New post 08 Nov 2008, 05:39
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

answer E

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Re: DS: Number line [#permalink]

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New post 08 Nov 2008, 11:58
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

Kudos [?]: 423 [0], given: 1

Re: DS: Number line   [#permalink] 08 Nov 2008, 11:58
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If m and r two numbers on a number line, what is the value

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