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m and r on number line

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m and r on number line

by queenisabella » Sat Mar 31, 2012 6:24 pm
If m and n 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 E

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Source: — Data Sufficiency |
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by killer1387 » Sat Mar 31, 2012 9:43 pm
queenisabella wrote:If m and n 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 E

help to solve this question faster?
Source: GMATPrep
just draw a number line place m,r, anywhere with respect to 0.

1) doesnt specify the fixed position of r and m with respect to 0 hence insufficient
2) same; doesnt say regarding r and m i.e. whether they are on left of 0 or right of 0--> insufficient

1+2
doesnt specifies anything hence insufficient.

P.S. main thing here is whether you can fix the position if r m are on what side then only yo u can have specific value of r. Just look out for that in the statement you need to calculate nothing here.
wont take more than 1 min.

HTH
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by GMATGuruNY » Sun Apr 01, 2012 5:55 am
queenisabella wrote:If m and n 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 E

help to solve this question faster?
Source: GMATPrep
Translate the words into math.
The DISTANCE between x and 0 is |x|.
HALFWAY between two numbers is the AVERAGE of the two numbers.

Statement 1: The distance between r and 0 is 3 times the distance between m and 0.
|r| = 3|m|
r = 3m or r=-3m.
No way to solve for r.
INSUFFICIENT.

Statement 2: 12 is halfway between m and r.
(m+r)/2 = 12
m+r = 24.
No way to solve for r.
INSUFFICIENT.

Statements 1 and 2 combined:
Substituting r=3m into m+r=24, we get:
m+3m=24
4m=24
m=6.
r=3m=18.

Substituting r=-3m into m+r=24, we get:
m+(-3m)=24
-2m=24
m=-12.
r=-3m=-3(-12)=36.

Since it's possible that r=18 or that r=36, INSUFFICIENT.

The correct answer is E.
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