Data Sufficiency

This is a question from GMAT Prep. Would appreciate if a Math tutor can explain the number line concepts...

Q. 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

my little try
what is r-?
(1) |r-0|=3|m-0|. |r|=3*|m|, we can`t extract the value of r from here. so insuff
(2) (m+r)/2=12. m+r=24. also insuff
both
m=24-r, from 2st, and insert in 1 st
|r|=3*|24-r| we need to solve this one, but again no the only value for r,
r=36. 36=3*12.
r=18, 18=3*6
i would pick E

clock60 wrote:my little try
what is r-?
(1) |r-0|=3|m-0|. |r|=3*|m|, we can`t extract the value of r from here. so insuff
(2) (m+r)/2=12. m+r=24. also insuff
both
m=24-r, from 2st, and insert in 1 st
|r|=3*|24-r| we need to solve this one, but again no the only value for r,
r=36. 36=3*12.
r=18, 18=3*6
i would pick E

ohh i like this solution... very nice

clock60 wrote:my little try
what is r-?
(1) |r-0|=3|m-0|. |r|=3*|m|, we can`t extract the value of r from here. so insuff
(2) (m+r)/2=12. m+r=24. also insuff
both
m=24-r, from 2st, and insert in 1 st
|r|=3*|24-r| we need to solve this one, but again no the only value for r,
r=36. 36=3*12.
r=18, 18=3*6
i would pick E

Be careful. You arrived at the correct answer, but your reasoning is faulty: r=36 and m=12 do not satisfy statement 2 because 12 is not halfway between 12 and 36.

Statement 1: |r|=3*|m|.
Statement 2: m+r = 24

The answer following values satisfy both statements:

r=18 and m=6:
|18| = 3*|6|
18+6 = 24

r=36 and m=-12:
|36| = 3*|-12|
36+-12 = 24

Since r=18 and r=36 both work, insufficient.

The correct answer is E.

Always consider negative values when asked about distances on a number line. And be very careful if you try to solve algebraically. Plugging in actual numbers is safer.

hi GMATGuruNY
thank you for checking my solution
but very sorry i don`t see any mistake, i came to the same result as yours
r=36, r=18
|r|=3*|24-r|
r=36. 36=3*12.
r=18, 18=3*6 here i only checked calculation to verify math operations, to avoid calculation mistakes

i 100% agree with you that if r=36. then m+36=24, m=-12. and r=18 m+18=24.m=6

clock60 wrote:hi GMATGuruNY
thank you for checking my solution
but very sorry i don`t see any mistake, i came to the same result as yours
r=36, r=18
|r|=3*|24-r|
r=36. 36=3*12.
r=18, 18=3*6 here i only checked calculation to verify math operations, to avoid calculation mistakes

i 100% agree with you that if r=36. then m+36=24, m=-12. and r=18 m+18=24.m=6

Oops! I misinterpreted your statement 36=3*12. I thought you were implying that r=36 and m=12. My bad. Great work, clock60!