IMO E
A) not sufficient. there are many possibilities
B) Not possible-because many possibilities
combining 1 and 2
if both m and r are positive
m=6,r=18
but there is one more possibility. when m is negative and r is positive
m=-12,r =36
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Source: Beat The GMAT — Data Sufficiency |
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tohellandback
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bluementor
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what is r?
Statement 1: The distance between r and 0 is 3 times the distance between m and 0
In absolute terms, this means: |r| = 3|m|, and from this you have the following possibilities:
i) r = 3m
ii) r = -3m
It is evident from here that even if we know m, we cannot solve for r. Insufficient.
Statement 2: 12 is halfway between m and r
If a number is halfway between two other numbers (say a and b), then essentially this number is also the average of a and b. So,
12 = (m + r)/2
24 = m + r
Once again, without sufficient knowledge of m, we cannot solve for r. Insufficient.
Both statements together:
if r = 3m, then 24 = 4m and m = 6, r = 18.
if r = -3m, then 24 = -2m and m = -12, r = 36.
Insufficient. Choose E.
-BM-
Statement 1: The distance between r and 0 is 3 times the distance between m and 0
In absolute terms, this means: |r| = 3|m|, and from this you have the following possibilities:
i) r = 3m
ii) r = -3m
It is evident from here that even if we know m, we cannot solve for r. Insufficient.
Statement 2: 12 is halfway between m and r
If a number is halfway between two other numbers (say a and b), then essentially this number is also the average of a and b. So,
12 = (m + r)/2
24 = m + r
Once again, without sufficient knowledge of m, we cannot solve for r. Insufficient.
Both statements together:
if r = 3m, then 24 = 4m and m = 6, r = 18.
if r = -3m, then 24 = -2m and m = -12, r = 36.
Insufficient. Choose E.
-BM-
