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(1) (a-b+b-a+a+b)/3 = a+b
=> 0 = 2(a+b)
This means that a+b = 0, or a = -b
Therefore, pick some numbers...(a,b)
(0,0) => median =0
(-1,1) => median =0
(1,-1) => median =0
Median will always equal to zero.
SUFFICIENT.

(2) We know that range = 2b
This means that a-b is minimum and a+b is maximum since a+b-a+b = 2b. However, it is impossible to find out b-a since we don't know the value of a and b.
INSUFFICIENT.

(1) (a-b+b-a+a+b)/3 = a+b => 0 = 2(a+b) This means that a+b = 0, or a = -b Therefore, pick some numbers...(a,b) (0,0) => median =0 (-1,1) => median =0 (1,-1) => median =0 Median will always equal to zero. SUFFICIENT.

(2) We know that range = 2b This means that a-b is minimum and a+b is maximum since a+b-a+b = 2b. However, it is impossible to find out b-a since we don't know the value of a and b. INSUFFICIENT.

hmm......do we need to find the value of medain, mean or range.

for me it should be D.
1: mean should be medain. suff....
2: if 2b is range, lowest and highest values are (a - b) and (a+b) respectively. so (b-a) is the median. also suff...

but 1 and 2 give different answers. so seems something not like OG type/standard question.

(1) (a-b+b-a+a+b)/3 = a+b => 0 = 2(a+b) This means that a+b = 0, or a = -b Therefore, pick some numbers...(a,b) (0,0) => median =0 (-1,1) => median =0 (1,-1) => median =0 Median will always equal to zero. SUFFICIENT.

(2) We know that range = 2b This means that a-b is minimum and a+b is maximum since a+b-a+b = 2b. However, it is impossible to find out b-a since we don't know the value of a and b. INSUFFICIENT.

Great explanation. Thanks. I go with A as well. The answer cannot be D as Fistail said because though we know that the median is (b-a) from stat 2, we do not know the value of either a or b making it impossible to find the median.

(1) (a-b+b-a+a+b)/3 = a+b => 0 = 2(a+b) This means that a+b = 0, or a = -b Therefore, pick some numbers...(a,b) (0,0) => median =0 (-1,1) => median =0 (1,-1) => median =0 Median will always equal to zero. SUFFICIENT.

(2) We know that range = 2b This means that a-b is minimum and a+b is maximum since a+b-a+b = 2b. However, it is impossible to find out b-a since we don't know the value of a and b. INSUFFICIENT.

Great explanation. Thanks. I go with A as well. The answer cannot be D as Fistail said because though we know that the median is (b-a) from stat 2, we do not know the value of either a or b making it impossible to find the median.

Do agree with GK_Gmat, though 2b is a range we don't know whether a+b is higher or a-b (there is no values of a and b, they could be positive or negative numbers).

1) is sufficient because a=-b making median 0 IrinaOK explained above.

(1) (a-b+b-a+a+b)/3 = a+b => 0 = 2(a+b) This means that a+b = 0, or a = -b Therefore, pick some numbers...(a,b) (0,0) => median =0 (-1,1) => median =0 (1,-1) => median =0 Median will always equal to zero. SUFFICIENT.

(2) We know that range = 2b This means that a-b is minimum and a+b is maximum since a+b-a+b = 2b. However, it is impossible to find out b-a since we don't know the value of a and b. INSUFFICIENT.

hmm......do we need to find the value of medain, mean or range.

for me it should be D. 1: mean should be medain. suff.... 2: if 2b is range, lowest and highest values are (a - b) and (a+b) respectively. so (b-a) is the median. also suff...

but 1 and 2 give different answers. so seems something not like OG type/standard question.

Question is asking for specific value. Here median must be specific number. I made the same mistake.