Is c the median of a, b and c ? (1) b - c = a (2) c = a how

B 20 sec... was just studying number theory and then saw this question :-p thought at first that i was making a mistake but read the line "how quickly you solve this ? write down ur timings" and was sure that i was right

Official Solution:

For the value of c to be the median, it needs to be the middle number of those 3 numbers.

Statement 1: There are many possible situations arising from this statement. In some, c is the median, but in others, it is not. Here are some examples:

Yes, c is the median:

a = 2, c = 3, b = 5
b - c = a
5 - 3 = 2

No, c is not the median:

c = 2, a = 3, b = 5
b - c = a
5 - 2 = 3

This statement is insufficient.

Statement 2: If two out of the three numbers in a set are equal, then those two numbers must represent the median. For example:

2, 2, 3
c, c, b
or
1, 2, 2
b, c, c

The only way b could go in the middle is if it also equals c. However, if all three numbers in a set are equal, then they all must be the median. So if a = b = c, the value of c is still the median. For example:

2, 2, 2
c, b, c

But since b = c, that's really the same as:

2, 2, 2
c, c, c

Thus, from this statement, we know that the value of c is always the median. This statement alone is sufficient.

Got confused on whether integer and +ve,-ve should be considered

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