Data Sufficiency

Is b the median of the three numbers a, b and c ??

1) a x c = b

2) a+c=b

silverflamein wrote:Is b the median of the three numbers a, b and c ??

1) a x c = b

2) a+c=b

Option E

1) For the option 1 - this doesn't provide any additional information as we can have several different options.
a1 = 2
c1 = -1
b1 = -5
(isn't a median)

Or
a2 = 2
c2 = 1/2
b2 = 1
(is a median)

2) Same here, doesn't provide any info alone, for a=2 and c=-2 b=0 (is median), and for the a=2, c=2 b=4 - isn't a median.

Combined together, you can deduce c = b-a from (2), then from (1) ba - a*a = b, therefore b=a*a/(a-1) and c = a / (a-1)

So, for (1) and (2) combined you have:
a, a*a/(a-1), a(a-1)
which depends on a
For a=2 you have 2, 4, 2 - b isn't a median
For a=1/2 1/2, 1/2, 1 - b is a median

Therefore, the answer is E