The answer to first should be E.
A) is in sufficient
B) is in sufficient
D would be the answer if line OC made 90 degrees with the horizontal line.
Also you cannot combine A and B because OA = OB so OAB = OBA
if OAB = 45 then OBA = 45 and AOB = 90
if AOB = 100 then OAB = OBA = 40
The answer to second question is C. Angle x = 60
I think the answer D is ok for question 1
OA = OB so OAB = OBA
Statement 1: OAB = 45 then OBA = 45 and AOB = 90
So if we consider the angle AOB on larger arc, it would be 360 - 90 = 270.
Angle ACB is then = 270 /2 = 135
So statement 1 suffecient
Angle AOB = 100 (I undersatnd this is wrong. This statement should have been "Angle AOB = 90" because that is the value we derived in the first statement and on GMAT if both the statements are given values for a variable it is usually same)
Anyhow, AOB = 100 so the angle on the larger arc is = 260
So angle ACB = 260 / 2 = 130
Statement 2 is SUFFECIENT