Word Trans (Percents): Each person in a certain group suppor

Each person in a certain group supports only one of two candidates R and T. Of the people in the group, 45 percent support Candidate R and the rest support Candidate T. How many people in the group are in favor of a flat tax ?

(1) Of the people in the group who support Candidate R, 58 percent are in favor of flat tax

(2) Of the people in the group who support Candidate T, 22 are in favor of a flat tax.

Here's my working for this problem:

Lets assume no. of people in group = 100.
R supporters = 45 (45% of 100)
T supporters = 55 (55% ("the rest" of 100)

(1) 58% of 45 -> INSUFF ... as this only gives us number of people in favor of flat tax from the group supporting candidate R. We also need to know how many of candidate T's supporters are in favor of flat tax, to determine how many people in the group are in favor of flat tax.

(2) Of the people in the group supporting Candidate T (55) ... 22 are in favour of flat tax. -> INSUFF ... this doesnt give us information about Candidate R's supporters.

(1) and (2) ... we have both candidate R's flat tax supporters (58% of 45), and candidate T's flat tax supporters (22), and hence the total number of people in the group in favor of a flat tax is (0.58*45) + 22. SUFF

So my working points to the answer as being C.

However the this is coming out as incorrect. WHY? where am I going wrong here ? I suspect I am making a simple mistake and falling into a trap somewhere.

P.S. This question came from the GMATPrep CAT.