Statement II) alone tells us how much exactly was provided by each institution. Private grants=1/2(private endowments) and private endowments=1/3(18M), thus private endowments provided 6M and private grants 3M. II) alone is sufficient.

Statement I) merely tells us that total funding reached 60M last year. Question stem states that "from all remaining sources," so perhaps there were additional funding sources aside from the city, private endowments, and private grants. It's tricky, and in my opinion, poorly worded.

jc114 wrote:City X provided 18 million dollars of the total funding for its cultural center last year. from all of the remaining sources of funding, how many million dollars were provided by private grants and private endowments last year?
(1) Total funding for the center last year was 60 million dollars.
(2) Last year the amount of the center's funding provided by private grants was half the amount provided by private endowments and the amount provided by private endowments was one-third the amount provided by city X.

… A is not the answer bcoz it has not been mentioned that the only sources of funding is government and private grants and private endowments… remember there culd be other sources of funding .. so even after u subtract 18 from 60 .. the remaining culd be composed of sources other than private gratnts and endowments .. remember the most important thing while solving a DS do not assume anything …

jc114 wrote:The answer is B, but doesn't condition (1) work as well??

If a^2-b^2=0, does a=0?
(1) ab=0
(2) b=-b

.. ok … a^2-b^2 wuld be equal to 0 if a = b ..

the first statement says that ab = 0 .. that means that one of them – 0 .. but we know that a = b … so a = 0 .. so sufficient ..

the second statement says that b= -b .. this possible only if b = 0 … but if b = 0 then a = 0 .. so sufficient … so D