It is hard to talk about your chance for Oxford and Cambridge since I don't have knolwedge on a number of successfuly cases. But as I know, Cambridge last year recruited two young girls with outstanding GMAT score. I am not sure whether it has strong preference on high GMAT score for ranking climb-up. Although only two cases cannot lead to such a conclusion, but we might have a sense of its preference to some extent.
I know lilttle about Oxford.
1. LBS recruited over 20 students last year from Mainland China.
2. You have competitive leadership experience. However, your age and GMAT score is not interesting to a highly technical business school like LBS. Why not try the American schools with reputation in general management? Or you can try Chicago, which is no less recognized than LBS, but consider little about the age of its candidates.
