By the time you're all there, most people won't be so obsessed with competing in grad school admissions. Once you've decided where you'll be going, it's easy to forget most of the stress, anxiety and self-doubt brought on by the application process, and instead to be excited about your new program. People will be more focused on making friends and getting to know you and about your research interests. In my own personal experience, the annoying competitive people never bothered asking me about my own achievements or failures, so I never had to answer potentially embarrassing questions. They just naturally assumed (or wanted desperately to believe) that they were smarter or more qualified than me and others, so launched into spiels about how great and smart they were without bothering to ask about anyone else. People who do that are just acting on their own insecurities, so there's no need to worry about what they might think about your problems. Just be patient with them and change the subject. Chances are everyone else in the cohort will find their competitive attitude annoying as well, and no one will think any less of you for overhearing that you didn't get in to X University.