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This is 100% a scam. This person was not working for a reputable company and they would never call you for no reason.This is what is known as "phone phishing" it is can be a very serious problem if you do let them access your computer.Basically what they will do is call a lot of phone numbers and say that you have problems. Any actual computer problems you have will be entirely coincidental. Usually what they will do is show you the windows error log which always shows a lot of errors but these are normal and on all windows computers, they are not viruses.Next they log onto your computer and lie to you about the numerous problems they pretend to find. Next they will attempt to get you to pay a few hundred dollars to "fix" the issues when in fact they actually do nothing too helpful.Here is what Microsoft says on the subject as they usually claim to be affiliated with them:http://www.microsoft.com/security/online-privacy/msname.aspx
Always remember, no legitimate tech support company would ever call you. Your computer does not report to Microsoft or any other company so if any tech support person calls you can trust it is a scam and just hang up.
Please do me a favor and take a moment to rate my service by clicking the stars above, 3 or more is very appreciated, we can still chat after rating if you need more help. Also I sent through an offer for premium service, you could choose this option if you want me to connect to your computer and make sure they did not do any damage or leave themselves a way to get into your computer without your knowledge.