I know one trick to help you do this. First of all, you need to download the xcode 8 or 8.1.dmg file, but do not install. Here is the link to download the .dmg file of xcode 8.1 https://developer.apple.com/services-account/download?path=/Developer_Tools/Xcode_8.1/Xcode_8.1.xip. After downloading xcode, follow these steps. Click the right button of the newly downloaded xcode 8.1 and click Show package contents-> Content-> Developer-> Platform-> iPhoneOS.platform-DeviceSupport, here you can see the platform on which you can test your applications. So just copy the 10.1 folder and paste the same path into your xcode 7.3.1. When you connect your device with iOS 10.1, you will have to wait a few minutes, and then you can test your applications with xcode 7.3.1 on iOS 10.1. Please feel free to ask for any details.