When you first meet someone at a networking event, small talk starts the ball rolling. Ask about the other person's challenges in their line of work to open up the conversation.
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The Muse has a few questions you can ask to keep the conversation going. The key is to have your conversational partner talk about themselves so you'll learn more about them and their business:
There isn't a business on the planet that doesn't have its challenges. New competitors, integrating digital, recruiting the best people, or any one of a gazillion other factors are challenges that business needs to roll with.Asking about someone's biggest challenge not only adds some serious meat to the conversational platter, but it might just help frame things or provide a fresh insight in the mind of the person you're speaking to.
Don't try to solve their problem immediately. Continue with thoughtful questions by asking "How, When and Why". Hit the link for other questions to ask when you are meeting someone in a business setting.
5 Lines That Will Keep a Conversation Going [The Muse]