OK, "sell me this pencil" is not a question per se but it is an old school interview question that sales managers used to (and still might) ask potential job candidates.
This question might even be asked if you're not interviewing for a sales job simply to see how you respond to it!
It's an example of a trick interview question or stress interview question that hiring managers often ask interviewees to see how they respond to being thrown off guard.
It gives the interviewer a chance to see how the interviewee handles a difficult question that they weren't expecting and how they think on their feet.
For example, does the interviewee:
Look the interviewer in the eye when responding?
Give an intelligent and logical response?
Give good responses to any questions or concerns the interviewer raises?
Try to get the sale and actually sell the pencil?
Depending on what the interviewer is looking for, they might simply be looking to see how you answer the question and specifically, what your body language is like during a stressful situation.
The point is that sometimes during job interviews, you get asked questions that you weren't expecting that might seem off base and even silly. Your ability to remain calm and to respond to the question intelligently and in a logical way is generally what the interviewer will be looking for.
Carl Mueller is an Internet entrepreneur and professional recruiter who has written an ebook for career-minded individuals: http://www.RecruiterSecretsRevealed.com
Recruiter Secrets Revealed sheds light on job search and career management "secrets" that you can use to supercharge your career and distinguish yourself from other job searchers.