I applied for the Quantitative Analytics role and here is my experience (from what I can remember!)
Business insight 1 consisted of both SJT and numerical reasoning questions. This stage is not timed and I highly recommend you go through each question carefully as it is fairly easy to pass. Also the numerical reasoning is slightly different from other tests as you will have around 3-5 images to refer to and the question may only need data from one source.
Business Insight 2 (video interview) was much harder. The experience is quite similar to what RCO described below however there was a few differences.
The first part consisted of 5 multiple choice questions and I had 30 minutes to answer them all however they bombarded me with a lot of data and some complicated formulas. It took me quite a while to understand what it all meant, and I was rushed doing all the calculations. Also it was not possible to go back to a question and change an answer.
Next I had an interview question that asked what is my greatest strength. I had 3 minutes to prepare and 3 minutes to answer.
I receive an email from a colleague working on the project associated with the data from the first section. She ‘emailed’ me a table with calculated values from another colleague however ‘he is known to make mistakes’. I can’t remember how long I had but I had to check if the values were correct and write an email back.
I receive another email from the same colleague who informs me that an elderly home is interested in investing in a company. There was more information provided and based on all the data at hand I had 8 minutes to prepare and 8 minutes to give a video recommendation.
Finally the experience ended with a final video interview question basically asking how I found the experience and what makes me excited to work for Barclays. Again 3 minutes to prepare and 3 minutes to speak.
I completed the assessments just over a week ago and have not heard from Barclays yet although I am certain that I failed it. Hopefully you find this information useful and feel free to ask more questions, I’ll try to answer to the best of my ability