I'm chuckling imagining the 6 hour Putnam exam getting flash solved like that.
In that case the implanted "device" would be a small magnet just inserted into the ear canal, while the bluetooth device is just an induction loop.
https://www.ec21.com/product-details/China-Topro-GSM-Inducti...
Also, competitiveness for some disciplines is seriously no joke: to give you an idea, medicine at Harvard has an admission rate of around 3.5%. Medicine at University of Sao Paulo, Brazil has an admission rate of 0.8%. Admission rates for IIT, India are even worse, at around 0.59%.
And if that isn't discouraging enough, many of these schools have reputations of being "hard to get in, harder to get out" (meaning that actually graduating is ever harder than getting accepted into the program in the first place)
As for why they use a 1-way device: this method of cheating has been around for decades; you get someone to take the test, they leave early and radio answers in. I don't know the specifics for this particular exam, but India is certainly not the only place in the world w/ extremely competitive admission exams. Back in my days back home some twenty years ago, cram schools would be on stand-by outside school doors, they'd smuggle the question sheet out somehow and flash-solve them / publish answers on the spot for publicity. You could get a full answer sheet online from a cram school website before the exam was over (these exams are hours long) and test takers would frequently do so after finishing their exams to see how they did.
[0] https://www.bodycandy.com/blogs/news/microdermal-implants-bo...