Sian Gobbidon, 25, from Leeds, has made it through Week Four of the BBC show after candidate Alex Finn was given the boot.
Finn said he was "gutted" to be fired from the show as he thought he would make it to the final.
The IT analyst from Wirral was the fourth person to be shown the door by Lord Sugar on the current series of the BBC programme.
He was eliminated after failing to sell anything during a body building-themed task, which led the business tycoon to brand him "the squirrel from Wirral".
"I'm gutted," said Finn. "I wish I was in the process for longer but I can't change the past.
"I did not believe it was my time to go.
"I did intend to get to the final and win it."
Finn blamed the management style of his project leader Sabrina Stocker, and said "the way the team and the whole day was structured" led to his downfall.
Week four of the BBC show saw the candidates summoned to the Royal Albert Hall where Lord Sugar told the group - who are vying for the entrepreneur's Â£250,000 investment in their business - that they had to sell a product and a service at a body-building expo in Birmingham.
Once in Birmingham, the team led by solicitor Sarah Ann Magson picked massage as their service, but had to settle for selling saunas after Stocker's team did a deal over a range of specialist gym equipment that both sides were after.
The massages were a hit and Magson's team also sold some saunas, giving them total sales of Â£1,892.50.
Stocker's team also mastered their service, making more than Â£250 with their spray tanning booth.
But shifting the gym equipment proved to be tough, particularly for 21-year-old Finn.
He appeared to become flustered as he failed to lock down sales, leading Lord Sugar's aide Karren Brady to declare she would be "shocked" if he sold anything at all.
Stocker moved Finn to a different position but it proved to be too late as their team only made Â£1,638.99, meaning they lost the challenge.
In the boardroom, Lord Sugar told Finn: "You are the only one who didn't sell anything!
"I'm not sure whether you are made for this body-building business.
"Jean-Claude Van Damme was the muscles from Brussels. I have a picture of you being more like the squirrel from the Wirral."
Finn protested that he had been moved off selling before he managed to close any deals and insisted he had "a millionaire mindset", but Lord Sugar expressed his doubts.
Delivering his verdict, the businessman said: "Alex, you say you are a good salesman, but frankly I'm struggling with... what have you done?"
Speaking afterwards, Finn said it had been "a brilliant experience" despite the fact he was let go.
"I wouldn't change it for the world," he said.
"It was a once-in-a-lifetime opportunity.
"Roughly 250 people have been on it in all the series. It was a life-changing opportunity."
David Alden, 32, of East Yorkshire, had become the second candidate to be fired earlier in the series.