"Until as best we can surmise at this point in time ... the credit card, the money started to run out".
Things changed however in the days before their death.
Rotana Farea had been enrolled at George Mason University in Fairfax, Virginia, but left in the spring and may have moved to NY at some point, according to media reports.
The two young women had recently applied for United States asylum, the newspaper says, adding that their mother learned of this after receiving a call from the Saudi Arabian Embassy in Washington DC.
A passerby discovered the sisters' bodies, which had washed ashore on some rocks on the Upper West Side of Manhattan on Oct 24, police said. There were no obvious signs of trauma, police said. They were reported missing and then located near Fairfax, VA. In December 2017, they were found, "but they were not returned to the home", Shea said; "they were returned to - I'll call it a shelter-like type of facility due to some abuse allegations that came up".
They were also seen several times on security cameras in apparently good health, police said during a news conference on Friday afternoon.
Detectives used eye-witness testimonies, video evidence and evidence from the eldest sister's credit card purchases for food, hotel and transportation to determine that there likely was no foul play before their deaths.
Rotana was enrolled at George Mason University, in Fairfax, but left in the spring.
A witness reportedly saw the two girls early on October 24 on a playground near the Hudson, where they appeared to be praying. On Friday Shea dismissed reports that they had jumped from the George Washington bridge, saying, "We have absolutely zero information to lead us to that". They spent the next week making their way to New York, Shea said, citing electronic records including at least one Uber receipt.
"We are out to get justice for those two girls and to find out exactly what happened", Shea said.
Citing unnamed sources in Virginia, he said the pair "would rather inflict harm on themselves and commit suicide than return to Saudi Arabia", where they had lived until moving to the U.S. with their family in 2015.
A witness came forward on October 31, to tell the police that he had a story that was "haunting him".
Investigators are looking into reports the pair was allegedly physically abused in the past by family members.
"Reports that we ordered anyone related to the Saudi sisters to leave the U.S. for seeking asylum are absolutely false", Fatimah Baeshen said on Twitter on Saturday.
Officials from the Department of Homeland Security declined to comment and referred questions to the NY police.