The River Island Census

The Story: On a small river island in the Brahmaputra delta, a government census officer named Dipankar arrives by boat every five years to count the island's inhabitants. This year, he rows up to the island's only dock and meets the village elder, an ancient woman named Bina, who has lived there her entire life. 'How many people live on this island?' Dipankar asks, pen ready. Bina smiles. 'I will tell you this,' she says. 'If you arrange all of us into rows of three, two people are left over. If you arrange us into rows of five, three are left over. If you arrange us into rows of seven, two are left over. And I can tell you the total is less than one hundred.' Dipankar puts down his pen. He closes his eyes for a moment. Then he writes a number in his census book without asking another question. The Challenge: How many people live on the island?