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By Amanda Becker and Emily Stephenson MANCHESTER, N.H./COLUMBIA, S.C. (Reuters) - Hillary Clinton made the prospect of her being elected the first woman U.S. president a centerpiece of her campaign, then lost a critical nominating contest to a 74-year-old man in part because women preferred him. NBC News exit polls showed Clinton, a former secretary of state, U.S. senator and first lady, won 44 percent of the women's vote in Tuesday’s New Hampshire primary to 55 percent for her Democratic Party rival, U.S. Senator Bernie Sanders. Young women contributed significantly to Clinton's loss, and the candidate acknowledged that she struggled with young voters.