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Polls: Trump leads GOP nationally and in South Carolina

New polls show that Donald Trump has maintained his lead in the Republican presidential race, both nationally and in the key state of South Carolina.
Republican presidential candidate Donald Trump speaks during a campaign rally aboard the USS Iowa on September 15, 2015 in Los Angeles, California. Donald Trump is campaigning in Los Angeles a day ahead of the CNN GOP debate that will be broadcast from the Ronald Reagan Presidential Library in Simi Valley.

New polls show that Donald Trump has maintained his lead in the Republican presidential race, both nationally and in the key state of South Carolina.

Trump has 35% in a new national poll from CBS News and The New York Times, followed by Ted Cruz at 16%.

Trump and Cruz are also one-two in South Carolina, according to a survey released Thursday by Winthrop University, with the New York businessman leading the Texas senator 24%-16%.

In the CBS/New York Times national poll, Ben Carson has slipped to third place at 13%, with Marco Rubio in fourth place at 9%. Jeb Bush, meanwhile, is at 3%, his lowest showing in this poll.

"Most of the interviews for this poll were conducted before Trump made statements concerning a ban on Muslims entering the United States," CBS noted.

In South Carolina — which hosts the third delegate selection contest of the race, after Iowa and New Hampshire — Trump and Cruz are followed by Carson (14%), Rubio (11%), and Bush (9%) in the Winthrop Poll. No other candidate pulls more than 2%.

Trump's lead in the Palmetto State is pretty much across-the-board, said Scott Huffmon, director of the Winthrop Poll.

"Trump leads across multiple categories of voters from a high of 35% among those who wish to create a database of Muslims in the U.S. to a low of 22% among Evangelical Christians, who will make up nearly 60% of the S.C. GOP Presidential Primary electorate," Huffmon said.

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