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Donald J. Trump and Hillary Clinton are locked in tight races in three crucial states in November’s general election, according to new polls that show men and women sharply divided on the presidential candidates and the likelihood of a close overall contest.

The Quinnipiac University surveys, released on Tuesday, show Mrs. Clinton leading Mr. Trump by one percentage point in Pennsylvania and Florida and trailing him by four points in Ohio. The polls have margins of error of plus or minus three percentage points.

“At this juncture, Trump is doing better in Pennsylvania than the G.O.P. nominees in 2008 and 2012,” said Peter A. Brown, assistant director of the Quinnipiac Poll. “And the two candidates are about where their party predecessors were at this point in Ohio and Florida.”

Mr. Trump became the Republican Party’s presumptive nominee last week after Senator Ted Cruz of Texas and Gov. John Kasich of Ohio dropped out of the race. Mrs. Clinton holds a substantial delegate lead over Senator Bernie Sanders of Vermont in the Democratic contest, but he is continuing to compete in coming primaries, including Tuesday’s Democratic voting contest in West Virginia.

The polls do offer some support for Mr. Sanders’s argument to stay in the race, as he outperforms Mrs. Clinton in head-to-head matchups against Mr. Trump in the three states. The senator from Vermont tops Mr. Trump by two points in Florida and Ohio and by six points in Pennsylvania.

In the expected general election contest between Mr. Trump and Mrs. Clinton, the divide between men and women is stark. She holds wide leads with women in Pennsylvania and Florida and a smaller one in Ohio, while Mr. Trump holds big leads with male voters in all three states.

Mr. Trump has been showing early signs of trying to damage Mrs. Clinton’s appeal to women by bringing up her husband’s history of infidelity.

Voters generally think that Mr. Trump is better equipped to manage the economy and handle terrorism, but they view Mrs. Clinton as more intelligent and having “higher moral standards.” In all three states, Mrs. Clinton and Mr. Trump receive low marks from prospective voters when it comes to their honesty and trustworthiness.

Although Mr. Trump holds a wide lead among white men, some of his central proposals — such as deporting all undocumented immigrants and building a wall along the Mexican border — remain divisive. In Florida, Ohio and Pennsylvania, most voters think that undocumented immigrants should be able to stay in the United States while applying for citizenship. Floridians are split on the merits of a wall, while most Ohio and Pennsylvania voters are against it.

Mr. Brown noted that nonwhite voters in Florida are overwhelmingly against Mr. Trump’s wall, but that his support among white men is keeping him competitive in the state.

“Republicans’ weakness among minority voters is well-known,” Mr. Brown said. “But the reason this race is so close over all is Clinton’s historic weakness among white men.”