Vice President Joseph R. Biden’s claim that he heard the gunshots of a 2006 school massacre while playing golf is raising questions about his veracity or his memory.

Mr. Biden told a meeting of mayors in Washington Thursday that he was about a quarter-mile away from an Amish schoolhouse on Oct. 2, 2006, when a gunman shot and killed five students and wounded five others.

“I happened to be literally — probably, it turned out, to be a quarter of a mile [away] at an outing when I heard gunshots in the woods,” Mr. Biden recounted. “We didn’t know … we thought they were hunters.”

But a search of maps of the area in Lancaster County, Pa., shows the nearest golf course to the site of the shooting, Moccasin Run Golf Club, is about five miles away. Rodney King, the golf pro at Moccasin Run, said Friday he was working at the course on the day of the shooting and never saw Mr. Biden, who was then a U.S. senator.

“There’s a lot of things here that I find hard to believe,” Mr. King said. “I looked in my database, and he [Mr. Biden] is not in my database.”

Even if Mr. Biden had played at the course that day, Mr. King said, “It’s very far-fetched that he would have heard it.”

“I know he didn’t hear those gunshots,” Mr. King said. “They were inside the school. Even if they were outside, he wouldn’t have heard them.”

A spokeswoman for the vice president did not return a request seeking comment Friday. Mr. Biden told the story as he was describing for the mayors’ group the Obama administration’s efforts to enact new gun-control laws.

Another golf course in the region, the Lancaster Country Club, is about 10 miles away from the site of the shooting. Mr. King said it’s more likely that a group of golfers including a senator would play there.

“I would be honored to have Joe Biden play here because he’s a public figure,” he said. “But I put myself in his shoes — Moccasin Run Golf Club would not be the golf course I would go to if I’m going on a golf trip. We are a public facility.”

Mr. Biden said after the shooting, he saw helicopters flying to the scene. Medical helicopters were used to transport victims on that day.

Mr. King said there is a sportsman’s club about a mile from his golf course, and golfers can hear the shots from time to time during target practice. The schoolhouse has since been razed.

While running for the Democratic presidential nomination in 2007, Mr. Biden said in a debate that he had been “shot at” during a trip to Iraq. Pressed by reporters, he eventually described three incidents on two separate Iraq trips in which he felt that he was shot at or might have been shot at.

He ended up revising his description by saying: “I was near where a shot landed.”

Aides later said that on one occasion Mr. Biden heard mortars being fired a few hundreds yards away from the building where he was staying in the Green Zone, and on another occasion a bullet was fired at a helicopter in which he was flying.

• Staff Writer Susan Crabtree contributed to this article.

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