Graeme McDowell and Rory McIlroy came through one of the most difficult examinations in major golf with flying colours before being hit by one of the toughest questions an Ulsterman can be asked.

McDowell hit 16 greens in regulation when he carded two birdies in an immaculate 70 as McIlroy chipped in with a one under par 71 that promised to be even better after he had raced into the early lead with three birdies in his first six holes.

Both players have high hopes of challenging for the title on Sunday afternoon but as they will represent Ireland under the tricolour in November’s World Cup in China, they were canvassed about the news that golf has been recommended for inclusion in the Olympic Games from 2016.

Administrators must now decide who will present Ireland in golf and the result of their deliberations could result in a tough call for the Ulster pair.

“Never thought about it, obviously it’s a strange one. Golf’s an all Ireland sport. I’d play for anyone,” McDowell said. “I’ve never been able to explain why golf’s an all Ireland sport and rugby’s an all Ireland sport but soccer is two different teams. It’d be an honour to represent your country and I don’t mind which one I play for.

“It’s the biggest sporting event on the planet, love to be involved in it. Love to win a gold medal. It’s every young man’s dream, huge for golf around the world. Golf needs to go the masses.  I’m not a fan of golf being an elitist sport. Fingers crossed I get a chance to do it.”

McIlroy assumed that he would be part of the Great Britain team but indicated that he was fully supportive of the move after some initial misgivings about the inclusion of golf in the Olympic movement.

“If I'm lucky enough to be on Team GB or whatever, it would be great, like Tom Daley, the diver, it would be great if he won a gold medal there and I was able to watch it and be part of a team.  It would be awesome.

“At the start of the talk about getting golf into the Olympics, I was a little skeptical and apprehensive about it.  But the more I think about it, the more it will be great for golf just to globalise the game and get countries like Russia and India and China recognised on a global stage.

“I thought it's not fair on the other athletes who train four years Hopefully it will grow the game and get more people to play the game.”

The Olympics are still seven years away and McDowell and McIlroy have chance to win much gold here.

McDowell was certainly happy to find his game again after a rough week in Akron,  picking up his first shot of the day at the sixth, where he hit a 105-yard sand wedge to a foot before hitting with a two iron to 25 feet at the 218-yard 13th.

He said: “I haven't been 100% happy with my full swing of late, just chipping away at it, just waiting for that one little thing, that one little cog to fall into place and I feel very, very close to playing well. I hit a lot golf shots out there today, and I've got a bit of work to do this afternoon just to try and bed some changes in that I'm making, but I'm close.”

Refreshed after a relaxing day on Wednesday, McIlroy started on the back nine and birdied the 10th from two feet before hitting wedges to six feet at the 14th and 15th to share the lead on three under.

But he was disappointed to drop a couple of shots coming home, driving into the hazard left of the 16th and then three-putting the first from 30 feet before parring his way in.

“I wasn't able to keep that going but I felt as if I played very solid today,” McIlroy said. “One under was the worst I could have shot. It could have been a little better but I'll take it.

“I gave myself a lot of chances which wasn't like me the last few weeks.  I just felt as if my rhythm was a little better and I started to strike it a little better and I was able to bring that on to the golf course which was really nice.

“The last three tournaments I've played have been a really big grind, just trying to make pars and trying to shoot somewhere around level par, but I actually feel after today that I can go around this golf course and shoot a good number.

“I said to (my caddie) JP on the 11th tee box after I've just birdied the 10th, I said, "It's nice to see a red number by my name again."  Hopefully that's a sign of things to come this week.  I'm going to take it one day at a time and see what happens.”