BERLIN, Jan 6 - Germany's DIW economic think tank said on Tuesday the euro exchange rate could become a problem for the country's economy if it reached $1.30 and the European Central Bank should cut rates if it rose to $1.35. "We would not expect a rate of $1.25 to be a big problem. A rate of $1.30 would certainly cause some difficulty if it was reached," DIW President Klaus Zimmermann told a news conference to present the institute's latest economic forecasts. He was speaking as the single currency rose to fresh life highs against the dollar over $1.2750 . DIW chief economist Gustav Adolf Horn said the European Central Bank should act if the single currency strengthens much further. "Monetary policy makers must take responsibility for the recovery. They can't just keep their hands in their pockets and say it will come," Horn said. "There is a rule of thumb that a strengthening of 10 percent in the euro can be offset by a rate cut of about one percentage point. If the euro strengthens to $1.35 that would imply the need for a rate cut of one percentage point," he added.||