* U.S. consumer price data due at 1230 GMT * U.S. job openings hit record high in March (Updates prices) May 12 (Reuters) - Gold prices fell on Wednesday, weighed down by higher U.S. Treasury yields and a slight rebound in the dollar ahead of the much-awaited U.S. consumer price data due later in the day. Spot gold was down 0.4% at $1,829.94 per ounce by 0510 GMT. U.S. gold futures eased 0.3% to $1,830.30. “The dollar has strengthened a little bit ... if the inflation rate is higher than expected, it could encourage central banks to consider tightening their monetary policies faster than expected,” said Margaret Yang, a strategist at DailyFX.