April 23 (Reuters) - U.S. Treasury yields dipped on Tuesday after data showed that U.S. business activity cooled in April to a four-month low, though trading remained range bound before gross domestic product and inflation data later this week.

Business activity cooled due to weaker demand, while rates of inflation eased slightly even as input prices rose sharply, suggesting some possible relief ahead as the Federal Reserve looks for signs that the economy is ebbing enough to curb price pressures.

Inflation readings in Thursday’s GDP and Friday’s Personal consumption expenditures (PCE) reports will be evaluated on whether the market reaction to sticky consumer price pressures in March was justified.

“People will be focused on the specific trajectory of inflation,” said Vail Hartman, U.S. rates strategist at BMO Capital Markets in New York.

The PCE data is expected to show that core prices rose by 0.3% in March for an annual gain of 2.7%.

If the data comes in as anticipated, bonds could rally as a result, said Hartman.

“There’s greater potential for it to be traded as the passage of an event risk, and as long as it comes in at consensus or lower it will be more likely a relief rally,” he said. “If it comes in at 0.3%, that will imply much less inflationary angst than core CPI did in the month of March, so that might even suggest that the initial reaction to core CPI was overdone.”

Yields rose to five-month highs after hotter-than-expected consumer price pressures for March released earlier this month dashed hopes that elevated prices in January and February were an anomaly.

Benchmark 10-year note yields were last down 3 basis points on the day at 4.596%. They are holding below the 4.696% level reached on April 16 which, if broken, would be the highest since early November. Two-year yields fell 5 basis points to 4.925%. They reached 5.012% on April 11, the highest since mid-November.

The inversion in the yield curve between two-year and 10-year notes narrowed by 3 basis points to minus 33 basis points.

The Treasury saw strong demand for a $69 billion auction of two-year notes on Tuesday, the first sale of $183 billion in short and intermediate-dated supply this week.

The notes sold at a high yield of 4.898%, almost a basis point below where they had traded before the sale. The bid-to-cover ratio was 2.66 times, the highest since December.

The Treasury will also sell $70 billion in five-year notes on Wednesday and $44 billion in seven-year notes on Thursday.

(Reporting By Karen Brettell; editing by Christina Fincher and Marguerita Choy)