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The nation’s service sector expanded at a faster-than-expected pace in May, suggesting it could help sustain broader economic growth as the automotive and housing industries slump, a research group said Tuesday. The Institute for Supply Management, based in Tempe, Ariz., said its index of business activity in the non-manufacturing sector was 59.7 in May. The reading was higher than April’s reading of 56 and Wall Street’s expectation of 56. Areading above 50 indicates expansion, while one below indicates contraction.