LYNN – The state’s unemployment outlook brought both good and bad news during October. The unemployment rate dropped from 9.3 percent in September to 8.9 percent in October, but the state also lost 900 jobs during the same period.According to the Executive Office of Labor and Workforce Development (EOLWD), the unemployment rate showed improvement in Peabody, which had a 9.3 percent rating in September and 8.3 percent last month. Nahant also showed improvement, its September unemployment rate of 8.1 percent declining to 5.9 percent in October.In Lynn, the changed was less marked, declining from 11 percent in September to 10.1 percent in October.”The Amherst, Lowell-Billerica-Chelmsford, Peabody and Leominster-Fitchburg-Gardner areas recorded the largest over the month unemployment rate declines,” said Alison Harris, a spokeswoman for the EOLWD.Harris said two areas posted seasonal unemployment rate increases, noting that statewide the seasonally unadjusted unemployment rate decreased from 9.3 percent in September to 8.4 percent in October.The Massachusetts labor office reported this week that unemployment rates were lower in October than in September in 20 of the state’s 22 labor market areas. The EOLWD will release detailed unemployment data for November on Dec. 17, Harris said.The job search engine Juju.com also released information that rated the difficulty of finding a job in major cities across the country. Of the 50 cities, Boston ranked eighth from the top, putting it among the most attractive job markets. Washington ranked first, with only two unemployed residents per advertised job. In Boston, there were 4.5 persons for every advertised job.Other major cities with rosier employment pictures, in order from top to bottom after Washington, were Baltimore, San Jose, Salt Lake City, New York, Hartford and Denver.Detroit ranked as the nation’s worst major city in which to find a job, followed closely by St. Louis, Miami, Las Vegas, Riverside and Los Angeles.The state Office of Workforce Development reported that the steep decline in job postings seen in the fourth quarter of 2008 has begun to level off. Job postings, which plummeted from 75,000 to 54,600 between the second and fourth quarters of 2008, are holding steady at 49,200. Further, the job vacancy vacancy rate currently stands at 1.7 percent after dropping from 2.6 to 1.9 percent in 2008.According to the labor office, “The job market, nevertheless, remains very weak. Full-time permanent job postings have fallen over the year from 62 to 52 percent.” The office noted that employers are able to hold out for experienced workers because the current supply/demand ratio of 5.7 is the highest recorded since its Job Vacancy Survey began.The office also reported that high-paying industries such manufacturing, information, and financeand insurance, accounted for a smaller share of job postings in 2008 compared to 2008. Only health care and the social assistance sectors added jobs during the current recession, accounting for 25 percent of all job postings during the second quarter of 2009, up from 21 percent last year.AREA UNEMPLOYMENT RATESThe Executive Office of Labor and Workforce Development has released unemployment rates for October. The following is a look at the last three months of unemployment percentages by community:LYNNOctober 10.1September 11August 10.8LYNNFIELDOctober 7.7September 7.9August 7.6MARBLEHEADOctober 6.5September 7.6August 6.9NAHANTOctober 5.9September 8.1August 7.6PEABODYOctober 8.3September 9.3August 8.7REVEREOctober 8.9September 9.9August 9.2SAUGUSOctober 8.7September 9.5August 8.9SWAMPSCOTTOctober 7.2September 8.1August 7.2STATE AVERAGEOctober 8.4September 9.3August 8.9SOURCE: Executive Office of Laborand Workforce Development