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Vera and David Denmark knew what they wanted: a house in Milton, with plenty of room for children. It had to be renovated, move-in ready, in their price range, and on a street with a neighborhood feel.

They picked Milton for the schools, and because the town was about halfway between their jobs, as physicians at area hospitals.

After a year and a half and three lost bids, they bought a 4,000-square-foot modified Cape on Brush Hill Lane last fall. Houses on the street were farther apart than they had hoped. And they exceeded their initial price range to get a house in good shape with the space they wanted, paying just over $1 million, she said.

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The couple found themselves smack in the middle of a market with low inventory and surging prices that have been most evident in the inner Boston metropolitan area, but have also seeped into farther-afield communities with a reasonable commute to Boston jobs.

The price of a single-family home has now leapt above 2005 levels — the state’s peak market before a long decline — in 46 communities, according to a report by the Warren Group, a Boston company that tracks real estate statistics. Prices from the peak through the end of 2014 rose a chart-busting 80 percent in Cambridge to $1.2 million, and 41 percent in Boston’s Jamaica Plain, to $700,000.

South of Boston, prices have bested the peak only in a handful of cities and towns, but Milton leads the way, with prices 11 percent higher than in 2005. The median there was $525,000 last year.

Next is Sharon, where prices have risen 7 percent above peak, making the latest median $488,425. Cohasset is 1 percent above peak at $775,000; most other communities south of Boston are flat or below peak, some of them substantially so. But prices in general have made significant gains from the bottom of the market.

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Median single-family home prices in many cities and towns have made double-digit gains in the last three years. From 2011 to 2014, prices rose 32 percent in Brockton and more than 25 percent in Freetown, Rockland, Stoughton, and Quincy. Three-year gains of at least 20 percent took place in Dedham, Hanson, Middleborough, Sharon, and Weymouth. More than a dozen others saw prices rise at least 15 percent.

Normally, few homes come onto the market during the cold months, but this winter, even with the historic snowfall, homes were selling well in Milton, according to Kevin Keating, owner and broker at the Keating Brokerage. He kept a shovel in the back of his car for the days when newly fallen snow made it tough to get into a house for a showing.

Location and price are key for Milton buyers, he said. The town is close enough to Boston for quick commutes and is more affordable than western suburbs like Brookline and Wellesley, he said.

Bonnie Klayman outside a home on Lakeview Street in Sharon, a fixer-upper she and her husband recently bought to renovate and resell or rent out.
Bonnie Klayman outside a home on Lakeview Street in Sharon, a fixer-upper she and her husband recently bought to renovate and resell or rent out.John Tlumacki/Globe Staff

Buyer Bonnie Klayman concurred that homes seem to be selling quickly. She and her husband, David, who are longtime Sharon residents, buy single-family and two-family homes, all in Sharon, to renovate and sell, and sometimes to rent. About two months ago, they made an offer on a house that had just come on the market. They offered more than the asking price, in cash, but did not get the house.

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“It seems like if you don’t jump on something, it won’t be there,” she said.

One of their most recent purchases, a 2,400-square-foot house with attached two-car garage on Lakeview Street, has not been redecorated in decades, she said. The home needs a lot of updating, including in the kitchen and bathrooms. The couple paid about $365,000, she said.

Amenities like good schools, Lake Massapoag, and summer camps in town help make Sharon attractive, according to real estate agent Deb Piazza of Coldwell Banker’s Sharon office. And the attention the town got from Money magazine in 2013 — named best place to live among small towns — put it on the map, not only with buyers but also with relocation agents, she said.

This year, she expects the busy spring market to start late because of snow. She said it usually heats up around March 1, but some sellers were still dealing with ice dams on their roofs at that time. Her office had 25 homes on the market in early March, whereas when the spring season hits, the office aims to have 75 to 100 for sale, she said.

With inventory low, she said sales have been competitive. One buyer drove all the way from Connecticut for a showing. Sometimes, a house would be gone before it really hit the market, she said.

Competition like that drives prices up.

In economic terms, jobs are generally the biggest influence on home prices, according to Michael J. Murphy, an economist in the New England office of the US Department of Housing and Urban Development. Preliminary 2014 data show the Boston metropolitan area added about 38,800 net jobs last year, an increase of 1.6 percent.

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Although jobs grew 1.9 percent nationally, Boston typically grows slower than the nation, so its growth was strong. Every private employment sector added net jobs in 2014, with education and health services leading the pack, he said.

Timothy Warren, chief executive officer of the Warren Group, said that in general, Massachusetts prices are rising the most in communities with the best-paying jobs and easy access to employers in and around the Boston, Cambridge, and Brookline areas.

Those communities also tend to have higher real estate values. Among the top 10 communities in Massachusetts ranked by the increase in single-family home prices since 2005, seven had median prices of $899,000 or higher. They included Brookline, where the median home cost $1.5 million; Lexington, where the price was $950,000; and Newton, at $941,000.

“It’s clearly the richer communities that are doing better,” Warren said.

None of the south suburbs made the top 10, but on the other end of the spectrum, where prices remain in the biggest hole compared with 2005, Randolph was the ninth-worst in the state, with the median price still 27 percent below peak, at $255,000. The others in the bottom 10 had particularly low median home prices, all below $175,000.

Locales with fewer than 50 sales in 2005 were not included in the report.

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Income data from the US Census show an inexact but noticeable correlation between home-price recovery since the peak and household income. The best recoveries in Boston’s south suburbs — in Milton, Sharon, Cohasset, and Westwood — occurred in towns with median household income above $111,000. The area’s worst recoveries — in Randolph, Wareham, Brockton, and Holbrook — occurred in places with household income of less than $63,000.

Nationally, prices are rising, but prices are not the only indicator of a good housing market. Home construction and new-home sales remain weak, according to S&P Dow Jones Indices, in a press release in February.

In 20 major US metropolitan areas, taken together, real estate prices rose 4.5 percent last December compared with the previous December, as measured by the S&P/Case-Shiller 20-City Composite Home Price Index. The Northeast and Midwest regions were weaker than others, but Boston performed the best in those two regions, with prices increasing 3.8 percent.

Jennette Barnes can be reached at jennettebarnes@yahoo.com.