NORTH ADAMS, Mass. — The local district attorney's race was the hottest ticket in Tuesday's primary but there were plenty of other races on the ballots for both parties. 

 

On the Democratic side, Jay Gonzalez outpolled Bob Massie by nearly double to move onto the general election. A former administrator under Gov. Deval Patrick, he'll face popular Republican Gov. Charlie Baker, who's pursuing a third term. 

 

For lieutenant governor, Quentin Palfrey bested Jimmy Tingle to win the nomination with nearly 60 percent of the vote. Palfrey's been in the Berkshires fairly frequently over the past months. 

 

William Galvin easily swept challenger Josh Zakim to for the Democratic nomination for secretary of state. Galvin, who's been in office since 1995, has no competition in the general election. 

 

Veteran Congressman Richard Neal easily fended off his opponent Tahirah Amatul-Wadud, a Springfield attorney, to move onto the general election for the 1st Massachusetts District for which he faces no competition. Though he outpolled Amatul-Wadud by nearly 70 percent, she was a known figure in Berkshire County, coming within 70 votes of him in Williamstown and was doing better comparably to some other towns. 

 

The only other local race was for state senator in which incumbent Adam Hinds won easily over challenger Thomas Wickham with nearly 90 percent of the vote.

 

There was more jockeying on the Republic side as candidates vied to take on their Democratic compatriots. 

 

Baker easily outpolled his primary opponent Scott Lively in a light election. Only about 227,000 votes were cast in the Republican gubernatorial primary compared to 467,000 in the Democratic. Lt. Gov. Karyn Polito had no primary opponent.

 

James McMahon won more than 60 percent of the vote against Daniel Shores for the Republican nomination for attorney general. He will face off with incumbent Democrat Maura Healey, who had no primary opponent. 

 

Geoff Diehl, a state representative, won the Republican nomination for U.S. Senate over John Kingston and Beth Lindstrom. Democrat Elizabeth Warren, the state's senior senator, immediately accepted three televised debates with Diehl in the coming months: one on Oct. 21 at the Western Mass Consortium with local news; one on Oct. 30, in Boston on WCVB; and a third on WBZ to be announced.