Farquhar attended Archbishop Edward A. McCarthy High School in Southwest Ranches, Florida, where he played for the school's baseball team as a pitcher and outfielder. He batted .436 as a sophomore. As an outfielder, Farquhar was named to the All-District Second Team in 2004, his junior year. As a senior, he had a 0.89 ERA, a school record.

Farquhar enrolled in college at the University of Louisiana at Lafayette, where he played for the Louisiana–Lafayette Ragin' Cajuns baseball team, competing in the Sun Belt Conference. As a college freshman, he was 6–1 with four saves and a 2.17 ERA. He led the Sun Belt Conference in ERA. In 2007, as a sophomore, Farquhar went 6–3 with six saves, a 3.08 ERA and 115 strikeouts to 22 walks in 87 ²⁄₃ IP. He was fourth in the conference in ERA and second in strikeouts. As a junior, he had a 3–8 record with a 4.95 ERA.

Farquhar was drafted by the Toronto Blue Jays in the tenth round, with the 309th overall selection, of the 2008 MLB Amateur Draft. He signed with Toronto.

Farquhar began the 2008 season with the Auburn Doubledays of the Class A-Short Season New York–Penn League, and was promoted to the Lansing Lugnuts of the Class A Midwest League. He finished 2008 with 2–2 win–loss record, 32.1 innings pitched (IP), and a 1.95 Earned run average (ERA). In 2009, he started the season with the Dunedin Blue Jays of the Class A-Advanced Florida State League and finished the season with the New Hampshire Fisher Cats of the Class AA Eastern League. In 2009, Farquhar had a 2–4 record, 1.87 ERA and 22 saves, in 62 ²⁄₃ IP. He was traded to the Oakland Athletics along with Trystan Magnuson for outfielder Rajai Davis after the 2010 season.

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