Querrey, who won the Los Angeles event in 2009 and 2010, dispatched Igor Sijsling of the Netherlands 6-2, 6-2 in second-round action.
Argentina's Mayer moved on when his opponent, Flavio Cipolla of Italy, bowed out in the second set with an injury. Mayer was leading 6-0, 4-0 at the time.
Rajeev Ram of the United States posted an easy win, rolling to a 6-3, 6-1 win over Chilean Paul Capdeville with the help of 10 aces.
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