Laois were dealt a harsh lesson from Galway on Friday night.
Westmeath and Offaly enjoyed victories in the Leinster Minor Hurling Championship over the weekend while Laois were left licking their wounds after a big defeat to Galway on Friday.
In their third round game, Westmeath were comfortable winners over Down where it finished 3-14 to 0-9.
Offaly beat Kerry by 12 points, 1-15 to 0-6, and the final score between Laois and Galway was 4-28 to 0-11.
Westmeath will next play Antrim, Offaly have Meath, and Laois are home to Carlow.