T-Mobile US Inc. is cutting prices and increasing data allocations on family plans to challenge larger rivals, including Verizon Communications Inc.

For families of two, T-Mobile is offering 10 gigabytes of data to each person for a total of $100, with each additional line costing $20 more, according to a statement. For families of four who sign up through Labor Day, the carrier is offering the fourth line for free, bringing the total to $120. A Verizon plan that includes 40 gigabytes of data would cost $300 plus an additional $60 in access charges for four phones.

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T-Mobile's price cut, like its announcement last week to add service in Canada and Mexico to its Simple Choice plan, is aimed at gaining customers and overtaking Sprint Corp. as the third-largest U.S. wireless carrier.

Offers including free music streaming and rollover data credits helped T-Mobile gain 2.1 million customers last quarter and put pressure on AT&T Inc. and Verizon to follow suit.

With the new offer, T-Mobile eliminates its two-person, $100 a month unlimited data plan. Verizon, which moved away from unlimited data plans three years ago, was one of the first carriers to introduce family shared-data options.

T-Mobile's 10-gigabyte, per-person offer is the lowest- priced plan of the top four carriers, according to Bloomberg Intelligence. Yet that amount of data is almost four times the 2.4 gigabyte average monthly usage of mobile customers in North America this year, according to ABI Research.

"Our plans match the way customers use wireless service," said Debi Lewis, a Verizon spokeswoman. "Sharing, not only among family members but across devices, is the way wireless works today."