By Kate Gibson, MarketWatch

NEW YORK (MarketWatch) -- U.S. stocks rose sharply Tuesday after their worst session since November as investors considered a deal by Dell Inc. to be taken private and quarterly earnings that beat estimates.

After briefly clearing 14,000, a level last week breached for the first time in more than five years, the Dow Jones Industrial Average (DJI) was up 116.53 points, or 0.8%, to 13,996.61.

The S&P 500 index (SPX) climbed 13.63 points, or 0.9%, to 1,509.34.

The Nasdaq Composite (RIXF) advanced 29.31 points, or 0.9%, to 3,160.49.

For every stock that fell, three advanced on the New York Stock Exchange, where 184 million shares traded as of 10:55 a.m. Eastern.

The momentum for U.S. equities for the remainder of the year is a favorable one, Jim O'Neill, Goldman Sachs Asset Management chairman, told CNBC Tuesday.

Archer-Daniels-Midland Co. (ADM) gained after reporting quarterly profit that beat forecasts. Kellogg Co. (K) shares gained 2% after the cereal maker reported less of a quarterly loss. Yum Brands Inc. (YUM) fell 3.7% after the owner of the Pizza Hut chain reduced its profit outlook.

Virgin Media Inc. (NTLID) jumped almost 17% after the U.K. pay-television provider said it was in talks with Liberty Global Inc. (LBTYA) about "a possible transaction."

Dell Inc. (DELL) shares rose 0.8% after the personal-computer maker agreed to be taken private in a deal valued at $24.4 billion.

U.S. home prices climbed 0.4% in December to bring the year-on-year gain to 8.3%, the best advance since May 2006, CoreLogic reported Tuesday.

The Institute for Supply Management's services index fell to 55.2% in January from 55.7% in December. Any number above 50% signals expansion.

When considered in combination with the better-than-expected manufacturing report last week, "one can't help but feel that the private-sector economy is holding up fairly well despite the public sector's best efforts to cause turbulence," Dan Greenhaus, chief global strategist at BTIG LLC, emailed after the data.

U.S. stocks fell hard Monday on worries about Europe's handling of its debt crisis, with Spain's Mariano Rajoy facing calls from opposition leaders that he step down.

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