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* STOXX Europe 600 up 0.6 pct
* UK mid-cap index hits record high
* Deutsche Bank climbs to 2-week high
By Atul Prakash
LONDON, Oct 4 (Reuters) - European shares advanced on Tuesday, with Germany's Deutsche Bank hitting a two-week high following recent steep losses and the world's biggest education company Pearson gaining after encouraging comments by Morgan Stanley.
Pearson rose 5.6 percent, the top gainer in the pan-European STOXX 600 index, after Morgan Stanley said the company was unlikely to issue a profit warning, "meaning the shares could recover sharply on the Q3 results".
Deutsche Bank rose 2.7 percent to a two-week high. Its shares had slumped to a record low on Friday before bouncing back on expectations of a swift deal with U.S. authorities over a multi-billion dollar penalty.
HSBC said that despite Deutsche Bank's obvious operational shortcomings, fears over the bank's solvency were overdone. However, HSBC cut its target price for the bank, forecasting challenging conditions for the banking environment.
"Deutsche Bank should be well equipped to deal with this short-term lack of confidence," HSBC analysts said. "We maintain our 'hold' rating despite the selling pressure on the market as we believe the fundamentals of the company have not changed."
The STOXX Europe 600 index was up 0.6 percent, while Germany's DAX, which resumed trading after a holiday on Monday, was up 0.5 percent.
Britain's domestically-focused mid-cap FTSE 250 rose 1 percent to a record high, while the FTSE 100 index, dominated by international firms, gained 1.2 percent to 7,063 points - the first time since the mid-2015 it breached the 7,000 mark - helped by a weaker sterling following the Brexit vote.
"The (sterling) depreciation has been orderly thus far and is delivering the needed boost to UK exporters," Peel Hunt strategist Ian Williams said.
Among sector movers, BMW rose 2.5 percent and helped the European auto and parts index to gain 1.7 percent after Exane BNP Paribas raised its target price for the automaker to 87 euros from 70 euros.
Shares in Intertek rose 4.5 percent after Jefferies raised its stance on the stock to "buy" from "underperform" and lifted its target price to 4,300 pence from 3,000 pence. (Editing by Andrew Heavens)