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I don't think either of these links can help me: http://www.oxfordlearnersdictionaries.com/definition/english/draw-on?=draw+on http://www.macmillandictionary.com/dictionary/british/draw-on Does it mean "MUFG officials have no idea whether the graduates could become the CEO of the company"?

"MUFG officials wouldn’t be drawn on whether the graduates could end up running the company. Unlike international banks such as Deutsche Bank AG, Credit Suisse Group AG and Morgan Stanley, Japan’s largest lenders have never had a foreign chief executive. In recent years, however, foreigners have led other Japanese companies, such as Nissan Motor Co. and Sony Corp. and smaller lenders Shinsei Bank Ltd. and Aozora Bank Ltd."

Source:https://www.bloomberg.com/news/articles/2017-08-09/global-push-leads-japan-s-biggest-bank-to-u-s-college-campuses

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This is not a distinct verb-plus-preposition idiom but the ordinary verb draw with a complementary preposition phrase headed by on.

Draw has its oldest meaning, “pull, drag”, employed in the metaphorical sense described in Macmillan, 10:

10 [TRANSITIVE] [USUALLY PASSIVE] to persuade someone to tell you something I asked her if a decision had been made, but she would not be drawn (=would not tell me).
draw someone on something: Journalists tried to draw him on the subject of his wife.

As the Macmillan definition shows you, draw in this sense takes the source of the information as its object and on introduces the topic of the inquiry.

Bloomberg tried to elicit the information, to “pull” MUFG toward providing it, but MUFG refused.

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