Explanation

The sentence contrasts the economy’s current struggles with the secretary’s predictions for its long-term prospects. Since the secretary believes that technology
will lead to economic growth, the secretary’s outlook is an optimistic one. Thus the correct answer is “sanguine,” which can mean optimistic. Since there is no indication that the secretary’s view has wavered or is open to alternate interpretations, “irresolute,” “ambivalent,” and “equivocal” are all incorrect. The straightforward explanation of the rationale for the secretary’s outlook suggests that it is not an “arcane” one, making that choice incorrect as well. Thus the correct answer is sanguine (Choice B).
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ambivalent is : having or showing very different feelings (such as love and hate) about someone or something at the same time. so why not it the answer as there was two emotions working here, hope and struggle.
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Even as the economy struggled, the secretary stood by his (i) ________ long-term outlook, saying that technology was allowing businesses to make deep-rooted improvements in their productivity, the best indicator of an economy’s ability to grow.

The word "even" at the beginning of the sentence contrasts the phrase "as the economy struggled" with "the secretary stood by his (i)_________ long-term outlook". Clearly since the economy was struggling which is a negative event, one would expect the secretary to have a positive long-term outlook, thanks to the contrasting word "even".

Also the sentence fragment following the comma after "long-term outlook" continues the idea, and it says that the secretary was sure that technology will allow business to make deep-rooted improvements in their productivity which is the best indicator of an economy's ability to grow. Thus the word describing the "long-term outlook" should be a positive one.

Therefore, sanguine, which means optimistic is the best choice.

In fact, it is easier to eliminate the rest of the choices. The choices equivocal, ambivalent and irresolute do not connote a positive attitude and can be eliminated. The word arcane means not open to the un-initiated, understood by a few, but the secretary has a very clear and easily understood idea of how technology will allow business to become more productive. Hence we can eliminate arcane.

We are thus left with sanguine which is the correct choice.
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