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The question is - The risk of living near a volcano is more than offset by the benefits. To what extent is this true?

If I agree with this statement, does it mean that I agree that there are more benefits than the risk in living near a volcano?

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    When you say, "If I agree with this statement", do you mean that the statement is everything from "The risk of living" to "extent is this true?" (two separate sentences)?. The reason I ask is because there are two elements given- one is a statement that makes a claim ("risks are offset by the benefits"), and the other is a question about that claim ("to what extent is this true?"). It doesn't make sense to agree with a question – elmer007 Jun 27 '16 at 19:14
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    The sentence should really read "The risks of living near a volcano are" or "The risk of living near a volcano is", so that the subject and verb agree in number. – stangdon Jun 27 '16 at 20:21
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The answer to your question is "Yes." If you agree with the statement "The risk of living near a volcano are more than offset by the benefits," you believe that the benefits of living near a volcano are more important than the risks.

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The poster probably just wants to know the meaning of A is more than offset by B

This simply means that the problem of A is smaller than the benefit of B. For example:

The cost of living in Tokyo is more than offset by the high average Tokyo salary.

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There are two questions here: What does the first sentence mean, and what is the correct response to the second sentence?

The risk(s) of living near a volcano are more than offset by the benefits.

(I corrected a typo - "risk" is singular, and "are more" is plural.)

To simplify this idea, we can split it up:

Living near a volcano has risks.

Living near a volcano also has benefits.

The benefits of living near a volcano offset the risks of living near a volcano.

The benefits more than offset the risks.

The most complex idea here is "offset", which in this context means "to balance out". (Definition #1 here: http://www.dictionary.com/browse/offset ) In this case, the author is weighing the benefits against the risks on an imaginary scale, and believes that the good balances the bad. In fact, the good more than balances the bad.

To use it in another way, I might say that the benefits of exercise more than offsets the inconveniences of exercise. That is to say, exercise is worth the costs.

To what extent is this true ?

If the author asked "Is this true?", we could provide a simple "Yes, that is true" and be done with it. However, by asking "To what extent is this true?" the author is saying this is true only to a point, and is asking us where that point is.

For instance, consider: "It is perfectly safe to drink beer. To what extent is this true?" Beer is safe to drink, as long as you stop before you make yourself sick, or impair your judgement enough to be dangerous. It's true that beer is safe to drink...to a point.

So, to what extent is it true that the benefits of living near a volcano outweigh the risks? I would say that the benefits outweigh the risks, until the volcano erupts.

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