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In this test, the right answer is invaluable:

The new GPS is ________. I don't know how we managed without it before.

  1. priceless
  2. worthy
  3. invaluable
  4. valueless

Is priceless wrong? If yes, why?

  • see this: books.google.com/ngrams/… – Cardinal Jul 12 '16 at 13:21
  • As the answers indicate, it would be "priceless" if you were lost in the wilderness and would die except that the rescue personnel could use the location data to find you. – user3169 Jul 12 '16 at 17:19
  • If this is a question from an actual test, the question is poorly formed. Depending upon context, any of the first three choices could be "right," and either 1 or 3 might be heard in normal usage by a native speaker. "Priceless" is certainly not "wrong," in any case. – P. E. Dant Reinstate Monica Jul 12 '16 at 21:38
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Priceless is usually used to mean "so precious that its value cannot be determined".

This priceless painting by Monet is the pinnacle of art.

A nation's cultural heritage is priceless.

Invaluable usually means "extremely useful; indispensable".

Cloud storage is invaluable for companies.

Public transportation is an invaluable part of city life.

There are circumstances where priceless and invaluable look interchangeable, but there's a shade of difference.

At sea, a navigational chart is priceless.

When at sea, a navigational chart is very precious. However, the sentence doesn't tell us why it's priceless. We have to piece that together ourselves from our knowledge of what a navigational chart is used for.

At sea, a navigational chart is invaluable.

When at sea, a navigational chart is (almost) necessary and extremely useful. However, it could very well be not precious. For instance, in the developed world water is invaluable but usually not precious.

As for:

The new GPS is ________. I don't know how we managed without it before.

I feel that the reason priceless isn't the answer is because the speaker is talking about how useful the GPS is in the second sentence. Thus, we want to use invaluable. However, this is a very fine distinction and I can see a native speaker also using priceless in this case by defining the worth of the GPS to be calculated in usefulness rather than money.

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Personally I think the answer is invaluable and not priceless because the second sentence is not strong enough for priceless to be an appropriate fit. The writer says he "doesn't know how he managed before" which doesn't mean that the GPS is of incalculable worth, which is what priceless means.

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