Can I use the expression 'look through' with the adverb 'carefully'?

[Leonhardt]

English Language Proficiency Tests, Advanced Level

ESL/EFL Test #70 "What the Devil", question 9

You should really look through that agreement carefully before you sign because the devil is in the ..........

(a) detail
(b) exact
(c) finery
(d) precise

English Language Proficiency Tests, Advanced Level

ESL/EFL Test #70 "What the Devil", answer 9

You should really look through that agreement carefully before you sign because the devil is in the detail.

Correct answer: (a) detail
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Can I use the expression "look through" with the adverb "carefully"? I mean, they have opposite senses, once "To look through something" is "to read something quickly", right?

Leonhardt

[Mister Micawber]

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Not in my book. 'Looking through' something can be done carefully or quickly-- or perfunctorily, lazily, meticuloiusly, etc. 'Through' means 'completely, from end to end'.
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Native English teacher at Mister Micawber's