The suspect is facing charges that he illegally published telephone credit card numbers, intending that they be used by others to avoid telephone billings.
A.
intending that
they be used by others to avoid telephone billings.
"with the intent" sounds more idiomatic than "intending" modifier. "they" is used to refer people
INCORRECT_____________________________________________________________
B. with the
intent of others using them to avoid telephone billings.
Meaning error. "intent of others" indicates that it is not the intent of suspect but of others.
INCORRECT_____________________________________________________________
C.
intending that telephone billings could be avoided by others using them.
"with the intent" sounds more idiomatic than "intending" modifier.
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D. with the intent of
their use by others to avoid telephone billings.
"their" is associated with people but this sentence uses it for credit card numbers.
INCORRECT_____________________________________________________________
E. with the
intent that telephone billings
would be avoided by others through their use.
suspects intent is correctly written using "would" to represent a certain event
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Hence option E