What is the difference between "without trace" and "without a sign

[heidi]

English Grammar Error, Intermediate level

ESL/EFL Test #22 "Gerunds and Idioms", question 6

They've searched everywhere for the thieves who stole half of their possessions but they've simply disappeared without sign.

(a) searched
(b) thieves
(c) sign

English Grammar Error, Intermediate level

ESL/EFL Test #22 "Gerunds and Idioms", answer 6

They've searched everywhere for the thieves who stole half of their possessions but they've simply disappeared without trace.

Correct entry: trace
The error was: (c) sign

You have found the error but your entry is incorrect.
They've searched everywhere for the thieves who stole half of their possessions but they've simply disappeared without a sign.
_________________________

Why don't you use "a trace"?

heidi

[Conchita]

The indefinite article 'a' is optional in that expression.