Firms say this explicitly. Several publish that they are assessing how you approach a problem and whether you take hints well, which means silence is not neutral - it is missing data about the thing being scored.
But "think out loud" is bad advice on its own, because narrating everything is worse than narrating nothing.
Narrate structure, not arithmetic
Say this: "I will condition on the first draw, because that splits the problem into two cases I can handle separately."
Do not say this: "Seven times eight is fifty-six, plus three is fifty-nine, carry the one..."
The interviewer is listening for whether you chose a sensible decomposition. They do not need to audit your multiplication, and doing it aloud makes you slower and more error-prone.
State assumptions before computing
Most problems are slightly underspecified, deliberately. "Are the draws with replacement?" is not a stalling question - it is the question, and asking it demonstrates exactly the care being tested.
This is also where hints appear. An interviewer who watches you assume something wrong will usually correct you, and that correction is free.
Say when you are stuck
The instinct is to go quiet and hope something arrives. It never does, and the silence reads as either panic or arrogance.
"I do not see the trick here. My instinct is to try small cases first" is a strong thing to say. It shows a fallback strategy, which is exactly what the job needs when a trade goes wrong.
Take the hint, visibly
If you are offered a hint, use it and say you are using it. Ignoring a hint to preserve some idea of independence is the most reliably fatal mistake in these interviews - one firm names taking hints well as an explicit criterion.
Correct yourself out loud
Catching your own error is a positive signal, not a negative one. Say "wait - that double-counts the case where both are red" and fix it. That is the sound of someone who will catch their own bad trade.
Practise it alone
It feels ridiculous and it works. Solve practice questions with your voice on, or record yourself. The gap between thinking clearly and speaking clearly is much wider than people expect, and it only closes with reps.