“The finding was that people who use an answer key when taking a test see their score as a sign of their innate ability, selectively forgetting that the key helped them achieve the score,” said the lead author, Zoe Chance, a doctoral student in marketing at Harvard Business School.

Without the answers handy, those confident students did no better on an actual second test than the others.

Anyone who has ever peeked at the answers at the back of the physics or chemistry textbook already suspects this. It’s one thing to study a solution when the problem itself is totally unfamiliar, requiring techniques that haven’t yet been learned. It is another to scan the answers when problems are familiar but difficult. Those problem sets go more smoothly, confidence goes up, the temptation to take a study break grows stronger.

These sensations reflect more than simple self-deception.

Even hints or answers that are not consciously remembered alter how the brain processes a problem or question, making the experience very different from an unaided exam question. In a 1996 study, researchers at Macalester College and New York University had subjects solve 60 anagrams and rate how difficult each one would be for others to solve. One group of participants had already seen the answers to half of the puzzles in an earlier phase of the study, scattered like so many detective-novel clues in a long list of random words. As a result, they solved those anagrams faster and rated them as significantly easier to solve than the other half — without consciously remembering having seen the answers.

“Studying something in the presence of an answer, whether it’s conscious or not, influences how you interpret the question,” Dr. Bjork said. “You don’t appreciate all of the other things that would have come to mind if the answer weren’t there.

“Let’s say you’re studying capitals and you see that Australia’s is Canberra. O.K., that seems easy enough. But when the exam question appears, you think: ‘Uh oh, was it Sydney? Melbourne? Adelaide?’ ”