Best way to approach a Multiple Choice exam

I have an exam tomorrow with 100 multiple choice questions. Each question has 4 options, only 1 is correct.

If I answer the question and get it right, I get 1 mark. If I leave it blank, I get 0. If I answer incorrectly, I lose 0.25 marks.

How should one approach the test? Mathematically/statistically are my odds better if I guess if I don't know the answer?

• What kind of test is this? The only test I've ever taken where they take marks off for incorrect answers is the SAT. – Chris K Dec 10 '13 at 4:35
• I'm from Australia and it's an exam for a course I'm studying at uni. – user2342435 Dec 10 '13 at 9:16

Imagine if you had $4$ questions you don't understand.

If you leave them blank, you will get a mark of $0$.
If you guess all of them, the expected result is getting $1$ right and $3$ wrong. This will get you an expected mark of: $$1-3(0.25)=0.25$$

Therefore it is better to guess than to leave questions blank.

• You need to divide your result by four... – Potato Dec 10 '13 at 6:41
• This is for 4 questions and don't confuse the OP – Abraham Zhang Dec 10 '13 at 6:42
• The question seems to be about individual questions, though. It's not obvious from this result that guessing is still the right move when confronted with 1,2, or 3 questions. – Potato Dec 10 '13 at 6:44
• I'm just showing that is better to guess, this will account for every individual question – Abraham Zhang Dec 10 '13 at 6:46
• You have shown that given 4 questions that the test-taker does not know the answer to, it is better to guess on all 4 than leave all 4 blank. This doesn't immediately generalize to the case of 1 question. – Potato Dec 10 '13 at 6:47

If you can eliminate at least one choice on a question, then you should guess from the remaining choices.

• It would be nice to give a proof... – Potato Dec 10 '13 at 4:36
• Also, maybe I'm making an error, but it seems like one should guess even if no answers can be ruled out. The expected value of guessing is $.25(1-.25-.25-.25)>0$, which is better than leaving it blank. – Potato Dec 10 '13 at 4:38
• While I did not give a proof, it most certainly does answer the question as stated "How should one approach the test?" – Carl Love Dec 10 '13 at 5:04
• @CarlLove What you say is true, but misleading. You should guess even if you can't eliminate an answer. – Potato Dec 10 '13 at 5:25
• @Potato You're right about the expected value of guessing always being positive. – Carl Love Dec 10 '13 at 5:32