He answered 12 questions correctly, so this means there are 8 other questions which are either incorrectly answered or unanswered.


For those 12 correctly answered questions, he would score :

12 × 6 points = 72 points


So for the other 8 questions,

72 - 68 = 4

He would have been deducted a total of 4 points and obtained an overall score of 68.

Next ,

if we pair every wrongly answered question with an unanswered question,

2 points are scored for the unanswered one but 3 points are deducted for the wrongly answered one.

So there would be an overall deduction of 1 point.

For 4 such pairs, that would be :

4 x 1 = 4

There would be a deduction of 4 points. And 4 such pairs means 8 questions in total, which fits the remaining number of questions.

So there were 4 unanswered questions.

Or if you want to do the normal supposition/assumption way,


① Assume all 8 questions were unanswered.

Number of points scored here

= 8 × 2
= 16

② Since there must be an overall deduction of 4 points from these questions, we need to change some of these to wrongly answered questions.

For every one unanswered question changed, the 2 points awarded must be taken back. Another 3 points must be deducted since it is now a wrongly answered question.


2 + 3 = 5

For each question changed, 5 points are removed.


③ 16 + 4 = 20

So in order to have an overall deduction of 4 marks, 20 marks must be removed.


④ 20 ÷ 5 = 4

So 4 questions have to be changed. Which means there were 4 wrongly answered questions in the first place.


⑤ 8 - 4 = 4

There were 4 questions unanswered.