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Peter participated in a Math competition. There was a total of 35 questions. For each correct answer, 3 marks were awarded. For each wrong answer, 2 marks were deducted. For each question left blank, 1 mark was deducted. Peter did not answer 5 questions and scored a total of 70 marks. How many questions did he answer correctly?

Solution

For supposition method to work, there need to be only 2 scenarios. In this question there are 3 scenarios, namely:

Scenario 1 – Correct answer + 3 marks

Scenario 2 – Wrong answer − 2 marks

Scenario 3 – Blank answer − 1 mark

To begin we shall remove scenario 3 from the question.

Number of questions left to consider → 35 − 5 = 30

If there are no Blank answers, the actual score would be → 70 + 5 = 75 (marks)

Assume all answers are correct → 30 x 3 = 90 (marks)

Total difference between assumed and actual → 90 − 75 = 15 (marks)

Difference in 1 group → 3 + 2 = 5 (Difference in marks between a correct answer and a wrong answer)

Number of groups → 15 ÷ 5 = 3 (Number of wrong answers)

Number of correct answers → 30 − 3 = 27

Answer: 27