1. **Problem statement:** A student answered 120 True/False questions, scoring 90 marks. Each correct answer gives 1 mark, each wrong answer deducts 1/4 mark. The student knew some answers and guessed the rest. If all guessed answers were wrong, find: i. How many questions did he answer correctly? ii. How many questions did he guess? 2. **Formula and rules:** - Let $c$ = number of correct answers. - Let $g$ = number of guessed questions (all wrong). - Total questions: $c + g = 120$ - Total marks: $1 \times c - \frac{1}{4} \times g = 90$ 3. **Step-by-step solution:** i. From total questions: $$c + g = 120 \implies g = 120 - c$$ ii. Substitute $g$ into marks equation: $$c - \frac{1}{4}(120 - c) = 90$$ Simplify: $$c - 30 + \frac{c}{4} = 90$$ Multiply both sides by 4 to clear fraction: $$4c - 120 + c = 360$$ $$5c - 120 = 360$$ $$5c = 480$$ $$c = \frac{480}{5} = 96$$ iii. Find $g$: $$g = 120 - 96 = 24$$ 4. **Answer:** i. The student answered **96** questions correctly. ii. The student guessed **24** questions (all wrong).