In an examination, there were 75 questions. 3 marks were awarded for each correct answer, 1 mark was deducted for each wrong answer and 1 mark was awarded for each unattempted question. Rayan scored a total of 97 marks in the examination. If the number of unattempted questions was higher than the nu

Question

In an examination, there were 75 questions. 3 marks were awarded for each correct answer, 1 mark was deducted for each wrong answer and 1 mark was awarded for each unattempted question. Rayan scored a total of 97 marks in the examination. If the number of unattempted questions was higher than the number of attempted questions, then the maximum number of correct answers that Rayan could have given in the examination is:

Accepted Answer

24 — Easy Let correct/wrong/unattempted be $c,w,u$. Write the count equation and the score equation, add them to eliminate $w$, then use the constraint $u>c+w$ to push $u$ as low as allowed (which maximises $c$). 1 The two equations: $$\begin{aligned} &c+w+u=75 &&(1)\ &3c-w+u=97 &&(2) \end{aligned}$$ 2 Add (1) and (2) to remove $w$: $$4c+2u=172\ \Rightarrow\ 2c+u=86\ \Rightarrow\ 2c=86-u$$ 3 Apply $u>c+w=75-u$: $$u>75-u\ \Rightarrow\ u>37.5\ \Rightarrow\ u_{\min}=38$$ 4 $c$ is largest when $u$ is sm

CAT 2022 Slot 2 — QA Question 17

Answer & solution