CAT (QA) PYQs

If $a - 6b + 6c = 4$ and $6a + 3b - 3c = 50$, where $a$, $b$ and $c$ are real numbers, the value of $2a + 3b - 3c$ is

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

A fruit seller has a stock of mangoes, bananas and apples with at least one fruit of each type. At the beginning of a day, the number of mangoes make up $40 \%$ of his stock. That day, he sells half of the mangoes, $96$ bananas and $40 \%$ of the apples. At the end of the day, he ends up selling $50 \%$ of the fruits. The smallest possible total number of fruits in the stock at the beginning of the day is