CAT (QA) PYQs

Let a and b be natural number. If $a^2 + ab + a = 14$ and $b^2 + ab + b = 28$, then $(2a + b)$ equals

Let $A, B$ and $C$ be three positive integers such that the sum of $A$ and the mean of $B$ and $C$ is $5.$ In addition, the sum of $B$ and the mean of $A$ and $C$ is $7.$ Then the sum of $A$ and $B$ 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