CAT (QA) PYQs

The average of all 3-digit terms in the arithmetic progression $38, 55, 72, \dots$, is

Let $a_{1}, a_{2}, \ldots \ldots . . . a_{3 n}$ be an arithmetic progression with $a_{1}=3$ and $a_{2}=7$. If $a_{1}+a_{2}+\ldots .+a_{3 n}=1830$, then what is the smallest positive integer $m$ such that $m\left(a_{1}+a_{2}+\ldots .+a_{n}\right)>1830$ ?

The number of common terms in the two sequences: $15, 19, 23, 27,......., 415$ and $14, 19, 24, 29,........,464$ is