The number of common terms in the two sequences $18, 24, 30, 36, \ldots, 606$ and $14, 24, 34, 44, \ldots, 604$ is:
Answer and solution
Correct answer: C
Solution
First common term $= 24$; common terms repeat every $\text{LCM}(6, 10) = 30$.
Common terms: $24, 54, 84, \ldots, 594$ (last one $\le 604$)
Count $= \dfrac{594 - 24}{30} + 1 = 19 + 1 = 20$
Common terms: $24, 54, 84, \ldots, 594$ (last one $\le 604$)
Count $= \dfrac{594 - 24}{30} + 1 = 19 + 1 = 20$