Question

Small lights are hung on a string $6$ inches apart in the order red, red, green, green, green, red, red, green, green, green, and so on continuing this pattern of $2$ red lights followed by $3$ green lights. How many feet separate the $3$ rd red light and the $21$ st red light?

Note: $1$ foot is equal to $12$ inches.

$18$

$18.5$

$20$

$20.5$

$22.5$

Solution:

The lights repeat in blocks of $5,$ so consecutive blocks start $5\cdot6=30$ inches, or $2.5$ feet, apart.

Each block has one odd-numbered red light beginning it. The $3$ rd red light begins the $2$ nd block and the $21$ st red light begins the $11$ th block.

The distance between them is $(11-2)\cdot2.5=22.5$ feet.

Thus, the correct answer is E.

2012 AMC 12B Problem 7

Solution:

Problem 7 in Other Years