2012 AMC 12B Problem 7

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

Group the lights into repeating blocks of

5

(two red, three green)

The

3

rd red light starts block

2

and the

21

st red light starts block

11

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.

Problem 7 in other years