Question

Consider the dark square in an array of unit squares, part of which is shown. The first ring of squares around this center square contains $8$ unit squares. The second ring contains $16$ unit squares. If we continue this process, the number of unit squares in the $100$ th ring is

$396$

$404$

$800$

$10{,}000$

$10{,}404$

Answer: C

Concepts:difference of squares pattern recognition

Difficulty rating: 1070

Solution:

The $n$ th ring is the border of a $(2n+1)\times(2n+1)$ square surrounding a $(2n-1)\times(2n-1)$ square, so it contains $(2n+1)^2-(2n-1)^2=8n$ unit squares.

For $n=100,$ that is $800.$ Thus, the correct answer is C.

2001 AMC 10 Problem 11

Answer: C

Difficulty rating: 1070

Solution:

Problem 11 in Other Years