Question

A “stair-step” figure is made up of alternating shaded and unshaded squares in each row. Rows $1$ through $4$ are shown. All rows begin and end with an unshaded square. The number of shaded squares in the $37$ th row is

$34$

$35$

$36$

$37$

$38$

Answer: C

Concepts:pattern recognition basic counting

Difficulty rating: 860

Small Hint:

Row $n$ has $2n - 1$ squares, and they alternate starting and ending with an unshaded square

Big Hint:

Since the ends are unshaded and the squares alternate, there is one more unshaded square than shaded square in each row

Solution:

Row $n$ contains $2n - 1$ squares. Because both ends are unshaded and the squares alternate, each row has one more unshaded square than shaded square, so the number of shaded squares is $n - 1.$

For the $37$ th row, this is $37 - 1 = 36.$

Thus, the correct answer is C .

1985 AMC 8 Problem 7

Answer: C

Difficulty rating: 860

Small Hint:

Big Hint:

Solution:

Problem 7 in Other Years