Carcass wrote:

A rectangular game board is composed of identical squares arranged in a rectangular array of r rows and r + 1 columns. The r rows are numbered from 1 through r, and the r + 1 columns are numbered from 1 through r + 1. If r > 10, which of the following represents the number of squares on the board that are

neither in the 4th row nor in the 7th column?

A) \(r^2\) — r

B) \(r^2\) — 1

C) \(r^2\)

D) \(r^2\) + 1

E) \(r^2\) + r

NOTE: After creating the graphics, I see that I used n instead of r.

Please forgive me!

Let's start with an n by n+1 grid

The number of squares = (n)(n + 1) =

n² + nIn the 4th row, we can see there are

n+1 squaresIn the 7th column, there are n squares.

HOWEVER one of the squares is already shaded blue.

So, there are

n-1 red squares

TOTAL number of UNSHADED squares =

n² + n - (

n + 1) - (

n - 1)

= n² - n

Answer: A

Cheers,

Brent

_________________

Brent Hanneson – Creator of greenlighttestprep.com

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