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 squares
In 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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