The answer choices have been transcribed incorrectly.
They should read as I have posted them below:
sukriti2hats 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 then which of the following represents number of squares 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
Ignore the constraint that r>10.
Let r=6, with the result that the number of rows = 6 and that the number of columns = r+1 = 6+1 = 7.
Let X = a square on the board.
The board looks as follows:
XXXXXX
X
XXXXXX
X
XXXXXX
X
XXXXXXX
XXXXXX
X
XXXXXX
X
Total number of squares = 6*7 = 42.
The 4th row and the 7th column are composed of the squares in red.
Total number of squares in red = 12.
Thus:
Toral number of squares in NEITHER the 4th row nor the 7th column = 42-12 = 30. This is our target.
Now plug r=6 into the answers to see which yields our target of 30.
Only
A works:
r² - r = 6² - 6 = 30.
The correct answer is
A.
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