Question

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

Answer 1

The correct answer is A r^2 - r. Here is the procedure to give you an idea on to why is it like that:
Lets say that total rows : r
And lets say that total columns : r + 1
Now the total squares = r(r+1) ------------(1)
squares in 4th row = r+1
squares in 7th column = r
squares common to above = 1
total squares in 4th row, and 7th column = 2r ------- (2)
Now what we cca do after describing all this facts is that
- 1 from both row will be r-1
column will be r
and then multiply (will be r*r-1 or r^2-r)!
I hope this can help you greatly