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 r10, 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

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

ganeshie8 · Answer

A

ganeshie8 · Answer

total rows : r
total columns : r + 1

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)

so far ok ?

anonymous · Answer

- 1 from both row (will be r-1) and column (will be r) and then multiply (will be r*r-1 or r^2-r)!