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

shubhamsrg · Answer

total sq. = r(r+1)
sq. in 3rd row = r
sq. in 7th column = r+1

our ans = r(r+1) - r - r -1 + 1

1 is added since there is 1 sq. common

just simplify.