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A rectangular game board is composed of identical squares ar

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A rectangular game board is composed of identical squares ar [#permalink] New post 17 Feb 2017, 02:33
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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
[Reveal] Spoiler: OA

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Re: A rectangular game board is composed of identical squares ar [#permalink] New post 17 Feb 2017, 11:08
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Explanation

If we were just counting all of the squares in the board game we could use multiplication: r rows times r+1 columns.

This would give us r^2+r squares.

If we take one row out (doesn't matter if its the first, second, third, etc) then we would have r-1 rows times r+1 columns.

If we also then take a column out, we would have r-1 rows times r columns.

So the total number of squares without a column and without a row is r\times(r−1)=r^2−r.

So option A is correct.
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Re: A rectangular game board is composed of identical squares ar   [#permalink] 17 Feb 2017, 11:08
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