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A rectangular game board is composed of identical squares ar [#permalink]
Expert's post 00:00

Question Stats: 55% (02:00) correct 44% (01:39) wrong based on 47 sessions

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]
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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 $$r*(r-1)=r^2-r$$.

So option A is correct.
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Re: A rectangular game board is composed of identical squares ar [#permalink]
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what if we calculate all the cells in total first likeso r*(r +1) = r^2 + r

and then calculate the total cells missing likeso r + r + 1 = 2r + 1

and then substract one value from another

likeso r^2 + r - 2r - 1 = r^2 -r -1 here we have one extra one. Why is that?
Intern Joined: 19 Jan 2018
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Re: A rectangular game board is composed of identical squares ar [#permalink]
nevermind... got it GRE Instructor Joined: 10 Apr 2015
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Re: A rectangular game board is composed of identical squares ar [#permalink]
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Carcass 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, 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

NOTE: After creating the graphics, I see that I used n instead of r.
Please forgive me!  The number of squares = (n)(n + 1) = n² + n

In the 4th row, we can see there are n+1 squares In the 7th column, there are n squares. So, there are n-1 red squares

TOTAL number of UNSHADED squares = n² + n - (n + 1) - (n - 1)
= n² - n

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com  Re: A rectangular game board is composed of identical squares ar   [#permalink] 28 Mar 2019, 15:01
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