Q: A rectangular game board is composed of identical squares 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?
Answer: r2(that 2 is a square)-r
I would like to understand why that's the answer... This is a problem from the official guide test. Thank you.
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- yeji_dwaji
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- tommywallach
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Re: Official guide math
Hey Yeji,
Well, let's imagine a situation in which there are 10 rows and 11 columns. If we take off one whole column, now it's just 10 by 10. So r^2. However, we also need to remove one whole row (and remember that each row now has 10 squares in it, since we removed a column, and 10 is our original "r"). So we have to subtract r squares.
This gets us to r^2 - r
Make sense?
-t
Well, let's imagine a situation in which there are 10 rows and 11 columns. If we take off one whole column, now it's just 10 by 10. So r^2. However, we also need to remove one whole row (and remember that each row now has 10 squares in it, since we removed a column, and 10 is our original "r"). So we have to subtract r squares.
This gets us to r^2 - r
Make sense?
-t
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