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In a certain conference room, each row of chairs has the [#permalink]

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15 Apr 2006, 15:34

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In a certain conference room each row of chairs has the same number of chairs, and the number of rows is 1 less than the number of chairs in a row. How many chairs are in a row?

(1) There is a total of 72 chairs (2) After 1 chair is removed from the last row, there is a total of 17 chairs in the last 2 rows

Statement 1: We know that each row has the same number of chairs, so 72/r must be an integer. We also know that rows*chairs per row (let's denote as C) = 72, and that r + 1 = c. So let's get at it.

r*c = 72 r*(r+1) = 72 r^2 + r - 72 = 0. (r+9)(r-8) There cannot be a negative number of rows, so r = 8. Therefore, chairs per row is 9.

Statement 2: This one is much easier to work with. Remembering that each row has the same number of chairs, if we add two rows, we get 2c. So if we add back in the chair taken out, we get 18. Therefore, there are 9 chairs per row.

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In a certain conference room each row of chairs has the same number of chairs, and the number of rows is 1 less than the number of chairs in a row. How many chairs are in a row?

Say # of rows is R and # of chairs per row is C. Given: R=C-1. Question: C=?

(1) There is a total of 72 chairs --> CR=72 --> C(C-1)=72 --> C=9. Sufficient.

(2) After 1 chair is removed from the last row, there is a total of 17 chairs in the last 2 rows --> C+(C-1)=17 --> C=9. Sufficient.

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