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In a certain conference room, each row of chairs has the

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In a certain conference room, each row of chairs has the [#permalink] New post 15 Apr 2006, 14:34
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A
B
C
D
E

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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?

A. There are a total of 72 chairs
B. After 1 chair is removed from teh last row, there are a total of 17 chairs in the last two rows.

Answer is D.

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.
Senior Manager
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 [#permalink] New post 15 Apr 2006, 14:51
D.

n cahirs in each row,
so no of rows = (n-1)

n(n-1) = total number of chairs

Stat 1 sufficient

Stat 2 sufficient
  [#permalink] 15 Apr 2006, 14:51
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