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conference chairs (GMAT Prep)

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by alex.gellatly » Sat Jun 30, 2012 12:38 am
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.
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Source: — Data Sufficiency |

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by Anurag@Gurome » Sat Jun 30, 2012 1:09 am
alex.gellatly wrote: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.
Say, number of chairs in a row = n
Hence, number of rows = (n - 1)
Hence, total number of chairs = n(n - 1)

Statement 1: n(n - 1) = 72
72 can be written as the product of two consecutive integers in only one way, 8*9
Hence, n = 8

Sufficient

Statement 2: Each row has n chairs.
Hence, before removing one chair, the last two row had 2n chairs.

Hence, (2n - 1) = 17 --> n = 8

Sufficient

The correct answer is D.
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by GMATGuruNY » Sat Jun 30, 2012 4:47 am
alex.gellatly wrote: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: There is a total of 72 chairs.
(rows)(chairs per row) = 72.
Thus, the number of rows and the number of chairs per row must be a factor pair of 72:
1*72
2*36
4*18
6*12
8*9
Since the number of rows must be 1 less than the number of chairs per row, only the last factor pair works:
8 rows, 9 chairs per row, for a total of 72 chairs.
SUFFICIENT.

Statement 2: After 1 chair is removed from the last row, there is a total of 17 chairs in the last 2 rows.
Thus, before the 1 chair is removed, the number of chairs in the last two rows is 18, implying that there are 9 chairs per row.
SUFFICIENT.

The correct answer is D.
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by sandeep_thaparianz » Sat Jun 30, 2012 4:59 am
OA is D
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