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by j_shreyans » Mon Nov 03, 2014 10:09 am
In a certain conference room each row of chairs has the same numbers of chairs, and the number of rows is 1 less that the number of chairs in a row. How many chairs are in a row?

1) There is total of 72 chairs.

2) After 1 chair is removed from the last row, there is total of 17 chairs in the last 2 rows.
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Source: — Data Sufficiency |
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by GMATGuruNY » Mon Nov 03, 2014 10:12 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.
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.
Last edited by GMATGuruNY on Tue Nov 04, 2014 9:53 am, edited 1 time in total.
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by Brent@GMATPrepNow » Mon Nov 03, 2014 10:23 am
j_shreyans wrote:In a certain conference room each row of chairs has the same numbers of chairs, and the number of rows is 1 less that the number of chairs in a row. How many chairs are in a row?

1) There is total of 72 chairs.
2) After 1 chair is removed from the last row, there is total of 17 chairs in the last 2 rows.
Target question: How many chairs are in a row?

Let n = the number of chairs in a row
So, n - 1 = number of rows [since we're told that the number of rows is 1 LESS than the number of chairs in a row]

REPHRASED target question: What is the value of n?

Statement 1: There is total of 72 chairs.
Total # of chairs = (number of chairs per row)(# of rows)
So, 72 = n(n - 1)
Expand: 72 = n² - n
Rewrite as: n² - n - 72 = 0
Factor: (n - 9)(n + 8) = 0
Solve: n = 9 or n = -8
Since n cannot be NEGATIVE, we can be certain that n = 9
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: After 1 chair is removed from the last row, there is total of 17 chairs in the last 2 rows.
Each row has n chairs.
So, the last 2 rows have 2n chairs
If we remove 1 chair, there are 2n - 1 chairs.
So, statement 2 tells us that 2n - 1 = 17
Solve to get: n = 9
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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