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
