Bunuel wrote:
The number of seats in the first row of an auditorium is 18 and the number of seats in each row thereafter is 2 more than in the previous row. What is the total number of seats in the rows of the auditorium?
(1) The number of rows of seats in the auditorium is 27.
(2) The number of seats in the last row is 70.
We are given that there are 18 seats in the first row of an auditorium and that in each row after the first there are 2 more seats than in the previous row. Thus, we could say:
row 1 = 18
row 2 = 18 +
2(1) = 20
row 3 = 18 +
2(2) = 22
row 4 = 18 +
2(3) = 24
Seeing the pattern, we can set up the following expression for the number of seats in the nth row:
row n = 18 + 2(n – 1)
We need to determine the total number of seats in the auditorium. Thus, if we know the total number of rows in the auditorium, we will be able to make this determination.
Statement One Alone:The number of rows of seats in the auditorium is 27.
Since we know that the first row has 18 seats and we know that each row following has 2 more seats than the preceding row, we could use the pattern developed above to determine the number of seats in rows 1 through 27, inclusive, and then add those values together to determine the total number of seats in the auditorium.
Note that since this is a data sufficiency question, we do not want to waste time determining the actual total number of seats. Since we know that we
could determine this value, we can move on to the next statement. We eliminate answer choices B, C, and E.
Statement Two Alone:The number of seats in the last row is 70.
We can use the equation, 18 + 2(n – 1), to determine the total number of rows.
70 = 18 + 2(n – 1)
52 = 2n – 2
54 = 2n
27 = n
Since we know that n is 27, we know that there are 27 total rows in the auditorium. We see that this is the same information we were given in statement one, and since statement one was sufficient, statement two is also sufficient, using the same reasoning.
The answer is D.
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