Question

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.

• A. Statement I alone is sufficient to answer the problem.
• B. Statement II alone is sufficient to answer the problem.
• C. Statement I and II both are needed.
• D. Either of the statements I or II is sufficient
• E. Statement I and II both are not sufficient.

Answer 1

The correct option is D Either of the statements I or II is sufficient

Arithmetic Sequences and series

Determine the number of seats in the auditorium.It is given that the first row has 18 seats, and since each row after the first row has 2 more seats than the previous row, the second row has 20 seats, the third row has 22 seats, and so on. The total number of seats in the auditorium can be determined if and only if the number of rows in the auditorium can be determined.

(1) The number of rows is given to be 27, so the total number of seats can be determined; SUFFICIENT.

(2) The last row has 70 seats. Let n be the number of rows in the auditorium. Since the first row has 18 seats, the second row has $18+2=20$ seats, and the third row has $20+2=18+2\left(2\right)=22$ seats, it follows that the nth row has $18+(n-1)\left(2\right)$ seats. Then

$18+(n-1)\left(2\right)=70$

$18+2n-2=70$

$2n=54$

$n=27$

Thus the number of rows can be determined; SUFFICIENT.

The correct answer is D; each statement alone is sufficient.