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## The number of seats in the first row of an auditorium is 18

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jjjinapinch Senior | Next Rank: 100 Posts
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#### The number of seats in the first row of an auditorium is 18

Mon Jul 24, 2017 9:25 am
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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.

Official Guide question

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### GMAT/MBA Expert

Jay@ManhattanReview GMAT Instructor
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Mon Jul 24, 2017 11:21 pm
jjjinapinch 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.

Official Guide question
We have,

The number of seats in the first row = 18;
The number of seats in the second row = 20;
The number of seats in the third row = 22

Statement 1:

This way, we can get the number of seats in each of the other rows; thus, we can count the number of seats in 27 rows. Sufficient.

Statement 2: The number of seats in the last row is 70.

The number of seats in the last row = 70;
The number of seats in the second last row = 68;
The number of seats in the third last row = 66;
.
.
.
The number of seats in the first row = 18

This way, we can get the number of seats in each of the other rows; thus, we can count the number of seats in all the rows. Sufficient.

The correct answer: D

Hope this helps!

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Rich.C@EMPOWERgmat.com Elite Legendary Member
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Tue Jul 25, 2017 6:10 pm
Hi jjjinapinch,

Certain DS questions are really just 'logic' questions - meaning that if you understand the logic involved, then you can correctly answer the question without doing much (if any) math.

Here, we're told that the 1st row in an auditorium has 18 seats and each row after has 2 more seats than the row that immediately precedes it. Thus....

2nd row = 20 seats
3rd row = 22 seats
4th row = 24 seats
Etc.

So, if you know the row number, then you'll know the number of seats AND if you know the number of seats, you'll know the row number. We're asked for the total number of rows in the auditorium.

1) The number of rows of seats in the auditorium is 27.

With this Fact, we can absolutely calculate the total number of seats (we'd just have to count them all up). Thankfully, we don't actually have to do that math to know that this is enough information to answer the given question.
Fact 1 is SUFFICIENT.

(2) The number of seats in the last row is 70.

With this Fact, we could figure out the number of seats in each of the preceding rows (68, 66, 64, etc.), so we could figure out the total number of seats. Just as in Fact 1, we don't actually have to do that math though.
Fact 2 is SUFFICIENT.

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Rich

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Scott@TargetTestPrep GMAT Instructor
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Wed Jul 26, 2017 3:25 pm
jjjinapinch 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 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, so the 2nd row has 20 seats, the 3rd row has 22 seats, and so on.

We need to determine the total number of seats in the auditorium.

Statement One Alone:

The number of rows of seats in the auditorium is 27.

Since we know the starting number of seats is 22 and the number of seats in each row thereafter is 2 more than in the previous row, by knowing the total number of rows in the auditorium, we can determine the total number of seats. Statement one alone is sufficient to answer the question.

Statement Two Alone:

The number of seats in the last row is 70.

Thus, the number of seats in the second-to-last row is 68, third-to-last row is 66, and so on.

We see that we can determine the total number of seats in the auditorium, since we can determine the number of seats in each row. Statement two alone is sufficient to answer the question.

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