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

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

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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.

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Question: 18
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Difficulty: 600
[Reveal] Spoiler: OA

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Re: The number of seats in the first row of an auditorium is 18 [#permalink]

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SOLUTION

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?

The number of seats in the first row is 18;
The number of seats in the second row is 18+2=20;
The number of seats in the third row is 18+2*2=22;
The number of seats in the fourth row is 18+3*2=24;
...
The number of seats in the nth row is 18+(n-1)*2.

Notice that if we knew the total number of rows we would be able to sum the number of seats in each row and get the total number of seats.

(1) The number of rows of seats in the auditorium is 27. Sufficient.
(2) The number of seats in the last row is 70 --> 18+(n-1)*2=70, where n is the number of rows. We can get n. Sufficient.

Answer: D.
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Re: The number of seats in the first row of an auditorium is 18 [#permalink]

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New post 13 Aug 2012, 12:11
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We know the number of seats in the first row and each row increases by 2.
1. Sufficient, since we know the total number of rows.
2. Sufficient, since we know the number of seats in the last row we can compute the number of seats in each preceding row.

D.

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Re: The number of seats in the first row of an auditorium is 18 [#permalink]

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New post 15 Aug 2012, 09:00
Bunuel wrote:
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

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.

Practice Questions
Question: 18
Page: 276
Difficulty: 600


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I think its D.

in the first row, we have 18 seats.
2nd = 18+2
3rd= 18 + 4, and so on
So, its 18 +2n where n starts from 0
So, total no of seats = (18+2n)n .
If, we know n , we can calculate the answer.
1. gives the value of n Sufficient
2. gives us the no of rows in the last row, so, 18+ 2n = 70, we get n, Sufficient

Hence, D.

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Re: The number of seats in the first row of an auditorium is 18 [#permalink]

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SOLUTION

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?

The number of seats in the first row is 18;
The number of seats in the second row is 18+2=20;
The number of seats in the third row is 18+2*2=22;
The number of seats in the fourth row is 18+3*2=24;
...
The number of seats in the nth row is 18+(n-1)*2.

Notice that if we knew the total number of rows we would be able to sum the number of seats in each row and get the total number of seats.

(1) The number of rows of seats in the auditorium is 27. Sufficient.
(2) The number of seats in the last row is 70 --> 18+(n-1)*2=70, where n is the number of rows. We can get n. Sufficient.

Answer: D.
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Re: The number of seats in the first row of an auditorium is 18 [#permalink]

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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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Re: The number of seats in the first row of an auditorium is 18 [#permalink]

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New post 17 Sep 2017, 22:40
S=n/2{2a+(n-1)d} is the formula for ap as the question is in AP i.e. constantly increasing with 2 eg 18,20,22 and so on
Now, a = 1st term which is known=18
d = difference =2
1 n =27 so putting a,d,n in the first equation we can know S which is the sum of the progression.
2 number of seats in the last row is 70.
n=(final term of the series -initial term of the series)/d -1 so n can be calculated and once we know n , S can be found out .
hence answer is D

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Re: The number of seats in the first row of an auditorium is 18 [#permalink]

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New post 22 Oct 2017, 03:04
The auditorium seats are in AP. So sum of total seats shall be

Sn=n/2{ 2a+(n-1) d } , where a=18 , d=2

(1) says, n=27, so we can find the value of Sn. SUFFICIENT

(2) says, l = 70, 70 (tn) can be also written as tn=a+(n-1)d . SUFFICIENT

Both are individually sufficient. Thus answer D.

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Re: The number of seats in the first row of an auditorium is 18   [#permalink] 22 Oct 2017, 03:04
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