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All of the seats in a lecture hall are arranged in 15 rows.

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All of the seats in a lecture hall are arranged in 15 rows. [#permalink]

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New post 17 Sep 2013, 00:40
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All of the seats in a lecture hall are arranged in 15 rows. After the front row, each row has one more seat than the row in front of it. how many seats are in the 8th row from the front?

1) The lecture hall has a total of 285 seats.
2) The last row in the back has 26 seats

[Reveal] Spoiler:
Is there a better way to form the equations. I assumed first row as X,X+1,X+2.... X+14

We have to find X+7 = ?

FS 1 --> X + 14 = 26, X = 12 sufficient
FS 2 --> 15 X + 105 = 285, X = 12 sufficient
[Reveal] Spoiler: OA

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Re: All of the seats in a lecture hall are arranged in 15 rows. [#permalink]

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All of the seats in a lecture hall are arranged in 15 rows. After the front row, each row has one more seat than the row in front of it. how many seats are in the 8th row from the front?

x+(x+1)+...+(x+14)=total

(1) The lecture hall has a total of 285 seats. We know (total), hence we can find x. Sufficient.

(2) The last row in the back has 26 seats --> x+14=26 --> we can find x. Sufficient.

Answer: D.
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Re: All of the seats in a lecture hall are arranged in 15 rows. [#permalink]

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New post 17 Sep 2013, 03:02
fozzzy wrote:
All of the seats in a lecture hall are arranged in 15 rows. After the front row, each row has one more seat than the row in front of it. how many seats are in the 8th row from the front?
1) The lecture hall has a total of 285 seats.
2) The last row in the back has 26 seats


Total no of rows = 15
Assume the no of seats in 1st row- x
then the no of seats in 2nd row - x+1
& so on

We want the value of x+7 or basically the value of x
Statement 1
x + (x+1) + (x+2)+........+(x+15) = 285
We can find the value of x
Thus Sufficient

Statement 2
x+ 14 = 26
We can find the value of x
Thus Sufficient

Answer D
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Re: All of the seats in a lecture hall are arranged in 15 rows. [#permalink]

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New post 17 Sep 2013, 04:21
All of the seats in a lecture hall are arranged in 15 rows. After the front row, each row has one more seat than the row in front of it. how many seats are in the 8th row from the front?
1) The lecture hall has a total of 285 seats.
2) The last row in the back has 26 seats

1) let the number of seats in 1st row is x. Second rox will have x+1 seats, third X+2.. so.. on


this is in a Arithmatic progression with first term as X and common difference as 1.
Sum = 15/2 (2x+(15-1)*1) = 285. We can solve for X. Hence A is sufficient.

2) the last row has 26 seats. Therefore, second last has 25, third last has 24.. 8th from the last has 26-8=18 seats.
Hence B is also sufficient.

Therefore D

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Re: All of the seats in a lecture hall are arranged in 15 rows. [#permalink]

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New post 25 Aug 2017, 13:42
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Re: All of the seats in a lecture hall are arranged in 15 rows.   [#permalink] 25 Aug 2017, 13:42
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