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# In a certain conference room, each row of chairs has the

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Manager
Joined: 09 Feb 2006
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Location: New York, NY
In a certain conference room, each row of chairs has the [#permalink]

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15 Apr 2006, 15:34
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Difficulty:

25% (medium)

Question Stats:

72% (01:15) correct 28% (01:25) wrong based on 138 sessions

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In a certain conference room each row of chairs has the same number of chairs, and the number of rows is 1 less than the number of chairs in a row. How many chairs are in a row?

(1) There is a total of 72 chairs
(2) After 1 chair is removed from the last row, there is a total of 17 chairs in the last 2 rows

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-a-certain-conference-room-each-row-of-chairs-has-the-same-129389.html

[Reveal] Spoiler:

Statement 1: We know that each row has the same number of chairs, so 72/r must be an integer. We also know that rows*chairs per row (let's denote as C) = 72, and that r + 1 = c. So let's get at it.

r*c = 72
r*(r+1) = 72
r^2 + r - 72 = 0.
(r+9)(r-8)
There cannot be a negative number of rows, so r = 8. Therefore, chairs per row is 9.

Statement 2: This one is much easier to work with. Remembering that each row has the same number of chairs, if we add two rows, we get 2c. So if we add back in the chair taken out, we get 18. Therefore, there are 9 chairs per row.
[Reveal] Spoiler: OA

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Senior Manager
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Re: In a certain conference room, each row of chairs has the [#permalink]

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15 Apr 2006, 15:51
D.

n cahirs in each row,
so no of rows = (n-1)

n(n-1) = total number of chairs

Stat 1 sufficient

Stat 2 sufficient

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Re: In a certain conference room, each row of chairs has the [#permalink]

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03 Jan 2015, 21:05
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Re: In a certain conference room, each row of chairs has the [#permalink]

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05 Jan 2015, 05:28
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In a certain conference room each row of chairs has the same number of chairs, and the number of rows is 1 less than the number of chairs in a row. How many chairs are in a row?

Say # of rows is R and # of chairs per row is C.
Given: R=C-1. Question: C=?

(1) There is a total of 72 chairs --> CR=72 --> C(C-1)=72 --> C=9. Sufficient.

(2) After 1 chair is removed from the last row, there is a total of 17 chairs in the last 2 rows --> C+(C-1)=17 --> C=9. Sufficient.

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-a-certain-conference-room-each-row-of-chairs-has-the-same-129389.html
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Kudos [?]: 133013 [0], given: 12402

Re: In a certain conference room, each row of chairs has the   [#permalink] 05 Jan 2015, 05:28
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