In a certain room each row of chairs has the same number of : DS Archive
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# In a certain room each row of chairs has the same number of

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In a certain room each row of chairs has the same number of [#permalink]

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12 Jul 2009, 11:51
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In a certain room each row of chairs has the same number of chairs, and the no. of rows is one less than the no. 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 two rows.

My approach:

1) If there are "n" chairs in a row, there will be "n-1" rows .
So total no. of chairs in the room would be = n(n-1)
Hence, n(n-1)=72, thus, Sufficient.

2) I cldnt really work on this.
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Re: How to approach this one [#permalink]

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12 Jul 2009, 11:58
ahh dont consider that one i got it.

2) no. of chairs in last two rows would be "n+n-1"

Hence, 2n-1=17
And thus, we can get the no. of chairs

that time it just didnt clicked . M sry for posting it as a doubt.
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Re: How to approach this one [#permalink]

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13 Jul 2009, 06:33
Another method:

For statement 1, consider the factors of 72:
1 x 72
2 x 36
3 x 24
4 x 18
6 x 12
8 x 9

We know from the stem that the number of rows is one less than the number of chairs in each row. The only pair of factors for which this holds true is 8 x 9. Thus, we know that there are 8 rows consisting of 9 chairs each.

From Statement 2, we know that each row must have (17+1)/2 = 9 chairs. Because the number of rows is one less than the number of chairs per row, we know that there are 9-1 = 8 rows. Statement 2 is sufficient.

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Re: How to approach this one [#permalink]

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13 Jul 2009, 06:43
Quote:
In a certain room each row of chairs has the same number of chairs, and the no. of rows is one less than the no. 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 two rows.

My approach:

1) If there are "n" chairs in a row, there will be "n-1" rows .
So total no. of chairs in the room would be = n(n-1)
Hence, n(n-1)=72, thus, Sufficient.

2) I cldnt really work on this.
In a certain room each row of chairs has the same number of chairs, and the no. of rows is one less than the no. 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 two rows.

My approach:

1) If there are "n" chairs in a row, there will be "n-1" rows .
So total no. of chairs in the room would be = n(n-1)
Hence, n(n-1)=72, thus, Sufficient.

2) I cldnt really work on this.

Posted: Sun Jul 12, 2009 12:51 pm

Thats the exact approach i took x(x+1)= 72 so x is 8 or -9, it cant be negative so A is enuf..and as you said B is enuf.. so answer is 'D'

are you in doubt ? or you want to share your method ?
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Re: How to approach this one [#permalink]

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13 Jul 2009, 09:44
I was in doubt regarding the second statement but on the very next look i could make it out.. n hence, answered my query ..

It happens ... sometimes it just doesnt clicks u n after a moment u find everything so clear ..
Re: How to approach this one   [#permalink] 13 Jul 2009, 09:44
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