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In a certain theater, the first row has 16 seats and the next row has

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Math Revolution GMAT Instructor
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In a certain theater, the first row has 16 seats and the next row has  [#permalink]

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New post 15 Mar 2016, 17:49
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Question Stats:

79% (01:47) correct 21% (02:42) wrong based on 80 sessions

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In a certain theater, the first row has 16 seats and the next row has 2 more seats than previous row. If the last row has 64 seats, what is the total number of seats?

A. 640
B. 720
C. 1,000
D. 1,200
E. 1,240


* A solution will be posted in two days.

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Re: In a certain theater, the first row has 16 seats and the next row has  [#permalink]

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New post 17 Mar 2016, 14:43
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MathRevolution wrote:
In a certain theater, the first row has 16 seats and the next row has 2 more seats than previous row. If the last row has 64 seats, what is the total number of seats?

A. 640
B. 720
C. 1,000
D. 1,200
E. 1,240


* A solution will be posted in two days.


There can be various ways to do it..

1) Brute force


calculate 16+18+10....64

2) AP


\(16+18+10....64= 2(8+9+...32)\)
=> \(2(1+2+3....+32)-2(1+2..+7)\)
formula for sum of first n positive integers is n(n+1)/2
\(2\frac{(32*33)}{2}-2\frac{(7*8)}{2}= 32*33-7*8=1056-56=1000\)

3) Average method--


Best method
sum in AP is the average * number of terms..
Number of terms
=\(\frac{(64-16)}{2}+ 1= 25\)..
average=\(\frac{(64+16)}{2}=40\)
\(SUM = 25 * 40=1000\)
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Math Revolution GMAT Instructor
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Re: In a certain theater, the first row has 16 seats and the next row has  [#permalink]

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New post 19 Mar 2016, 21:58
In a certain theater, the first row has 16 seats and the next row has 2 more seats than previous row. If the last row has 64 seats, what is the total number of seats?

A. 640
B. 720
C. 1,000
D. 1,200
E. 1,240


A1=16, A2=16+2, A3=16+2*2,…..,An=16+(n-1)2=2n+14. In order make 2n+14=64, n should be 25. That is, there are 25 rows. Thus, in total, 25(16+64)/2=1,000 is derived. The answer is C.
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Re: In a certain theater, the first row has 16 seats and the next row has  [#permalink]

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New post 03 Jul 2016, 18:42
1
64-16=48
48/2=24
24 +1 = 25 rows of seats.
64+16=80
80*(24/2)+40=1000
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Re: In a certain theater, the first row has 16 seats and the next row has   [#permalink] 03 Jul 2016, 18:42

In a certain theater, the first row has 16 seats and the next row has

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