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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 9006
GMAT 1: 760 Q51 V42
GPA: 3.82
In a certain theater, the first row has 16 seats and the next row has  [#permalink]

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Difficulty:   25% (medium)

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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Math Expert V
Joined: 02 Aug 2009
Posts: 8610
Re: In a certain theater, the first row has 16 seats and the next row has  [#permalink]

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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=$$\frac{(64+16)}{2}=40$$
$$SUM = 25 * 40=1000$$
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 9006
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: In a certain theater, the first row has 16 seats and the next row has  [#permalink]

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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

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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Manager  S
Joined: 25 May 2016
Posts: 84
Location: Singapore
Concentration: Finance, General Management
GMAT 1: 620 Q46 V30 Re: In a certain theater, the first row has 16 seats and the next row has  [#permalink]

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1
64-16=48
48/2=24
24 +1 = 25 rows of seats.
64+16=80
80*(24/2)+40=1000 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  