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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
Joined: 16 Aug 2015
Posts: 8992
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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15 Mar 2016, 17:49
00:00

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.

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Expert Joined: 02 Aug 2009 Posts: 8593 Re: In a certain theater, the first row has 16 seats and the next row has [#permalink] ### Show Tags 17 Mar 2016, 14:43 2 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 Joined: 16 Aug 2015 Posts: 8992 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] ### Show Tags 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. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
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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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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
Re: In a certain theater, the first row has 16 seats and the next row has   [#permalink] 03 Jul 2016, 18:42