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# In a certain sculpture, coils of wire are arranged in rows.

Author Message
Manager
Joined: 05 May 2005
Posts: 76
In a certain sculpture, coils of wire are arranged in rows.  [#permalink]

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21 Aug 2007, 16:20
In a certain sculpture, coils of wire are arranged in rows. The second row has two more coils than the first, the third two more than the second, and so on, to the tenth and final row. If there is a total of 120 coils of wire in the sculpture, how many coils are in the final row?

a) 22

b) 21

c) 20

d) 19

e) 18

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Manager
Joined: 20 Aug 2007
Posts: 63

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21 Aug 2007, 16:28
above720 wrote:
In a certain sculpture, coils of wire are arranged in rows. The second row has two more coils than the first, the third two more than the second, and so on, to the tenth and final row. If there is a total of 120 coils of wire in the sculpture, how many coils are in the final row?

a) 22

b) 21

c) 20

d) 19

e) 18

let first row = x
second row = x+2
third row = x+4
...
tenth row = x+18

total = 10x + 2(1+2+3+...+9)
total = 10x + 2*45 = 120
x = 3
thus, tenth row = x+18 = 21

ans B
Senior Manager
Joined: 18 Jul 2006
Posts: 484

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21 Aug 2007, 16:33
1
above720 wrote:
In a certain sculpture, coils of wire are arranged in rows. The second row has two more coils than the first, the third two more than the second, and so on, to the tenth and final row. If there is a total of 120 coils of wire in the sculpture, how many coils are in the final row?

a) 22

b) 21

c) 20

d) 19

e) 18

B i.e. 21

If x= coils in first row then
x+(x+2)+(x+4)+....(x+18) = 120
10x + 90 = 120
=> x = 3
x+18 => 21
Manager
Joined: 03 Sep 2006
Posts: 231

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21 Aug 2007, 17:58
Ans. B,

the same method as Juaz
Director
Joined: 14 Aug 2007
Posts: 676

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21 Aug 2007, 19:37
1
above720 wrote:
In a certain sculpture, coils of wire are arranged in rows. The second row has two more coils than the first, the third two more than the second, and so on, to the tenth and final row. If there is a total of 120 coils of wire in the sculpture, how many coils are in the final row?

a) 22

b) 21

c) 20

d) 19

e) 18

Every row has 2 elements more than previous row i.e. arithmetic progression

sum = n [ 2*x1 + [n-1]d ] / 2

120 = 10 [ 2x1 + [9]2]/2

x1= 3

nth term of AP is An= A1 + [n-1]d

A10 = 3 + [9*2]

A10 = 21
Non-Human User
Joined: 09 Sep 2013
Posts: 9115
Re: In a certain sculpture, coils of wire are arranged in rows.  [#permalink]

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25 Feb 2018, 11:49
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: In a certain sculpture, coils of wire are arranged in rows. &nbs [#permalink] 25 Feb 2018, 11:49
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