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

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Manager
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In a certain sculpture, coils of wire are arranged in rows.  [#permalink]

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New post 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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Re: PITA problem  [#permalink]

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New post 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
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Re: PITA problem  [#permalink]

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New post 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
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  [#permalink]

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New post 21 Aug 2007, 17:58
Ans. B,

the same method as Juaz
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Re: PITA problem  [#permalink]

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New post 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
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Re: In a certain sculpture, coils of wire are arranged in rows.  [#permalink]

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New post 25 Feb 2018, 11:49
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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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