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The figure above shows a pattern of beads with integer diameter length

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The figure above shows a pattern of beads with integer diameter length [#permalink]

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New post 16 Nov 2017, 21:54
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The figure above shows a pattern of beads with integer diameter lengths a, b and c centimeters. This five-bead pattern is to be repeated without variation to make one complete necklace. If a : b : c = 1 : 2 : 3, which of the following could be the total length of the beads on the necklace?

(A) 56 cm
(B) 57 cm
(C) 60 cm
(D) 63 cm
(E) 64 cm


[Reveal] Spoiler:
Attachment:
2017-11-17_0947_002.png
2017-11-17_0947_002.png [ 12.37 KiB | Viewed 477 times ]
[Reveal] Spoiler: OA

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Re: The figure above shows a pattern of beads with integer diameter length [#permalink]

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New post 16 Nov 2017, 22:55
Bunuel wrote:
Image
The figure above shows a pattern of beads with integer diameter lengths a, b and c centimeters. This five-bead pattern is to be repeated without variation to make one complete necklace. If a : b : c = 1 : 2 : 3, which of the following could be the total length of the beads on the necklace?

(A) 56 cm
(B) 57 cm
(C) 60 cm
(D) 63 cm
(E) 64 cm


[Reveal] Spoiler:
Attachment:
2017-11-17_0947_002.png

let the length of beads (a,b,c) be x, 2x, 3x

total length of each five bead (as in diagram) will be 9x
necklace can be formed by repeating (five bead structure) hence should be divisible by 9

D
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Re: The figure above shows a pattern of beads with integer diameter length [#permalink]

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New post 17 Nov 2017, 04:17
C.
a:b:c = 1:2:3
a=x
b=2x
c=3x
Assume x to be 1
now a+b+c = 6
once you extend the pattern of beads, the entire necklace will form series..so if we take 16 beads that form a necklace, the series will be 6*4 + 2(4) = 32
now keep extending this to limit to the answer choices:-
6*5+2(5) = 40
6*6+2(6) = 48
6*7 +2(7) = 56
6*8 +2(8) = 60
6*9 +2(9) = 66
therefore C.

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Re: The figure above shows a pattern of beads with integer diameter length [#permalink]

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New post 17 Nov 2017, 17:39
Bunuel wrote:
Image
The figure above shows a pattern of beads with integer diameter lengths a, b and c centimeters. This five-bead pattern is to be repeated without variation to make one complete necklace. If a : b : c = 1 : 2 : 3, which of the following could be the total length of the beads on the necklace?

(A) 56 cm
(B) 57 cm
(C) 60 cm
(D) 63 cm
(E) 64 cm


[Reveal] Spoiler:
Attachment:
The attachment 2017-11-17_0947_002.png is no longer available

Attachment:
necklacemin.png
necklacemin.png [ 35.57 KiB | Viewed 228 times ]

Bunuel , or anyone who has this crazy-making thing figured out, I am confused about "repeating."

The problem is that a necklace wraps around. See diagram:

I can make the pattern repeat with 8 beads, if the pattern is a-b-c-b-a

I can make the pattern repeat with 10 beads, if there must be five beads: a-b-c-b-a-a-b-c-b-a

Must there be a repeat a-a (and hence five beads per "pattern")?

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Re: The figure above shows a pattern of beads with integer diameter length [#permalink]

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New post 17 Nov 2017, 21:20
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yesh but the question states could be true.. your pattern would give a sequence of 9x+7 which is none of the options.

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Re: The figure above shows a pattern of beads with integer diameter length [#permalink]

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New post 18 Nov 2017, 00:59
The total length of one set of Beads is 9. We have to find an answer which is a multiple of 9. So, 63is the only choice available. Answer D

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The figure above shows a pattern of beads with integer diameter length [#permalink]

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New post 18 Nov 2017, 01:12
AkshatN wrote:
yesh but the question states could be true.. your pattern would give a sequence of 9x+7 which is none of the options.

Thanks for the heads up on the result of the pattern of 8 breads. I didn't catch it. Kudos.

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The figure above shows a pattern of beads with integer diameter length   [#permalink] 18 Nov 2017, 01:12
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