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A necklace is made by stringing N individual beads together

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Manager
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A necklace is made by stringing N individual beads together [#permalink] New post 18 Jan 2008, 10:14
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A necklace is made by stringing N individual beads together in the repeating pattern red bead, green bead, white bead, blue bead, and yellow bead. If the necklace design begin with a red bead and ends with a white bead, then N could equal

A. 16
B. 32
C. 41
D. 54
E. 68





-thanx
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Re: PS - probability [#permalink] New post 18 Jan 2008, 10:55
Expert's post
E

20-sec way.

we should find the reminder of n divisible by 5

red bead - 1
green bead - 2
white bead - 3
blue bead - 4
yellow bead - 0

only 68 has reminder 3.

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Re: PS - probability [#permalink] New post 18 Jan 2008, 11:06
walker wrote:
E

20-sec way.

we should find the reminder of n divisible by 5

red bead - 1
green bead - 2
white bead - 3
blue bead - 4
yellow bead - 0

only 68 has reminder 3.




can u explain me a more simpler way. m not getting your answer.
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Re: PS - probability [#permalink] New post 18 Jan 2008, 11:35
Here's how the necklace looks when it is strung:

RED-GREEN-WHITE-BLUE-YELLOW

We know that the length of the pattern is 5 beads (shown above). The necklace begins at the red bead and then ends in a white bead. The shortest necklace we could have would be RED-GREEN-WHITE, which would only be 3 beads and then fit the bill. The next shortest necklace we could have would be when the pattern of 5 beads has been repeated again. In other words (3+5=8 beads) In this case the pattern would loop once (5 beads), then start RED(6)-GREEN(7)-WHITE(8).

The pattern that emerges here is that the number of beads will be in this list:

3
3+5 = 8
3+5+5 = 13
3+5+5+5 = 18
etc

Any easier way of writing this pattern would be to say that the number of beads must be divisible by 5 with 3 left over. or, when the number is divided by 5 it has a remainder of 3. Then we move onto our choices:

16/5 = 3 remainder 1
32/5 = 6 remainder 2
41/5 = 8 remainder 1
54/5 = 10 remainder 4
68/5 = 13 remainder 3

BINGO! We see that 68 is our answer.

an even shorter method would be to realize that the number must end in 3 or 8 because multiples of 5 end in 0 or 5. Thus, the only choice that ends in 3 or 8 would be our answer!

Answer E
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Re: PS - probability [#permalink] New post 18 Jan 2008, 18:14
Recognize that we are going to have to look for an answer thats a multiple of 5, plus 3.

Mutliple of 5 because there are 5 beads in the pattern, and plus 3 because the bead ends on white, which is 3 into the pattern.

I just went through all the answer choices, and only E fits. 5x13 = 65, and 65+3=68
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Re: PS - probability [#permalink] New post 18 Jan 2008, 19:26
walker wrote:
E

20-sec way.

we should find the reminder of n divisible by 5

red bead - 1
green bead - 2
white bead - 3
blue bead - 4
yellow bead - 0

only 68 has reminder 3.


Walker, why it is not multiple of 8? I reason that it is multiple of 8 and I choose A and B, but bewteen A and B I can not decide which one? keke

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Re: PS - probability [#permalink] New post 18 Jan 2008, 22:16
Expert's post
sondenso wrote:
walker wrote:
E

20-sec way.

we should find the reminder of n divisible by 5

red bead - 1
green bead - 2
white bead - 3
blue bead - 4
yellow bead - 0

only 68 has reminder 3.


Walker, why it is not multiple of 8? I reason that it is multiple of 8 and I choose A and B, but bewteen A and B I can not decide which one? keke


I cannot write more in 20 sec :-D
Indeed, eschn3am give us a good explanation.

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Re: PS - probability   [#permalink] 18 Jan 2008, 22:16
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