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A necklace is made by stringing N individual beads together [#permalink]

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02 Nov 2006, 07:41

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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 begins with a red bead and ends with a white bead, then N could equal

A necklace is made by stringing N individual beads together in the repeating pattern red, green, white, blue and yellow. If the necklace begins with a red bead and ends with a white bead, then N could equal...

a. 16 b. 32 c. 41 d. 54 e. 68

there are 5 colors that repeat. so total beads=5k(number of repeated beads)+3(red, green, white)

basically, we have to find a number that is 3 more than a multiple of 5.

A necklace is made by stringing N individual beads together [#permalink]

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18 Jan 2008, 11:14

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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

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:

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!

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 _________________

There must a simple equation to aplly here, just need a little help setting it up. Counting by brute force is a time waster!

A fast way without heavy calculations is to look at the answers and subtract 3 from the answer, and find if its a multiple of 5. Only option that fits this criteria is E.

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 begins with a red bead and ends with a white bead, then N could equal

Re: A necklace is made by stringing N individual beads together [#permalink]

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02 Sep 2014, 02:37

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Re: A necklace is made by stringing N individual beads together [#permalink]

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05 Nov 2015, 13:36

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