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A necklace is made by stringing N individual beads together

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

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New post 02 Nov 2006, 07:41
5
23
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A
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D
E

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Question Stats:

73% (01:24) correct 27% (01:29) wrong based on 389 sessions

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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. 16
B. 32
C. 41
D. 54
E. 68
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Re: PS - probability  [#permalink]

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New post 18 Jan 2008, 11:55
5
1
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 Series  [#permalink]

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New post 02 Nov 2006, 07:57
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GMATT73 wrote:
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.

e.68 is the only number 65+3=68
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Re: PS - probability  [#permalink]

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New post 18 Jan 2008, 12:35
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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]

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New post 18 Jan 2008, 19:14
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]

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New post 18 Jan 2008, 20:26
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]

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New post 18 Jan 2008, 23:16
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:  [#permalink]

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New post 01 May 2013, 19:06
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GMATT73 wrote:
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.
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Re: A necklace is made by stringing N individual beads together  [#permalink]

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New post 02 May 2013, 04:09
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Re: A necklace is made by stringing N individual beads together  [#permalink]

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New post 17 Sep 2017, 09:06
Hi all

May i know what kind of this question is? I've been looking for some typical questions like the one above to solve.

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

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New post 17 Sep 2017, 09:29
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Re: A necklace is made by stringing N individual beads together  [#permalink]

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New post 22 Mar 2018, 10:41
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Hi All,

These types of "repeating sequence" questions tend to be easy to beat IF you draw a picture. We're given the repeating sequence of beads: RGWBY…RGWBY…

We're asked if a string starts with R and ends with W, then the total number of beads COULD be. The phrase "could be" is important because it means that there's more than one correct answer. We have to work until we find the correct answer that's listed OR we deduce the pattern.

Following the given rules, at the minimum, we'd have…

RGW = 3 beads

That answer's not there, so keep going with the pattern:

RGWBY
RGW = 8 beads

That answer's not there either, so keep going:

RGWBY
RGWBY
RGW = 13 beads

Now, that answer isn't there either, but we now KNOW the pattern. The total increases by 5 each time, and the correct answer will end in either a 3 or an 8. There's only one answer that fits this pattern...

Final Answer:

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

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New post 08 Apr 2018, 07:08
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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.

e.68 is the only number 65+3=68
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Re: A necklace is made by stringing N individual beads together  [#permalink]

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New post 23 Aug 2019, 04:38
Bunuel wrote:
tringuyenminh293 wrote:
Hi all

May i know what kind of this question is? I've been looking for some typical questions like the one above to solve.

Thanks


Basically this is a remainders question (check tags above the first post).

Similar question to practice: https://gmatclub.com/forum/12-easy-piec ... l#p1033936



Can you explain why the Remainder is not 2?

R,G,W,B,Y Begs w/ red and ends with white so B and Y are left over. I know I am confusing something here. I just can't explain it to myself haha.
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Re: A necklace is made by stringing N individual beads together  [#permalink]

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New post 23 Aug 2019, 14:36
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Hi gcantre3,

We're dealing with a repeating sequence of 5 colors - but the 'string' stops at W at some point (meaning we have two colors - B and Y - left out of the final group of 5).

This means that the TOTAL is a multiple of 5 MINUS 2. That's not the definition of a 'remainder' though.

You could also look at the calculation as the TOTAL is a multiple of 5 PLUS 3. In that way, we're looking for a number, that when divided by 5, has a remainder of 3.

Both options lead to the same answer (the correct one).

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

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New post 27 Aug 2019, 03:41
EMPOWERgmatRichC wrote:
Hi gcantre3,

We're dealing with a repeating sequence of 5 colors - but the 'string' stops at W at some point (meaning we have two colors - B and Y - left out of the final group of 5).

This means that the TOTAL is a multiple of 5 MINUS 2. That's not the definition of a 'remainder' though.

You could also look at the calculation as the TOTAL is a multiple of 5 PLUS 3. In that way, we're looking for a number, that when divided by 5, has a remainder of 3.

Both options lead to the same answer (the correct one).

GMAT assassins aren't born, they're made,
Rich


That makes perfect sense! I appreciate it!
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Re: A necklace is made by stringing N individual beads together  [#permalink]

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New post 16 Oct 2019, 16:55
Pattern is R-G-W-B-Y

We can translate this pattern to 5N
We know that it finishes on white, so the formula is 5n+3 = Integer
so N must be divisible by 5

E is the only answer that satisfies the constraints.
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Re: A necklace is made by stringing N individual beads together   [#permalink] 16 Oct 2019, 16:55
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