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Difficulty: 505-555 Level,    Remainders,                   
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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: A necklace is made by stringing N individual beads together [#permalink]
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GMATT73 wrote:
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


Similar question to practice: 12-easy-pieces-or-not-126366.html#p1033936
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Re: A necklace is made by stringing N individual beads together [#permalink]
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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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
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Re: A necklace is made by stringing N individual beads together [#permalink]
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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:

GMAT assassins aren't born, they're made,
Rich
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Re: A necklace is made by stringing N individual beads together [#permalink]
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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]
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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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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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.
Re: A necklace is made by stringing N individual beads together [#permalink]
EMPOWERgmatRichC wrote:
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:

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

EMPOWERgmatRichC
Thanks for the explanation with kudos.
Could you clarify the highlighted part, please?
I mean how the correct choice will end in 8?
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Re: A necklace is made by stringing N individual beads together [#permalink]
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Hi Asad,

Since the sequence of 5 colored beads will keep repeating - and will eventually 'end' on a white bead - we can spot a pattern in the total number of beads that might appear. Here are the first few possibilities:

3, 8, 13, 18, 23, 28.....

To fit the description in the prompt, the total has to increase by 5 each time, which means that the Units Digit of the total will end in either 3 or 8 (since those are the only two Units Digits that are possible under these circumstances).

GMAT assassins aren't born, they're made,
Rich
Re: A necklace is made by stringing N individual beads together [#permalink]
Quote:
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

EMPOWERgmatRichC wrote:
Hi Asad,

Since the sequence of 5 colored beads will keep repeating - and will eventually 'end' on a white bead - we can spot a pattern in the total number of beads that might appear. Here are the first few possibilities:

3, 8, 13, 18, 23, 28.....

To fit the description in the prompt, the total has to increase by 5 each time, which means that the Units Digit of the total will end in either 3 or 8 (since those are the only two Units Digits that are possible under these circumstances).

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

Thank you soooo much for the response. So, it seems that N could be 3 too. Should not N could be at least 8?
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Re: A necklace is made by stringing N individual beads together [#permalink]
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Asad wrote:
Quote:
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

EMPOWERgmatRichC wrote:
Hi Asad,

Since the sequence of 5 colored beads will keep repeating - and will eventually 'end' on a white bead - we can spot a pattern in the total number of beads that might appear. Here are the first few possibilities:

3, 8, 13, 18, 23, 28.....

To fit the description in the prompt, the total has to increase by 5 each time, which means that the Units Digit of the total will end in either 3 or 8 (since those are the only two Units Digits that are possible under these circumstances).

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

Thank you soooo much for the response. So, it seems that N could be 3 too. Should not N could be at least 8?


Hi Asad,

You bring up an interesting question - and whether the 'minimum' number of beads is 3 or 8 depends on how you interpret what the prompt tells you. We know that the sequence of bead colors WILL repeat as more and more beads are added to the necklace, but the prompt doesn't explicitly state that all 5 colors are on the necklace that is to be made. Thankfully, the 5 answers don't actually require that we consider this issue (since the answers are all numbers that are greater than 8).

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