A necklace is made by stringing N individual beads together

Question

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

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

walker · Accepted Answer

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.

eschn3am · Answer

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

kidderek · Answer

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

Bunuel · Answer

Similar question to practice: 12-easy-pieces-or-not-126366.html#p1033936

tringuyenminh293 · Answer

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

Bunuel · Answer

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

EMPOWERgmatRichC · Answer

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:  E

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

SidKan · Answer

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

gcantre3 · Answer

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.

EMPOWERgmatRichC · Answer

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

dcummins · Answer

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.

TheUltimateWinner · Answer

EMPOWERgmatRichC 
Thanks for the explanation with kudos.
Could you clarify the highlighted part, please?
I mean how the correct choice will end in 8?

EMPOWERgmatRichC · Answer

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

TheUltimateWinner · Answer

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

EMPOWERgmatRichC · Answer

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

bumpbot · Answer

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A necklace is made by stringing N individual beads together

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