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 beac, then N could euqal
A. 16
B. 32
C. 41
D. 54
E. 68
According to the answer, the number of beads in this design is 3 more than some multiple of 5. This can be expressed as 5n+3, where n is an integer. I don't understand this explanation. Thank you.
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- greenpepper
- dbernst
- ManhattanGMAT Staff
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- shaftbmf
further explaination?
i recognize that this is a combinatorics problem but it is still unclear. Can i get a fuller explanation on the approach? I don't understand how you get 68? :?
- StaceyKoprince
- ManhattanGMAT Staff
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- Location: Montreal
It's actually a sequences question - you want to use the pattern to get to the answer.
The pattern is RGWBY RGWBY RGWBY etc (keeps repeating)
So, for example, the red beads are #1, #(1+5), #(1+5+5), etc, or 1, 6, 11, etc.
The green beads are #2, #(2+5), #(2+5+5), etc, or 2, 6, 12, etc
and so on for the other colors
We want to find what N could be, and N represents the last bead. We're told the last bead is white, so what are the options for white? #3, #(3+5), #(3+5+5), etc, or 3, 8, 13, etc.
I can figure out what works from my answer choices in two different ways.
The easiest way (unique to this problem set-up): each time, I'm adding 5. So, for N, it could be 3, 8, 13, 18, 23, 28... noticing a pattern? It always ends with either 3 or 8. The only answer choice that ends with either 3 or 8 is E.
The common way (can use on any problem of this type) is to set it up algebraically. For white, I start with 3 and then each time I add 5 more. That can be expressed as 3 + 5x. The first white bead is just at 3, the second white bead is at 3 + 5(1) = 8, the third white bead is at 3 + 5(2) = 13, and so on. This means the answer will be 3 + some multiple of 5. Subtract 3 from every answer choice. The right answer should be a multiple of 5 (because we've removed the first 3). Only E fits this requirement.
The pattern is RGWBY RGWBY RGWBY etc (keeps repeating)
So, for example, the red beads are #1, #(1+5), #(1+5+5), etc, or 1, 6, 11, etc.
The green beads are #2, #(2+5), #(2+5+5), etc, or 2, 6, 12, etc
and so on for the other colors
We want to find what N could be, and N represents the last bead. We're told the last bead is white, so what are the options for white? #3, #(3+5), #(3+5+5), etc, or 3, 8, 13, etc.
I can figure out what works from my answer choices in two different ways.
The easiest way (unique to this problem set-up): each time, I'm adding 5. So, for N, it could be 3, 8, 13, 18, 23, 28... noticing a pattern? It always ends with either 3 or 8. The only answer choice that ends with either 3 or 8 is E.
The common way (can use on any problem of this type) is to set it up algebraically. For white, I start with 3 and then each time I add 5 more. That can be expressed as 3 + 5x. The first white bead is just at 3, the second white bead is at 3 + 5(1) = 8, the third white bead is at 3 + 5(2) = 13, and so on. This means the answer will be 3 + some multiple of 5. Subtract 3 from every answer choice. The right answer should be a multiple of 5 (because we've removed the first 3). Only E fits this requirement.
Stacey Koprince
Instructor
Director, Content & Curriculum
ManhattanPrep
Instructor
Director, Content & Curriculum
ManhattanPrep
6 posts Page 1 of 1