The preceding is a representation of the different colored beads on a

Since the repeating pattern is R-R-G-Y-Y-B, the missing pattern must be in this sequence, repeating n number of times
e.g R-R-G-Y-Y-B-R-R-G-Y-Y-B......

now, after the missing part, the series resumes with B-R-R, thus the missing string must end at R-R-G-Y-Y

So, there will be n-1 repetitions of R-R-G-Y-Y-B and one R-R-G-Y-Y

As for the patterns, n-1 has to be a multiple of 6 (R-R-G-Y-Y-B represents 6 beads) and later we subtract 1 from it (for last R-R-G-Y-Y)

Looking at the options, for B, if there are 10 repetitions of R-R-G-Y-Y-B => 60 beads and 1 of R-R-G-Y-Y => 5 beads

Thus, total no. of beads = 65.

Hence, answer is B

I replace the letters with numbers, to more easily see the pattern. Thus, we have:

112334112334
11:2, 33:4 is one set. 6 in each set. But the end of the string starts with 411. which means we have the last bead of the set.

Thus:
6K+5=beads 'hidden' from the set.

60+5 = 65, is the only one that fits. Otherwise we'd be looking at 59 or 71.

thus B.

edit:
miswrote E as answer, :p

The missing region of the set should be R-R-G-Y-Y to complete the repeating pattern as described in the question stem. Because there are 5 beads that must be used to complete the pattern as shown the answer must be a multiple of 5 giving us B. 65 as our only answer option.

IMO the answer is B.
R-R-G-Y-Y-B-R-R-G-Y-Y-B… B-R-R
If we see closely, there are 5 other beads between two blues B-R-R-G-Y-Y-B the number has to divide by 5 ,
the only option we have that is divisible by 5 is 65.

My answer might be a little bit too simple, but I chose 65 because it's the only multiple of 5 in the answer choices and there is 5 beads in between each B...

VERITAS PREP OFFICIAL SOLUTION:

The first step in ANY math problem on the GMAT is to figure out what kind of problem you are dealing with. The problem itself contains all the clues, we just need to be good sleuths and sleuth the answers (isn’t it fun when a word can be both a noun and a verb?). The biggest clues in this problem are the word “pattern” and the wording in the actual question at the end of problem. As a note, the sentence ending in a question mark is always a good place to look for clues. The pattern appears to be a six color repetition: R-R-G-Y-Y-B. We will get back to this later. The wording in the question states, “Which of the following is a possible number of beads in the missing section of the string represented above?” The operative words here have been placed in italics and bold. The question is asking for “a possible” solution, not the one and only solution. This implies that there is only answer choice that will fit the parameters established by the problem. We now know that this question needs us to figure out the parameters of a possible answer and apply them to the answer choices to see which one works (in other words, we will be testing answer choices).

Step one is complete, now we simply must determine what the parameters of a correct answer are. The question states that there is a repeating pattern. Often times, a pattern problem is testing the ability of the test taker to make an inference about the pattern or to determine which answers fit the pattern. A good place to start in a problem like this is to simply fill in the missing pieces as if the pattern continued normally to create a continuous string. Let’s do that and see if it reveals anything about the pattern.

R-R-G-Y-Y-B-R-R-G-Y-Y-B-R-R-G-Y-Y- B-R-R

The missing pieces are in bold italics above. So did we reveal anything? It seems that the smallest possible number of beads that could be inserted to finish the pattern is five. This is important! The missing piece is five beads or larger. After examining the answer choices, we still cannot eliminate anything, but it is a start. The most important thing about patterns is that they repeat, so what would be the second smallest number of beads possible to complete the pattern?

R-R-G-Y-Y-B-R-R-G-Y-Y-B-R-R-G-Y-Y-B-R-R-G-Y-Y- B-R-R

As is shown above, another full repetition of the pattern would be needed in order to complete the string, which would make the missing piece 11 beads long, or 6+5 beads long. The next smallest piece would require another repetition and be 17 beads long, or 6+6+5, or 2(6) + 5 beads long. Aha! We have found our parameter! The missing piece has to be some multiple of 6 with five more beads added on! Looking at the answer choices, the only choice that fits this parameter is (b) 65. We have done it! Well sleuthed friends!

We see that a pattern cycle is 6 beads (2 red, 1 green, 2 yellow and 1 blue). We see that the bead both right before and right after the ellipsis (i.e., the missing section) is blue, the number of beads in the missing section must be 5 more than a multiple of 6. Since 65 is the only number in the given choices that is 5 more than a multiple of 6, then 65 is the correct answer.

Answer: B

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