M7MBA wrote: ↑

Sun Apr 26, 2020 9:41 am

R-R-G-Y-Y-B-R-R-G-Y-Y-B… B-R-R

The preceding is a representation of the different colored beads on a string. The beads follow a repeating pattern and the colors Red, Green, Yellow, and Blue are represented by R, G, Y, and B respectively. Which of the following is a possible number of beads in the missing section of the string represented above?

A. 64
B. 65
C. 66
D. 67
E. 68

[spoiler]OA=B[/spoiler]

Source: Veritas Prep

We see that the pattern is RRGYYB, i.e., there are cycles of 6 beads.

R-R-G-Y-Y-B-R-R-G-Y-Y-B… B-R-R

In the missing section, we find that there is only one bead B (in black) that is left out. Thus, there must be at least RRGYY, 5 beats before it (B).

Moreover, there can certainly be many groups of RRGYYB (6 beads).

Thus, the missing section would have 6n + 5 beads, where n is a non-negative integer.

Only Option B satisfies that n is an integer. We see that 65 = 6n + 5 => n = 10, an integer.

The correct answer: B

Hope this helps!

-Jay
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M7MBA wrote: ↑

Sun Apr 26, 2020 9:41 am

R-R-G-Y-Y-B-R-R-G-Y-Y-B… B-R-R

The preceding is a representation of the different colored beads on a string. The beads follow a repeating pattern and the colors Red, Green, Yellow, and Blue are represented by R, G, Y, and B respectively. Which of the following is a possible number of beads in the missing section of the string represented above?

A. 64
B. 65
C. 66
D. 67
E. 68

[spoiler]OA=B[/spoiler]

Source: Veritas Prep

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