M7MBA wrote: ↑Sun Apr 26, 2020 9:38 am
Taylor is making a bracelet. He Starts with 4 blue knots, 6 red knots, and 2 yellow knots, in that order, and repeats the pattern until there is no more string. If the last Knot is yellow, which of the following could be the total number of knots on the bracelet?
A) 89
B) 90
C) 95
D) 97
E) 102
[spoiler]OA=C[/spoiler]
Source: Veritas Prep
We know that Taylor is making the bracelet with there color knots, starting with 4 blue knots, 6 red knots, and 2 yellow knots, in that order.
Since the last knot is yellow, there could be two possibilities: 1. The last two knots are yellow and 2. The last knot is yellow and the second last knot is red.
Case 1: The last two knots are yellow
The total number of knots on the bracelet = (4 + 6 + 2)n = 12n, where n is a positive integer
Since none of the options renders n as an integer, this is not a possibility.
Case 2: The last knot is yellow and the second last knot is red
The total number of knots on the bracelet = (4 + 6 + 2)(n – 1) + 4 + 6 + 1 = 12n – 1 where n is a positive integer
Only Option C (95) render n as an integer: the correct answer.
The correct answer:
C
Hope this helps!
-Jay
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