Taylor is making a bracelet. He Starts with 4 blue knots, 6 red knots, and 2 yellow knots, in that order, and repeats

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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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 see that the pattern cycle repeats every 12 knots and the last 2 knots of the pattern cycle are yellow. Since we are given that the last knot of a certain bracelet is yellow, the number of knots must be either a multiple of 12 or 1 less than a multiple of 12.

Since 95 is the only number that is 1 less than a multiple of 12 and no number is a multiple of 12, we see that 95 must be the correct answer.

Answer: C