Bunuel wrote:
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
Kudos for a correct solution.
VERITAS PREP OFFICIAL SOLUTION:At first glance, this may seem to be a listing problem. The question gives a repeating pattern that can be written out and it would be possible to keep listing the next knot in the pattern until one of the numbers listed in the answer choices was reached. This would be a long and laborious process and the GMAT, a timed test, tends to favor methods which conserve time.
So what is this problem really asking? The problem gives a pattern, so the problem is probably asking us to use the pattern to help us derive the answer more quickly. With many pattern problems, it is useful to think about the question as a division and remainder problem. Imagine you have a four unit repeating pattern and you want to figure out which number in the repetition is represented on the 7th unit of the total pattern. If we divide the measure of one repetition, in this case four, by the total units we are examining, we get 1 with a remainder of 3. Think of this as if one full pattern fits into the whole number but only three of the remaining units of the pattern can also fit in the total. This implies that we stop on the third unit of the repetition. We can check this by writing out seven units: 1-2-3-4-1-2-3. This is the same technique that can be used to solve the above problem!
In total in the problem above, there are 4 blue + 6 red + 2 yellow or 12 units in the repetition. The yellow units are the 11th and 12th units of the repetition, which means that if we divide the total units of the bracelet by 12, we should get a remainder of 11 (for the 11th unit) or 0 (if it is on the 12th unit it will be a full repetition and will give no remainder). So all that is left to do now is to divide the answer choices by twelve and check the remainders:
A) 89 / 12 = 7 R5 X
B) 90 / 12 = 7 R6 X
C) 95 / 12 = 7 R11 ←
D) 97 / 12 = 8 R1 X
E) 102 / 12 = 8 R6 X
As this problem shows, the actual thing being tested is the students ability to find the right method for solving the problem. There are a number of problems like this on the GMAT, but if a student is prepared to look for what is really being asked, he or she will have no problem finding the true question.
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