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Eight light bulbs numbered 1 through 8 are arranged in a

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by BTGmoderatorLU » Wed Aug 14, 2019 3:40 pm

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Source: Official Guide

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Eight light bulbs numbered 1 through 8 are arranged in a circle as shown above. The bulbs are wired so that every third bulb, counting in a clockwise direction, flashes until all bulbs have flashed once. If the bulb numbered 1 flashes first, which numbered bulb will flash last?

A. 2
B. 3
C. 4
D. 6
E. 7

The OA is D
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by Jay@ManhattanReview » Thu Aug 15, 2019 9:35 pm
BTGmoderatorLU wrote:Source: Official Guide

Image

Eight light bulbs numbered 1 through 8 are arranged in a circle as shown above. The bulbs are wired so that every third bulb, counting in a clockwise direction, flashes until all bulbs have flashed once. If the bulb numbered 1 flashes first, which numbered bulb will flash last?

A. 2
B. 3
C. 4
D. 6
E. 7

The OA is D
The meaning of every third bulb flashes means that you have to add 3 to get the count of the next bulb. Since the first one to flash is #1, the next ones are #4, #7, #2, #5, #8, #3, #6. By now all eight bulbs flashed once; thus, the last one to flash is #6.

The correct answer: D

Hope this helps!

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by deloitte247 » Sat Aug 17, 2019 8:08 am
The bulbs are wired so that every third bulb counts in a clockwise direction.
The bulb numbered 1 flashes first
There is a sequence in which the common difference = 3
T1 = a = 1st bulb flashes
T2 = a + d = 1 + 3 = 4th bulb flashes
T3 = a + 2d = 1 + 6 = 7th bulb flashes
T4 = a + 3d = 1 + 1 = 2nd bulb flashes ( bear in mind that last = 8 )
T5 = a + 4d = 1 + 4 = 5th bulb flashes
T6 = a + 5d = 1 + 7 = 8th bulb flashes
T7 = a + 6d = 1 + 2 = 3rd bulb flashes
T8 = a + 7d = 1 + 5 = 6th bulb flashes last
Therefore, answer = option D
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by Scott@TargetTestPrep » Sun Aug 18, 2019 6:29 pm
BTGmoderatorLU wrote:Source: Official Guide

Image

Eight light bulbs numbered 1 through 8 are arranged in a circle as shown above. The bulbs are wired so that every third bulb, counting in a clockwise direction, flashes until all bulbs have flashed once. If the bulb numbered 1 flashes first, which numbered bulb will flash last?

A. 2
B. 3
C. 4
D. 6
E. 7

The OA is D
So the bulbs will flash in the following order:

1, 4, 7, 2, 5, 8, 3 ,6

Answer: D

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by Ian Stewart » Thu Aug 22, 2019 5:48 am
Alternatively, if we let the bulbs flash forever, we'll cycle through all eight numbers, then the pattern will start to repeat. So the last number we'd get in that cycle before getting back to "1" must be three numbers before "1" in the circle, and thus must be "6".
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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