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


PS56602.01
Quantitative Review 2020 NEW QUESTION


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logical question
draw fig and solve
we see bulb 6 flashes last
IMO D


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I hope to help you with this.
In general, every third means that the difference is 3

on a number line, every third number is 3,6,9,..... --> if the initial integer is 0
but if the initial integer is 1, then the sequence is 4,7,10,...

if you assume a sequence of 1,3,6,9,.. ---> it will be an incorrect sequence as the difference between the second and the first is not equal the difference between the third and the second.
if you assume a sequence of 1,3,5,... ---> it will be a sequence of every second number (as the difference is 2)

in other words: if the bulb no. 1 is not the first to flash, then the first one to flash will be bulb no. 3 followed by 6.
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I would like to do it in manual way

Lighting happens like this

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

i.e. Bulb 6 flashes last

Answer: Option D
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Solution

Given
In this question, we are given

• Eight light bulbs numbered 1 through 8 are arranged in a circle, as shown in the diagram.
• The bulbs are wired so that every third bulb, counting in a clockwise direction, flashes until all bulbs have flashed once.
• The bulb numbered 1 flashes first.

To Find
We need to determine

• The number of the bulb that will flash last.

Approach & Working
As every third bulb is flashing, starting from bulb 1, we can determine the next bulbs as follows

• First: Bulb 1
• Second: Bulb 4
• Third: Bulb 7
• Fourth: Bulb 2
• Fifth: Bulb 5
• Sixth: Bulb 8
• Seventh: Bulb 3
• Eighth: Bulb 6

As we can see, all the eight bulbs are flashing at least once, and the last one to flash is bulb 6.

Hence, the correct answer is option D.


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