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# One wheel rotates once every 3 minutes and another rotates once every

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Math Expert
Joined: 02 Sep 2009
Posts: 64248
One wheel rotates once every 3 minutes and another rotates once every  [#permalink]

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31 Jul 2019, 22:45
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Difficulty:

15% (low)

Question Stats:

91% (00:46) correct 9% (01:42) wrong based on 32 sessions

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One wheel rotates once every 3 minutes and another rotates once every 7 minutes. If both wheels begin to rotateat the same time, after how many minutes will they both begin a rotation again ?

A. 5
B. 7
C. 14
D. 12
E. 21

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Joined: 03 Jun 2019
Posts: 2910
Location: India
GMAT 1: 690 Q50 V34
WE: Engineering (Transportation)
Re: One wheel rotates once every 3 minutes and another rotates once every  [#permalink]

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31 Jul 2019, 23:54
Bunuel wrote:
One wheel rotates once every 3 minutes and another rotates once every 7 minutes. If both wheels begin to rotateat the same time, after how many minutes will they both begin a rotation again ?

A. 5
B. 7
C. 14
D. 12
E. 21

Given: One wheel rotates once every 3 minutes and another rotates once every 7 minutes. Both wheels begin to rotate at the same time.

Asked: After how many minutes will they both begin a rotation again ?

After how many minutes will they both begin a rotation again = LCM (3,7) = 21

IMO E
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Kinshook Chaturvedi
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Posts: 590
Re: One wheel rotates once every 3 minutes and another rotates once every  [#permalink]

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01 Aug 2019, 00:23
We need to calculate the LCM (Least Common Multiple) of 3 and 7 in this question. This is because the time when they will start rotating again at the same time will be the LCM of 3 and 7.

If we make a RED mark on each of the wheels when they are at the starting position:

On the first wheel, this red mark will cross the starting position after every 3 minutes i.e. 3, 6, 9 and so on.
On the second wheel, this red mark will cross the starting position after every 7 minutes i.e. 7, 14, 21 and so on.

If we want them to begin a rotation together, we want both the red marks to be at the starting position at the same time. This happens every 21 minutes, since 21 is the common number in both the lists above.
So, the correct answer option is E.

When you first saw this question, if you were confused whether you have to find out HCF or LCM in this question, ask yourself these questions?

Do I need to divide 3 and 7 into smaller parts? If your answer is yes, then you have to find out the HCF.
Do I need to look at the multiples of 3? If your answer is yes, then you have to find out the LCM.

Clearly, in this question, we are looking at multiples of 3 and 7 and hence we have to find out the LCM. Here are some links to a few of our posts on HCF and LCM.

https://gmatclub.com/forum/factors-multiples-a-simple-way-of-understanding-them-296311.html
https://gmatclub.com/forum/factors-multiples-hcf-lcm-296385.html

Hope this helps!
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Re: One wheel rotates once every 3 minutes and another rotates once every  [#permalink]

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06 Aug 2019, 16:40
Bunuel wrote:
One wheel rotates once every 3 minutes and another rotates once every 7 minutes. If both wheels begin to rotateat the same time, after how many minutes will they both begin a rotation again ?

A. 5
B. 7
C. 14
D. 12
E. 21

Since the LCM of 3 and 7 is 21, the wheels will begin a rotation at the same time after 21 minutes.

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Re: One wheel rotates once every 3 minutes and another rotates once every   [#permalink] 06 Aug 2019, 16:40