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31 Jul 2019, 23:45
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E
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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
A. 5
B. 7
C. 14
D. 12
E. 21
01 Aug 2019, 00:54
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Bunuel
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
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
01 Aug 2019, 01:23
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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!
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!
