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Question

# Arun is instructed to clap every time the count of the instructor reaches a multiple of 3. Varun is instructed to clap every time the count reaches a multiple of 7. By the time when both of them clap simultaneously for the third time, how many times did Arun clap?

A

21

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B

22

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C

25

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D

27

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Solution

## The correct option is A 21 For Arun and Varun to clap together, the count has to be a multiple of both 3 and 7. LCM of 3 and 7 is 21. So, they will clap together every time the count reaches a multiple of 21. The third time they clap together, the count will be 21×3=63. We need to find the number of times Arun has clapped when the count reaches 63. Now, every time the count reaches a multiple of 3, Arun claps. The counts at which he claps forms an AP with the first term as 3 and the common difference also being 3. nth term of the AP =3+(n−1)3=3n 3n=63, or n=21 Hence, Arun would have clapped 21 times.

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