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I found the following problem in a book and don't understand exactly what is being asked.

(I) Kamal is available at home from 12 noon to 4 p.m. on Tuesday, thursday and Sunday.

(II) His younger brother Navin is available at home on Monday, Thursday, Friday and Sunday between 10 a.m. to 2 p.m.

(III) The eldest brother Rajiv is available between 9 a.m. to 12 noon on Monday, Wednesday and Thursday and 2 p.m. to 4 p.m. on Friday, Saturday and Sunday.

For how many days only one brother is available at a particular time in a week ?

The answer given in my book is as follows:

One brother is available at a particular time on all seven days of the week.

Please explain.

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    $\begingroup$ Flag yourself as "unclear what you're asking"! Ahah joking! $\endgroup$
    – leoll2
    Commented May 16, 2015 at 12:51
  • $\begingroup$ @leoll2 - Help :) $\endgroup$
    – Vibhu
    Commented May 16, 2015 at 12:53
  • $\begingroup$ "I don't understand what is exactly asked in the question". I'm guessing you didn't invent it yourself, then. Where did you hear it? Is this text a perfect transcription? Was it originally in English? I ask because "For how many days only one..." is rather unusual wording. $\endgroup$
    – Kevin
    Commented May 16, 2015 at 12:59
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    $\begingroup$ The words in the question make more sense when arranged as follows "For how many days in a week is only one brother available at a particular time?" $\endgroup$
    – Bob
    Commented May 16, 2015 at 13:13
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    $\begingroup$ @Bob -Yes, you are right. $\endgroup$
    – Vibhu
    Commented May 16, 2015 at 13:17

2 Answers 2

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I think the question is asking: for how many days of the week is there a time of day at which only one brother is present? The answer then is all days of the week, because we can rephrase the information as follows.

(I) Kamal is available at home from 12 noon to 4 p.m. on Tuesday, thursday and Sunday.

(II) His younger brother Navin is available at home on Monday, Thursday, Friday and Sunday between 10 a.m. to 2 p.m.

(III) The eldest brother Rajiv is available between 9 a.m. to 12 noon on Monday, Wednesday and Thursday and 2 p.m. to 4 p.m. on Friday, Saturday and Sunday.

Monday: only Rajiv is at home between 9 and 10, both Navin and Rajiv from 10 to 12, and only Navin from 12 to 2.

Tuesday: only Kamal is at home between 12 and 4.

Wednesday: only Rajiv is at home between 9 and 12.

Thursday: only Rajiv is at home between 9 and 10, Navin and Rajiv between 10 and 12, Kamal and Navin between 12 and 2, and only Kamal between 2 and 4.

Friday: only Navin between 10 and 2, only Rajiv between 2 and 4.

Saturday: only Rajiv between 2 and 4.

Sunday: only Navin between 10 and 12, Navin and Kamal between 12 and 2, Kamal and Rajiv between 2 and 4.

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I think that the question can be rephrased as:
Given a certain time, how many days have exactly one brother at home at that time?

For example, consider 11pm: nobody is available at home at that hour, doesn't matter the day. So, the answer for 11pm would be 0.

On the contrary, if you consider 1pm, you see that on Monday Navin is at home at that time (his brothers aren't), on Tuesday only Kamal is at home, Wednesday nobody, Tuesday both, Friday only Navin, Saturday nobody, Sunday both.
The answer for 1pm is 3 (Monday, Tuesday, Friday).

This is a simple calculation problem, as you can see!

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