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Few Questions on Number Theory and Counting (combined)

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  • Rajesh Balasubramanian
    HI all, CAT has been consistently asking questions combining basic number theory and counting. So, it is probably good practice to have a go at these. As
    Message 1 of 2 , Jun 2, 2011
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      HI all,
       
      CAT has been consistently asking questions combining basic number theory and counting. So, it is probably good practice to have a go at these. As always, the questions can also be found at our blog http://iimcat.blogspot.com/2011/06/few-questions-on-number-theory-and.html

      1. From the digits 2,3,4,5,6 and 7, how many 5-digit numbers can be formed that have distinct digits and are multiples of 12?

      2. All numbers from 1 to 200 (in decimal system) are written in base 6 and base 7 systems. How many of the numbers will have a non-zero units digit in both base 6 and base 7 notations?

      3. All numbers from 1 to 150 (in decimal system) are written in base 6 notation. How many of these will not contain any zero?

      4. How many factors of 1080 are perfect squares?
       
      Cheers,
      Rajesh
      99626 48484
      CAT 2011 Weekend batches starting @ Chennai, June 3rd @ Anna Nagar, June 4th@ Velachery
    • sanjeev kumar mishra
      Sir,  is the answer of 1st question is  54 ? --- On Fri, 3/6/11, Rajesh Balasubramanian wrote: From: Rajesh Balasubramanian
      Message 2 of 2 , Jun 2, 2011
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        Sir,
         
         
        is the answer of 1st question is  54 ?
         
        --- On Fri, 3/6/11, Rajesh Balasubramanian <rajesh@...> wrote:

        From: Rajesh Balasubramanian <rajesh@...>
        Subject: [2IIM CAT Prep] Few Questions on Number Theory and Counting (combined)
        To: ascent4cat@yahoogroups.com
        Date: Friday, 3 June, 2011, 8:02 AM

         
        HI all,
         
        CAT has been consistently asking questions combining basic number theory and counting. So, it is probably good practice to have a go at these. As always, the questions can also be found at our blog http://iimcat.blogspot.com/2011/06/few-questions-on-number-theory-and.html

        1. From the digits 2,3,4,5,6 and 7, how many 5-digit numbers can be formed that have distinct digits and are multiples of 12?

        2. All numbers from 1 to 200 (in decimal system) are written in base 6 and base 7 systems. How many of the numbers will have a non-zero units digit in both base 6 and base 7 notations?

        3. All numbers from 1 to 150 (in decimal system) are written in base 6 notation. How many of these will not contain any zero?

        4. How many factors of 1080 are perfect squares?
         
        Cheers,
        Rajesh
        99626 48484
        CAT 2011 Weekend batches starting @ Chennai, June 3rd @ Anna Nagar, June 4th@ Velachery
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