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Challenging Number Theory question

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  • Rajesh Balasubramanian
    Hi all, Post the World cup freebies, here is a challenging quesiton on Number Theory. The question can also be found at our blog at
    Message 1 of 4 , Mar 29, 2011
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      Hi all,
       
      Post the World cup freebies, here is a challenging quesiton on Number Theory. The question can also be found at our blog at http://iimcat.blogspot.com/2011/03/cat-number-theory-challenging-question.html .
       
      There is a 4-digit number 'abcd' that satisfies the following property. 'abcd' = ab ^2 + cd ^2. Find abcd.
       
      Cheers,
      99626 48484
      Weekend batches starting @ Chennai, Apr 3rd @ Velachery
    • kamal lohia
      The number is 1233 = 12² + 33². Let s say the four digit number = N = abcd = XY = 100X + Y = X² + Y² = (X - 50)² + (Y - 1/2)² = 50² + (1/2)² = 4(X -
      Message 2 of 4 , Mar 30, 2011
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        The number is 1233 = 12² + 33².

        Let's say the four digit number = N = abcd = XY = 100X + Y = X² + Y²
        => (X - 50)² + (Y - 1/2)² = 50² + (1/2)²
        => 4(X - 50)² + (2Y - 1)² = 10001 = 76² + 65²
        => X = 12, Y = 33 and the number is 1233.

        Kamal Lohia
        9953813320



        From: Rajesh Balasubramanian <rajesh@...>
        To: ascent4cat@yahoogroups.com
        Sent: Wed, March 30, 2011 10:20:23 AM
        Subject: [2IIM CAT Prep] Challenging Number Theory question

         

        Hi all,
         
        Post the World cup freebies, here is a challenging quesiton on Number Theory. The question can also be found at our blog at http://iimcat.blogspot.com/2011/03/cat-number-theory-challenging-question.html .
         
        There is a 4-digit number 'abcd' that satisfies the following property. 'abcd' = ab ^2 + cd ^2. Find abcd.
         
        Cheers,
        99626 48484
        Weekend batches starting @ Chennai, Apr 3rd @ Velachery
      • Rajesh Balasubramanian
        Spot on. This answer is correct. There is one more solution to this question. Any other attempts? Rajesh 99626 48484 ... Spot on. This answer is correct. There
        Message 3 of 4 , Apr 1 11:18 PM
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          Spot on. This answer is correct. There is one more solution to this question. Any other attempts?
           
          Rajesh
          99626 48484

          On Wed, Mar 30, 2011 at 2:46 PM, kamal lohia <kamallohia@...> wrote:
           

          The number is 1233 = 12² + 33².

          Let's say the four digit number = N = abcd = XY = 100X + Y = X² + Y²
          => (X - 50)² + (Y - 1/2)² = 50² + (1/2)²
          => 4(X - 50)² + (2Y - 1)² = 10001 = 76² + 65²
          => X = 12, Y = 33 and the number is 1233.

          Kamal Lohia
          9953813320



          From: Rajesh Balasubramanian <rajesh@...>
          To: ascent4cat@yahoogroups.com
          Sent: Wed, March 30, 2011 10:20:23 AM
          Subject: [2IIM CAT Prep] Challenging Number Theory question

           

          Hi all,
           
          Post the World cup freebies, here is a challenging quesiton on Number Theory. The question can also be found at our blog at http://iimcat.blogspot.com/2011/03/cat-number-theory-challenging-question.html .
           
          There is a 4-digit number 'abcd' that satisfies the following property. 'abcd' = ab ^2 + cd ^2. Find abcd.
           
          Cheers,
          99626 48484
          Weekend batches starting @ Chennai, Apr 3rd @ Velachery


        • sindhu n
          the other solution is 8833 50-x= -38  from kamal s solution.   -Sindhu ... From: Rajesh Balasubramanian Subject: Re: [2IIM CAT Prep]
          Message 4 of 4 , Apr 4 12:27 PM
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            the other solution is 8833 50-x= -38  from kamal's solution.
             
            -Sindhu

            --- On Fri, 1/4/11, Rajesh Balasubramanian <rajesh@...> wrote:

            From: Rajesh Balasubramanian <rajesh@...>
            Subject: Re: [2IIM CAT Prep] Challenging Number Theory question
            To: ascent4cat@yahoogroups.com
            Cc: "kamal lohia" <kamallohia@...>
            Date: Friday, 1 April, 2011, 11:18 PM

             
            Spot on. This answer is correct. There is one more solution to this question. Any other attempts?
             
            Rajesh
            99626 48484

            On Wed, Mar 30, 2011 at 2:46 PM, kamal lohia <kamallohia@...> wrote:
             
            The number is 1233 = 12² + 33².

            Let's say the four digit number = N = abcd = XY = 100X + Y = X² + Y²
            => (X - 50)² + (Y - 1/2)² = 50² + (1/2)²
            => 4(X - 50)² + (2Y - 1)² = 10001 = 76² + 65²
            => X = 12, Y = 33 and the number is 1233.

            Kamal Lohia
            9953813320



            From: Rajesh Balasubramanian <rajesh@...>
            To: ascent4cat@yahoogroups.com
            Sent: Wed, March 30, 2011 10:20:23 AM
            Subject: [2IIM CAT Prep] Challenging Number Theory question

             
            Hi all,
             
            Post the World cup freebies, here is a challenging quesiton on Number Theory. The question can also be found at our blog at http://iimcat.blogspot.com/2011/03/cat-number-theory-challenging-question.html .
             
            There is a 4-digit number 'abcd' that satisfies the following property. 'abcd' = ab ^2 + cd ^2. Find abcd.
             
            Cheers,
            99626 48484
            Weekend batches starting @ Chennai, Apr 3rd @ Velachery


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