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  • tina
    hi plp plz help me with these questions... Q.whats is the remainder on dividing 1) 4^44 by 44 .....answer 36 2) (3^102 + 4^48) by 7....answer 2 Q.if n^n is
    Message 1 of 9 , Aug 25, 2005
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      hi plp plz help me with these questions...

      Q.whats is the remainder on dividing

      1) 4^44 by 44  .....answer 36
      2) (3^102 + 4^48) by 7....answer 2


      Q.if n^n is odd....which of the following is true:

      1)n^(n-1)*n^(n+1)is odd integer
      2)n^{(n+1)\2)}*n^n^2 is odd integer
      here second part is n raised to n raised to 2

      3)n^2n+n^(n\2)is even integer

      answer.....both 1 and 2 are true

      Q.what are the last two digits of 707^444

      answer....01

      plzgive the complete solution with explainatio

      thanx

      Tina

    • abith
      Hi Tina I think the answer to (4^44)/44 is 0 Explanation: (4^44)/44=((4^4)^11)/44=(256^11)/44=(256/44)*256^10=4*256^10 hence the remainder is 0 the answer to
      Message 2 of 9 , Sep 6, 2005
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        Hi Tina

        I think the answer to (4^44)/44 is 0
        Explanation:
        (4^44)/44=((4^4)^11)/44=(256^11)/44=(256/44)*256^10=4*256^10
        hence the remainder is 0

        the answer to (3^102 + 4^48) by 7 is 2
        Explanation:
        (3^102)/7=(9^51)/7=(2^51)/7=(8^17)/7=(1^17)/7
        hence remainder is 1
        (4^48)/7=((4^3)^16)/7=(64^16)/7=(1^16)/7
        hence the remainder is 1
        so toghether we the remainder as 2

        Q3) given that n^n is odd which means that n is odd
        Which implies that n^(n-1)*n^(n+1) and
        n^{(n+1)\2)}*n^n^2 are odd

        Q4) 707^444=(7*101)^444=7^444*101^444
        101^444…… the last two digits will be 01
        7^444=(7^4)^101=2401^111….. the last two digits of
        this will be 01
        so in the product also the last two digits is 01


        --- tina <manisha_rai1484@...> wrote:

        > hi plp plz help me with these questions...
        >
        > Q.whats is the remainder on dividing
        >
        > 1) 4^44 by 44 .....answer 36
        > 2) (3^102 + 4^48) by 7....answer 2
        >
        >
        > Q.if n^n is odd....which of the following is true:
        >
        > 1)n^(n-1)*n^(n+1)is odd integer
        > 2)n^{(n+1)\2)}*n^n^2 is odd integer
        > here second part is n raised to n raised to 2
        >
        > 3)n^2n+n^(n\2)is even integer
        >
        > answer.....both 1 and 2 are true
        >
        > Q.what are the last two digits of 707^444
        >
        > answer....01
        >
        > plzgive the complete solution with explainatio
        >
        > thanx
        >
        > Tina





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      • Jayprakash Dembani
        Hi Tina, I have solved these questions to the best of my knowledge. Let me know in case of any corrections or alternate solutions. Here are the Answers to your
        Message 3 of 9 , Sep 7, 2005
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          Hi Tina,
           
          I have solved these questions to the best of my knowledge. Let me know in case of any corrections or alternate solutions.
           
          Here are the Answers to your Questions,
           
          Soln 1 :
           
          4^44 = (256)^11
           
          256 = 264 - 8
           
          (264 - 8) ^ 11
           
          Now,
           
          (264 - 8) ^ 11 / 44, since 264 is divisible by 44, -8 will be the remainder. As, (-8) ^ 11 will be  taken as -8 because of odd power, we are left with - 8 as remainder.Since, Remainder can't be negative , therefore answer is 
          - 8 + 44 = 36.
           
           
          Soln 2 :
           
          3 ^ 102 = (9) ^ 51,  since, 9 = 7 - 2
           
          (9) ^ 51 = (7 - 2) ^ 51 / 7  will give remainder - 2 (odd power);
           
          Similarly remainder can't be negative  therefore it is  - 2 + 7 = 5:
           
          4 ^ 48 = (2) ^ 96 = (8) ^ 32;
           
          8 = 7 - 1; (7 - 1) ^ 32 / 7 wiil give remainder 1;]
           
          therefore overall remainder will be 5 + 1 = 6. However your answer is 2.
           
          Soln 3 :n^n is even or odd depends on the value of n.
          Basic rule is (even) ^ n = even { irrespective of n is even or odd}
          Similarly,   (odd) ^ n = odd  { irrespective of n is even or odd}
           
           
          Soln 4:
           
          707 = 101 X 7;
           
          Remember the basic rule , (101) ^ n last two digits are always 01. For instance, (101) ^ 2 = 10201, (101) ^ 3 = 1030301......
           
          Now,
           
          (707) ^ 444 = ( 101 X 7 ) ^ 444 = (101) ^ 444 x (7) ^ 444. Since last digit of 7 ^ 4n is always 1. theerfore last two digits of (707) ^ 444 are 01.
           
          Regards,
           
          Jay
           
           
           
           
           
           
           
          ----- Original Message -----
          From: tina
          Sent: Friday, August 26, 2005 12:56 AM
          Subject: [ascent CAT] help

          hi plp plz help me with these questions...

          Q.whats is the remainder on dividing

          1) 4^44 by 44  .....answer 36
          2) (3^102 + 4^48) by 7....answer 2


          Q.if n^n is odd....which of the following is true:

          1)n^(n-1)*n^(n+1)is odd integer
          2)n^{(n+1)\2)}*n^n^2 is odd integer
          here second part is n raised to n raised to 2

          3)n^2n+n^(n\2)is even integer

          answer.....both 1 and 2 are true

          Q.what are the last two digits of 707^444

          answer....01

          plzgive the complete solution with explainatio

          thanx

          Tina

        • Indranil Choudhury
          Hi, i have read the msg today. i will surely give the answer. plz give explanation of the given problem x^y+y^x=17 & x+y=5. what`s the value of x,y ans x=3,y=2
          Message 4 of 9 , Sep 7, 2005
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            Hi, i have read the msg today. i will surely give the answer. plz give explanation of the given problem

            x^y+y^x=17 & x+y=5.

            what`s the value of x,y

            ans x=3,y=2  OR x=2, y=3

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          • reshma seth
            1) 4^44 by 44 4^4*11 by 44 256^11 by44 36^11 by 44 6^2*11 by 44 6^22 by 44 6^3*7. 6 by 44 216^7 . 6 by 44 40^7 . 6 by 44 40^2*3 . 6. 40 by 44 1600^3 .6.40 by
            Message 5 of 9 , Sep 7, 2005
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              1) 4^44 by 44
               
              4^4*11 by 44
              256^11 by44
              36^11 by 44
              6^2*11 by 44
              6^22 by 44
              6^3*7. 6 by 44
              216^7 . 6 by 44
              40^7 . 6 by 44
              40^2*3 . 6. 40 by 44
              1600^3 .6.40 by 44
              16^3 .6.40 by44
              16^2 .6 .40 .16 by 44
              256 .6 .40 .16 by44
              divide it individually and take the remainder
              256 by 44    remainder=36
              36 .6 .40 .16 by 44
              216 .40 .16 by 44
              divide 216 by 44
              remainder =40
              now
              40 .40 .16 by44
              1600 .16 by 44
              divide 1600 by 44
              remainder=16
              now
              16*16by 44
              256by44
              remainder =36   answer
               
               
              2)(3^102 + 4^48) by 7
               
              firstly take 3^102 by 7
              3^2*51 by 7
              9^51 by 7   on dividing 9 by 7 remainder is 2
              now it means
              2^51 by 7
              2^3*17 by 7
              8^17 by 7 divide 8 by 7  remainder is 1
              so
              1^17=1
               
               
              now take 2 one
               
              4^48by 7
              16^24 by 7
              on dividing 16/7
              remainder=2
              2^24 by 7
              8^8 by 7
              on dividing
              remainder =1
              1^8=8
               
              so now add both
                1+1=2 answer
               


              tina <manisha_rai1484@...> wrote:

              hi plp plz help me with these questions...

              Q.whats is the remainder on dividing

              1) 4^44 by 44  .....answer 36
              2) (3^102 + 4^48) by 7....answer 2


              Q.if n^n is odd....which of the following is true:

              1)n^(n-1)*n^(n+1)is odd integer
              2)n^{(n+1)\2)}*n^n^2 is odd integer
              here second part is n raised to n raised to 2

              3)n^2n+n^(n\2)is even integer

              answer.....both 1 and 2 are true

              Q.what are the last two digits of 707^444

              answer....01

              plzgive the complete solution with explainatio

              thanx

              Tina


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            • bala murugan
              hi, i have recently seen a advertisement about a institution called IIPM for MBA in a news paper called DECAN CHRONICLE.is it worthy to join there? please help
              Message 6 of 9 , Sep 9, 2005
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                hi,

                i have recently seen a advertisement about a
                institution called IIPM for MBA in a news paper called
                DECAN CHRONICLE.is it worthy to join there?
                please help me in this regard.

                bala.

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              • nikhlesh17
                ... hope u have got the solution by now,if not this might help u Q.whats is the remainder on dividing 1) 4^44 by 44 .....answer 36 2) (3^102 + 4^48) by
                Message 7 of 9 , Sep 24, 2005
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                  --- In ascent4cat@yahoogroups.com, "tina" <manisha_rai1484@r...> wrote:

                  hope u have got the solution by now,if not this might help u

                  Q.whats is the remainder on dividing

                  1) 4^44 by 44 .....answer 36
                  2) (3^102 + 4^48) by 7....answer 2

                  sol.

                  1)4=4(mod 44){its actually equivalent to instead of equal to}
                  2)16=16(mod 44)
                  3)64=20(mod 44)
                  4)256 or 16*16=36(mod 44)=-8(mod 44)
                  now lets multiply 1 and 4,so
                  5)4^5=36*4(mod 44) =12(mod 44)
                  6)4^6=4(mod 44){square up 3}
                  7)4^7=16(mod 44){6*1}
                  8)4^8=20(mod 44){7*1}

                  so now u can observre the repetition thus the answer is 36

                  u can apply the same for 2nd also and hope if u are clear with this
                  concept of mod function and power cycle will help u with other
                  solution also


                  > hi plp plz help me with these questions...
                  >
                  > Q.whats is the remainder on dividing
                  >
                  > 1) 4^44 by 44 .....answer 36
                  > 2) (3^102 + 4^48) by 7....answer 2
                  >
                  >
                  > Q.if n^n is odd....which of the following is true:
                  >
                  > 1)n^(n-1)*n^(n+1)is odd integer
                  > 2)n^{(n+1)\2)}*n^n^2 is odd integer
                  > here second part is n raised to n raised to 2
                  >
                  > 3)n^2n+n^(n\2)is even integer
                  >
                  > answer.....both 1 and 2 are true
                  >
                  > Q.what are the last two digits of 707^444
                  >
                  > answer....01
                  >
                  > plzgive the complete solution with explainatio
                  >
                  > thanx
                  >
                  > Tina
                • shyam arvind sawant
                   Hi, how to solve this : (100+50root2)*3 The answer is 511.5 i want the steps.. Thanks & regards Shyam sawant NSE.iT,Mumbai ltd Hi, how to solve this :
                  Message 8 of 9 , Dec 3, 2005
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                      Hi,

                    how to solve this :
                    (100+50root2)*3

                    The answer is 511.5 i want the steps..

                    Thanks & regards
                    Shyam sawant
                    NSE.iT,Mumbai ltd




                  • Sunil Kamat
                    This is a simple one Root2=1.41 (You must be knowing this) 1. 50*root2=50*1.41=70.52. 70.5+100=170.53. 170.5*3=511.5 Got it?? Regards,Sunil Kamat
                    Message 9 of 9 , Dec 18, 2005
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                      This is a simple one

                       

                      Root2=1.41 (You must be knowing this)

                       

                      1. 50*root2=50*1.41=70.5

                      2. 70.5+100=170.5

                      3. 170.5*3=511.5

                       

                      Got it??

                       

                       

                      Regards,

                      Sunil Kamat

                      Software Engineer | Infosys Technologies Ltd. | Bangalore

                      Extn: 63245 | Mobile: 91 99451 29390 | Direct: 91 80 515 63245


                      From: ascent4cat@yahoogroups.com [mailto:ascent4cat@yahoogroups.com] On Behalf Of shyam arvind sawant
                      Sent: Saturday, December 03, 2005 7:12 PM
                      To: ascent4cat@yahoogroups.com
                      Subject: [ascent CAT] help

                       

                        Hi,

                      how to solve this :
                      (100+50root2)*3

                      The answer is 511.5 i want the steps..

                      Thanks & regards
                      Shyam sawant
                      NSE.iT,Mumbai ltd

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