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please help me.............about PS......!!!

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  • Suprovo Das
    A room has 50 lockers all closed. There are 50 people waiting outside the room.The first person goes in and opens all lockers,the second person goes in and
    Message 1 of 4 , May 28, 2004
      A room has 50 lockers all closed. There are 50 people waiting outside
      the room.The first person goes in and opens all lockers,the second
      person goes in and closes lockers which are multiple of 2,the third
      person change the state of all the lockers which are multiple of 3,
      till 50.How many lockers are closed ?

      (a)32 (b) 25 (c) 43 (d) None of these.


      If you know this answer , please reply to me immediately
    • Sabyasachi Sen
      Suprovo, First of all the second person closes all the doors with even numbers on them ie (25 , Starting 2 and ending 50) State after 1st person comes out: 25
      Message 2 of 4 , Jun 3, 2004
        Suprovo,
        First of all the second person closes all the doors with even numbers on them ie (25 , Starting 2 and ending 50)
        State after 1st person comes out: 25 closed and 25 open
         
        Next the third person changes the state of all with multiple of 3
         
        Total number of doors divisible by 3 is 16 but this includes the ones divisible by 2 also... So got to check for the number of doors divisible by 6 (lcm of 2 and 3)
        Number of doors divisible by 6 is 8
        That leaves us with 8 doors that are only divisible by 3 and 8 that are also divisible by 2........
         
        So 8 doors will be closed which are divisible by 3 and 8 doors will be again opened which were closed by the second person......(so 17 will remain closed).
         
        Answer: 8+ 17 = 25 doors closed
         
         
         
         
         
         
        Regards
        Sabyasachi Sen
        National Grid Transco Plc.
        Wipro Technologies, Secunderabad.
        Tel: +91-40-55386000 Extn - 6312
        Dial Comm: 7122204
        Mobile: +91-40-32440560
        -----Original Message-----
        From: Suprovo Das [mailto:suprovo_2200@...]
        Sent: Saturday, May 29, 2004 12:23 AM
        To: ascent4cat@yahoogroups.com
        Subject: [ascent CAT] please help me.............about PS......!!!

        A room has 50 lockers all closed. There are 50 people waiting outside
        the room.The first person goes in and opens all lockers,the second
        person goes in and closes lockers which are multiple of 2,the third
        person change the state of all the lockers which are multiple of 3,
        till 50.How many lockers are closed ?

        (a)32 (b) 25 (c) 43 (d) None of these.


        If you know this answer , please reply to me immediately




        Ascent Education
        An IIM Alumni Venture
        Class for CAT, XAT, GRE, GMAT
        http://www.ascenteducation.com

        Archives of past CAT questions can be viewed at http://www.ascenteducation.com/india-mba/iim/cat/questionbank/questionbank.shtml



      • konik_sood
        Hi The answer would be 43 because there are only seven such nos which are perfect squares ie 1,4,9,16,25,36,49.So the Doors with these nos would be open as
        Message 3 of 4 , Jun 4, 2004
          Hi

          The answer would be 43 because there are only seven such nos which
          are perfect squares ie 1,4,9,16,25,36,49.So the Doors with these nos
          would be open as they have odd no factors,rest all would be closed.

          Konik Sood

          --- In ascent4cat@yahoogroups.com, "Suprovo Das" <suprovo_2200@y...>
          wrote:
          > A room has 50 lockers all closed. There are 50 people waiting
          outside
          > the room.The first person goes in and opens all lockers,the second
          > person goes in and closes lockers which are multiple of 2,the third
          > person change the state of all the lockers which are multiple of 3,
          > till 50.How many lockers are closed ?
          >
          > (a)32 (b) 25 (c) 43 (d) None of these.
          >
          >
          > If you know this answer , please reply to me immediately
        • harpreet
          hi.. i think the answer is 43.. the logic i put in is that all the perfect squares will be open as they have odd no of factors.. for example: take door no 4
          Message 4 of 4 , Sep 8, 2004
            hi..
             
            i think the answer is 43.. the logic i put in is that all the perfect squares will be open as they have odd no of factors.. for example: take door no 4  the door will be first open, close, open as it is divisible by 1, 2 and 4. Similarly, take 16 the door will be open, close, open, close, open as it is divisible by 1, 2, 4, 8 and 16.
             
            Now lets take a number that is not a perfect square like 2 the door will be open, close as it is only divisible by 1, 2 .
             
            The perfect squares upto 50 are 1,4,9,16,25,36,49.. i.e 7 so the no of doors closed will be 50-7= 43.
             


            Sabyasachi Sen <sabyasachi.sen@...> wrote:
            Suprovo,
            First of all the second person closes all the doors with even numbers on them ie (25 , Starting 2 and ending 50)
            State after 1st person comes out: 25 closed and 25 open
             
            Next the third person changes the state of all with multiple of 3
             
            Total number of doors divisible by 3 is 16 but this includes the ones divisible by 2 also... So got to check for the number of doors divisible by 6 (lcm of 2 and 3)
            Number of doors divisible by 6 is 8
            That leaves us with 8 doors that are only divisible by 3 and 8 that are also divisible by 2........
             
            So 8 doors will be closed which are divisible by 3 and 8 doors will be again opened which were closed by the second person......(so 17 will remain closed).
             
            Answer: 8+ 17 = 25 doors closed
             
             
             
             
             
             
            Regards
            Sabyasachi Sen
            National Grid Transco Plc.
            Wipro Technologies, Secunderabad.
            Tel: +91-40-55386000 Extn - 6312
            Dial Comm: 7122204
            Mobile: +91-40-32440560
            -----Original Message-----
            From: Suprovo Das [mailto:suprovo_2200@...]
            Sent: Saturday, May 29, 2004 12:23 AM
            To: ascent4cat@yahoogroups.com
            Subject: [ascent CAT] please help me.............about PS......!!!

            A room has 50 lockers all closed. There are 50 people waiting outside
            the room.The first person goes in and opens all lockers,the second
            person goes in and closes lockers which are multiple of 2,the third
            person change the state of all the lockers which are multiple of 3,
            till 50.How many lockers are closed ?

            (a)32 (b) 25 (c) 43 (d) None of these.


            If you know this answer , please reply to me immediately




            Ascent Education
            An IIM Alumni Venture
            Class for CAT, XAT, GRE, GMAT
            http://www.ascenteducation.com

            Archives of past CAT questions can be viewed at http://www.ascenteducation.com/india-mba/iim/cat/questionbank/questionbank.shtml





            Ascent Education
            An IIM Alumni Venture
            Class for CAT, XAT, GRE, GMAT
            http://www.ascenteducation.com

            Archives of past CAT questions can be viewed at http://www.ascenteducation.com/india-mba/iim/cat/questionbank/questionbank.shtml




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