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Re: [Ascent CAT] number system problems

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  • aarti jain
    hey pallavi, ssup ...lisn, al dese probs r quite simple...u jus have to use sum basic rules. solutions: 1) ans is (b) a perfect square can neva end in 2,3,7
    Message 1 of 13 , Jul 16, 2006
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      hey pallavi,
      ssup' ...lisn, al dese probs r quite simple...u jus have to use sum basic rules.
      solutions:

      1) ans is (b)
      a perfect square can neva end in 2,3,7 and 8
       
      2) i dint get ure Q...as in em not actualy clear bout d Q
       
      3) u can solve dis sum by takin few eg.
      square of a no. grater den 1000
      say for eg: 1001
      find the square of 1001 wid the formula (1000+1)^2
      ie 1000000+2000+1= 1002001
      test for divisibility for 3 is: sum of the digits of the no. shud b divisible by 3
      ( for eg: 453 : sum of digits is 12. therefore, the no. is divisible by 3
      and to find the remainder, divide the sum by 3
      for eg: 454 : sum of digits is 13, the no. is not divisible by 3 n d remaider is 1...( divide 13 by 3)
      here, is dis sum : sum of digits os 1002001 is 4 , so the remainder is 1
      next, square of 1002 is 1004004 and dis no. is divisible by 3
      square of 1003 is 1006009, it is not divisible by 3 and remainder is 1.... so on n so forth..
      so the ans is option (a) 1 always
       
      4) u get the upper limit for x+y wen d value for x and y is maximum which is 4 and 3 resp in dis case and the lower limit for x-y is wen d value for x and y is d lowest, which is 2 and 1 resp in dis case.
      therefore, x+y/x-y = 4+3/2-1
                                =7/1
                                =7
      which is ans option (b) 7
       
      5)
      pallavi aggarwal <pal_agg2003@...> wrote:
      1. which of the following is not a perfect square?
      a) 1,00,856                  b) 3,25,137      c) 9,45,729      d) all of these
      1. some birds settled on the branches of a tree. Ffirst, they sat one to a branch and there was one bird too many. Next they sat two to a branch and there was one branch too many. How many branches were there?
      a) 3      b) 4      c) 5      d) 6
      1. the square of a number greater than 1000 that is not divisible by 3, wen divided by 3, leaves a remainder of
      a) 1 always       b) 2 always       c) either 1 or 2              d)cant be said
      1. if 2<x<4 and 1<y<3, then find the ratio of the upper limit for x+y and the lower limit of x-y
      a) 6      b) 7      c) 8      d) none of these
       
       
       
      please explain all answers with proper methods

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    • Mitrabhanu Pati
      Hi there, Pl. solve the following puzzle. Q : My friend has four uncles of different height. Their average height is 74 inches & diference in height amongst
      Message 2 of 13 , Jul 16, 2006
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        Hi there,
        Pl. solve the following puzzle.
         
        Q : My friend has four uncles of different height. Their average height is 74 inches & diference in height amongst the first three uncle is two inches. The difference between the third & the fourth uncle is 6 inches. Find out the height of each uncle.
         
        PS : I am getting the answer as 63,65,67 & 61. But the answer is 70,72,74 & 80. Can anybody solve this for me ????
         
        Mit.


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      • tilakjha
        ... d) all of these ... souare.hence option b. ... one to a branch and there was one bird too many. Next they sat two to a branch and there was one branch too
        Message 3 of 13 , Jul 22, 2006
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          --- In ascent4cat@yahoogroups.com, pallavi aggarwal
          <pal_agg2003@...> wrote:
          >
          >
          > which of the following is not a perfect square?
          >
          > a) 1,00,856 b) 3,25,137 c) 9,45,729
          d) all of these
          > the no having 2,3,7 or 8 in the last can never b a perfect
          souare.hence option b.
          >
          >
          > some birds settled on the branches of a tree. Ffirst, they sat
          one to a branch and there was one bird too many. Next they sat two
          to a branch and there was one branch too many. How many branches
          were there?
          >
          > a) 3 b) 4 c) 5 d) 6
          > thi s one gets better solved through hit & trial th correct
          option would b a i.e.there r 3 branches 7 4 birdds
          >
          > the square of a number greater than 1000 that is not divisible
          by 3, wen divided by 3, leaves a remainder of
          >
          > a) 1 always b) 2 always c) either 1 or
          2 d)cant be said
          >
          > souare of a no when divided by 3 always leaves a remainder 1 hance
          option a chek it for any no.
          >
          > if 2<x<4 and 1<y<3, then find the ratio of the upper limit for
          x+y and the lower limit of x-y
          >
          > a) 6 b) 7 c) 8 d) none of these
          >
          > the correct option wouold b bi.e. 7 because max value of x & y
          would b near 4& 3 approx respectively.& min 2& 1 approx .hence 7
          >
          > please explain all answers with proper methods
          >
          >
          > sorry for being late.please confirm if u r satisfied with
          >
          > ---------------------------------
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        • punit
          Dear Aarti, Commendable solutions.Though, i differ with u in these respects. Q2) Suppose the no. of branches is x, then the no. of birds will b x+1.According
          Message 4 of 13 , Aug 2, 2006
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            Dear Aarti,

            Commendable solutions.Though, i differ with u in these
            respects.

            Q2) Suppose the no. of branches is x, then the no. of
            birds will b x+1.According to the question,
            (x+1)/2 + 1=x....solving this it will give, x=3

            q3)If u start taking examples like that, u cant say
            anything with surity....plus u will waste time.

            Any no. which is not divisible by 3 is given as (3m+1)
            or (3m+2). where we can choose suitable m according to
            the range of values.

            Now, Square of such no. = (3m+1)*(3m+1)=9m^2+6m+1. so
            remainder will b 1.
            Similarly for (3m+2)*(3m+2)

            q4) please clarify ur concept in this regard.Suppose
            we take x=2 and y=3....then wat is the value of
            x-y???Yes, it is -1. So , taking lowest values of x
            and y wont give the lowest value of x-y. So, answer
            will b none of these.

            Please contact me in case of any querry/doubt.

            Punit

            --- aarti jain <aartirjain@...> wrote:

            > hey pallavi,
            > ssup' ...lisn, al dese probs r quite simple...u
            > jus have to use sum basic rules.
            > solutions:
            >
            > 1) ans is (b)
            > a perfect square can neva end in 2,3,7 and 8
            >
            > 2) i dint get ure Q...as in em not actualy clear
            > bout d Q
            >
            > 3) u can solve dis sum by takin few eg.
            > square of a no. grater den 1000
            > say for eg: 1001
            > find the square of 1001 wid the formula (1000+1)^2
            >
            > ie 1000000+2000+1= 1002001
            > test for divisibility for 3 is: sum of the digits
            > of the no. shud b divisible by 3
            > ( for eg: 453 : sum of digits is 12. therefore,
            > the no. is divisible by 3
            > and to find the remainder, divide the sum by 3
            > for eg: 454 : sum of digits is 13, the no. is not
            > divisible by 3 n d remaider is 1...( divide 13 by 3)
            > here, is dis sum : sum of digits os 1002001 is 4 ,
            > so the remainder is 1
            > next, square of 1002 is 1004004 and dis no. is
            > divisible by 3
            > square of 1003 is 1006009, it is not divisible by
            > 3 and remainder is 1.... so on n so forth..
            > so the ans is option (a) 1 always
            >
            > 4) u get the upper limit for x+y wen d value for x
            > and y is maximum which is 4 and 3 resp in dis case
            > and the lower limit for x-y is wen d value for x and
            > y is d lowest, which is 2 and 1 resp in dis case.
            > therefore, x+y/x-y = 4+3/2-1
            > =7/1
            > =7
            > which is ans option (b) 7
            >
            > 5)
            > pallavi aggarwal <pal_agg2003@...> wrote:
            >
            > which of the following is not a perfect square?
            >
            > a) 1,00,856 b) 3,25,137 c)
            > 9,45,729 d) all of these
            >
            >
            >
            > some birds settled on the branches of a tree.
            > Ffirst, they sat one to a branch and there was one
            > bird too many. Next they sat two to a branch and
            > there was one branch too many. How many branches
            > were there?
            >
            > a) 3 b) 4 c) 5 d) 6
            >
            >
            > the square of a number greater than 1000 that is
            > not divisible by 3, wen divided by 3, leaves a
            > remainder of
            >
            > a) 1 always b) 2 always c) either 1 or
            > 2 d)cant be said
            >
            >
            >
            > if 2<x<4 and 1<y<3, then find the ratio of the
            > upper limit for x+y and the lower limit of x-y
            >
            > a) 6 b) 7 c) 8 d) none of these
            >
            >
            >
            > please explain all answers with proper methods
            >
            >
            >
            > ---------------------------------
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            > India Click here
            >
            >
            >
            >
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          • Havi Arora
            Hi Mitrabhanu Pati, First of all you should realize that, the average of the answer that you are getting i.e. 63, 65, 67, 61 can never be 74 (all no. are
            Message 5 of 13 , Aug 2, 2006
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              Hi Mitrabhanu Pati,

              First of all you should realize that, the average of the answer that you are getting i.e. 63, 65, 67, 61 can never be 74 (all no. are smaller than 74).

              Assume the shortest of them to be 'x', then the next one is 'x+2', and after that is 'x+4', and finally 'x+10'. Taking their average to be 74, we get the answer as 70, 72, 74, 80.

              Hope it solves your problem. I know you must be thinking that how can we assume them to be standing in the increasing order, so i solved all the possible combinations of it( there were 16 of those) as given below:
              x, x+2, x+4, x+10
              x,
              x+2, x+4, x-2
              x, x-2, x-4, x-10
              x, x-2, x-4, x+2
              x-2, x, x+2, x+8
              x-2, x, x+2, x-4
              x+2, x, x-2, x-4
              x+2, x, x-2, x-8
              x+4, x+2, x, x+6
              x+4, x+2, x, x-6
              x-4, x-2, x, x+6
              x-4, x-2, x, x-6
              x+10, x+8, x+6, x
              x+2, x+4, x+6, x
              x-10, x-8, x-6, x
              x-2, x-4, x-6, x

              Solving all the possible combinations, there were three different answers as:

              78, 76, 74, 68
              70, 72, 74, 80
              73, 75, 77, 71

              All three are correct answers, may be the options had just the second one as option. So they marked only this as correct. But your answer can never be correct.




              On 7/16/06, Mitrabhanu Pati <mitrabhanu_p@...> wrote:

              Hi there,
              Pl. solve the following puzzle.
               
              Q : My friend has four uncles of different height. Their average height is 74 inches & diference in height amongst the first three uncle is two inches. The difference between the third & the fourth uncle is 6 inches. Find out the height of each uncle.
               
              PS : I am getting the answer as 63,65,67 & 61. But the answer is 70,72,74 & 80. Can anybody solve this for me ????
               
              Mit.

               




            • rajasekar
              HI, For the second question, There are 3 branches and four birds = if one bird per branch then one bird left if two birds per br then one branch left
              Message 6 of 13 , Aug 6, 2006
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                HI,
                For the second question,
                There are 3 branches and four birds
                =>> if one bird per branch then one bird left
                if two birds per br then one branch left
                ans:3branches
                --- In ascent4cat@yahoogroups.com, aarti jain <aartirjain@...> wrote:
                >
                > hey pallavi,
                > ssup' ...lisn, al dese probs r quite simple...u jus have to use
                sum basic rules.
                > solutions:
                >
                > 1) ans is (b)
                > a perfect square can neva end in 2,3,7 and 8
                >
                > 2) i dint get ure Q...as in em not actualy clear bout d Q
                >
                > 3) u can solve dis sum by takin few eg.
                > square of a no. grater den 1000
                > say for eg: 1001
                > find the square of 1001 wid the formula (1000+1)^2
                > ie 1000000+2000+1= 1002001
                > test for divisibility for 3 is: sum of the digits of the no.
                shud b divisible by 3
                > ( for eg: 453 : sum of digits is 12. therefore, the no. is
                divisible by 3
                > and to find the remainder, divide the sum by 3
                > for eg: 454 : sum of digits is 13, the no. is not divisible by 3
                n d remaider is 1...( divide 13 by 3)
                > here, is dis sum : sum of digits os 1002001 is 4 , so the
                remainder is 1
                > next, square of 1002 is 1004004 and dis no. is divisible by 3
                > square of 1003 is 1006009, it is not divisible by 3 and
                remainder is 1.... so on n so forth..
                > so the ans is option (a) 1 always
                >
                > 4) u get the upper limit for x+y wen d value for x and y is
                maximum which is 4 and 3 resp in dis case and the lower limit for x-
                y is wen d value for x and y is d lowest, which is 2 and 1 resp in
                dis case.
                > therefore, x+y/x-y = 4+3/2-1
                > =7/1
                > =7
                > which is ans option (b) 7
                >
                > 5)
                > pallavi aggarwal <pal_agg2003@...> wrote:
                >
                > which of the following is not a perfect square?
                >
                > a) 1,00,856 b) 3,25,137 c) 9,45,729
                d) all of these
                >
                >
                >
                > some birds settled on the branches of a tree. Ffirst, they sat
                one to a branch and there was one bird too many. Next they sat two
                to a branch and there was one branch too many. How many branches
                were there?
                >
                > a) 3 b) 4 c) 5 d) 6
                >
                >
                > the square of a number greater than 1000 that is not divisible
                by 3, wen divided by 3, leaves a remainder of
                >
                > a) 1 always b) 2 always c) either 1 or
                2 d)cant be said
                >
                >
                >
                > if 2<x<4 and 1<y<3, then find the ratio of the upper limit for
                x+y and the lower limit of x-y
                >
                > a) 6 b) 7 c) 8 d) none of these
                >
                >
                >
                > please explain all answers with proper methods
                >
                >
                >
                > ---------------------------------
                > Yahoo! India Answers: Share what you know. Learn something new
                Click here
                > Catch all the FIFA World Cup 2006 action on Yahoo! India Click
                here
                >
                >
                >
                >
                > ---------------------------------
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                Great rates starting at 1¢/min.
                >
              • ankit_heartless
                ... height is ... two inches. ... Find out ... 70,72,74 ... hey firsst suppose the age of the first to be x than second will be x+2 third will be x+4 and the
                Message 7 of 13 , Aug 19, 2006
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                  >
                  > > Q : My friend has four uncles of different height. Their average
                  height is
                  > > 74 inches & diference in height amongst the first three uncle is
                  two inches.
                  > > The difference between the third & the fourth uncle is 6 inches.
                  Find out
                  > > the height of each uncle.
                  > >
                  > > PS : I am getting the answer as 63,65,67 & 61. But the answer is
                  70,72,74
                  > > & 80. Can anybody solve this for me ????
                  > >
                  > > Mit.
                  > >
                  >
                  hey firsst suppose the age of the first to be x than second will be
                  x+2 third will be x+4 and the last will be x+10 now the avg is 74
                  so x+x+4+x+2+x+10=74*4
                  4x+16=296
                  4x=280
                  x=70
                  so u can get the age of all ur uncles
                • just_frnd_1_me
                  ... U CAN TRY THIS TOO AVG. HIGHT OF 4 UNCLES = 74 inc So total hgt = 74*4 = 296 now let hgt of 1st uncle is x there4 2nd s = x+2, 3rd s = x+4, 4th s= x+10
                  Message 8 of 13 , Aug 24, 2006
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                    --- In ascent4cat@yahoogroups.com, "Havi Arora" <haviarora@...> wrote:
                    > HI ALL

                    U CAN TRY THIS TOO
                    AVG. HIGHT OF 4 UNCLES = 74 inc
                    So total hgt = 74*4 = 296
                    now let hgt of 1st uncle is "x"
                    there4 2nd's = x+2, 3rd's = x+4, 4th's= x+10
                    hence x+(x+2)+(x+4)+(x+10)=296
                    4x+16 =296
                    x=70
                    hence 70, 72, 74, 80
                    hope i m right.
                    bye
                    anjali
                    > Hi Mitrabhanu Pati,
                    >
                    > First of all you should realize that, the average of the answer
                    that you are
                    > getting i.e. 63, 65, 67, 61 can never be 74 (all no. are smaller
                    than 74).
                    >
                    > Assume the shortest of them to be 'x', then the next one is 'x+2',
                    and after
                    > that is 'x+4', and finally 'x+10'. Taking their average to be 74,
                    we get the
                    > answer as 70, 72, 74, 80.
                    >
                    > Hope it solves your problem. I know you must be thinking that how
                    can we
                    > assume them to be standing in the increasing order, so i solved all
                    the
                    > possible combinations of it( there were 16 of those) as given below:
                    > x, x+2, x+4, x+10
                    > x, x+2, x+4, x-2
                    > x, x-2, x-4, x-10
                    > x, x-2, x-4, x+2
                    > x-2, x, x+2, x+8
                    > x-2, x, x+2, x-4
                    > x+2, x, x-2, x-4
                    > x+2, x, x-2, x-8
                    > x+4, x+2, x, x+6
                    > x+4, x+2, x, x-6
                    > x-4, x-2, x, x+6
                    > x-4, x-2, x, x-6
                    > x+10, x+8, x+6, x
                    > x+2, x+4, x+6, x
                    > x-10, x-8, x-6, x
                    > x-2, x-4, x-6, x
                    >
                    > Solving all the possible combinations, there were three different
                    answers
                    > as:
                    >
                    > 78, 76, 74, 68
                    > 70, 72, 74, 80
                    > 73, 75, 77, 71
                    >
                    > All three are correct answers, may be the options had just the
                    second one as
                    > option. So they marked only this as correct. But your answer can
                    never be
                    > correct.
                    >
                    >
                    >
                    >
                    > On 7/16/06, Mitrabhanu Pati <mitrabhanu_p@...> wrote:
                    > >
                    > > Hi there,
                    > > Pl. solve the following puzzle.
                    > >
                    > > Q : My friend has four uncles of different height. Their average
                    height is
                    > > 74 inches & diference in height amongst the first three uncle is
                    two inches.
                    > > The difference between the third & the fourth uncle is 6 inches.
                    Find out
                    > > the height of each uncle.
                    > >
                    > > PS : I am getting the answer as 63,65,67 & 61. But the answer is
                    70,72,74
                    > > & 80. Can anybody solve this for me ????
                    > >
                    > > Mit.
                    > >
                    >
                  • gaurav agarwal
                    I came across a few good problems and would like to share it. but I couldn’t get the solutions to them. Kindly help me out. Q1 A survey was conducted on the
                    Message 9 of 13 , Aug 25, 2006
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                      I came across a few good problems and would like to share it. but I couldn’t get the solutions to them. Kindly help me out.
                       
                      Q1 A survey was conducted on the eating habits of a group of 1000 people. Results show that 92 % of the people surveyed eat south Indian food, 91 % eat North Indian food, 82 % eat American food, 78 % eat Chinese food, 79 % eat Italian food and 80 % eat Continental food. What must be the minimum number of people who eat all the 6 types of food, if 7 people do not eat any of the six types of food?
                       
                      (1)  0                (2) 13               (3) 27               (4) 55
                       
                      Q 2 There are 2n integers [0,0,1,1,2,2,3,3……..(n-1),(n-1)]. From these 2n integers, n integers are chosen such that their average is an integer. Find the minimum average of those chosen n integers, given that n=23.
                       
                      (1) 4                 (2) 5                 (3) 6                 (4) 7
                       
                      Q 3 How many integral pairs (x,y) exist such that   x² + 10y² - 4xy + 2x + 8y – 18 = 0 ?
                       
                      (1) two             (2) three           (3) four             (4) six
                       
                      Q 4 The polynomial equation x4 + ax2 + bx – 15 = 0 has 4 real integral solutions. Which among the following may be a possible value of b?
                       
                      (1)  -15                        (2)  18              (3)  -32            (4) None of these
                       
                       
                                                  P(a-b,b)      if  a>= b
                      Q 5      P(a,b) =      
                               a            if  a < b
                       
                      it is given that  P(a,7) = 4; P(a,11) = 6 and P(a,13) = 3.
                      Find P(a,17), if ‘a’ is a positive integer between 2000 and 3000.
                       
                      (1) 6                 (2)  8                (3)  11              (4)  12



                      GAURAV AGARWAL
                      ELECTRONICS ENGINEERING
                      FINAL YEAR
                      INDIAN SCHOOL OF MINES


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                    • Nitin Chawla
                      Hi Gaurav, I could solve first two ques, trying 3 &4 and could not understand ques 5. answer: 1) they have asked minimum no, so for each tye of food try
                      Message 10 of 13 , Sep 24, 2006
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                        Hi Gaurav,
                         
                        I could solve first two ques, trying 3 &4 and could not understand ques 5.
                         
                        answer:
                        1) they have asked minimum no, so for each tye of food try getting the no of ppl not eating that type of food.
                        100-92=8 , 100-91=9  and so on
                        add them and it comes to 98% and 7 ppl dont eat any type of food, so ans is 2% of 1000 -7=13
                         
                        2)minimum average of 23 nos is 66/23, so 4 should be the minimum integer from given choices.
                         
                         
                        Cheers!
                         
                        Nitin
                         


                        gaurav agarwal <chota_newton@...> wrote:


                        I came across a few good problems and would like to share it. but I couldn’t get the solutions to them. Kindly help me out.
                         
                        Q1 A survey was conducted on the eating habits of a group of 1000 people. Results show that 92 % of the people surveyed eat south Indian food, 91 % eat North Indian food, 82 % eat American food, 78 % eat Chinese food, 79 % eat Italian food and 80 % eat Continental food. What must be the minimum number of people who eat all the 6 types of food, if 7 people do not eat any of the six types of food?
                         
                        (1)  0                (2) 13               (3) 27               (4) 55
                         
                        Q 2 There are 2n integers [0,0,1,1,2,2, 3,3……..(n-1), (n-1)]. From these 2n integers, n integers are chosen such that their average is an integer. Find the minimum average of those chosen n integers, given that n=23.
                         
                        (1) 4                 (2) 5                 (3) 6                 (4) 7
                         
                        Q 3 How many integral pairs (x,y) exist such that   x² + 10y² - 4xy + 2x + 8y – 18 = 0 ?
                         
                        (1) two             (2) three           (3) four             (4) six
                         
                        Q 4 The polynomial equation x4 + ax2 + bx – 15 = 0 has 4 real integral solutions. Which among the following may be a possible value of b?
                         
                        (1)  -15                        (2)  18              (3)  -32            (4) None of these
                         
                         
                                                    P(a-b,b)      if  a>= b
                        Q 5      P(a,b) =      
                                 a            if  a < b
                         
                        it is given that  P(a,7) = 4; P(a,11) = 6 and P(a,13) = 3.
                        Find P(a,17), if ‘a’ is a positive integer between 2000 and 3000.
                         
                        (1) 6                 (2)  8                (3)  11              (4)  12



                        GAURAV AGARWAL
                        ELECTRONICS ENGINEERING
                        FINAL YEAR
                        INDIAN SCHOOL OF MINES

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                      • Sumit Sarda
                        Answer to Q 2. *Ans : (3) 6* *Solution *: Lets pick the first 23 numbers of the series as our selection i.e. [ 0,0,1,1,2,2,.....9,9,10,10,11.] The sum of these
                        Message 11 of 13 , Sep 25, 2006
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                          Answer to Q 2.
                           
                          Ans : (3) 6
                          Solution : Lets pick the first 23 numbers of the series as our selection i.e. [ 0,0,1,1,2,2,.....9,9,10,10,11.] The sum of these 23 numbers is 2*(1+2+3+....+10)+11 i.e. 2*55+11 = 121. The average will be 121/23 = 5.26 . THis is not an integer.
                          The nearest interger is 6. We need 23*6 i.e.138 in numerator to get 6. This means 17 more to the total of 121. We can replace a number in the above set so that the net impact is 17+ (Say replacing 0 by 17, 1 by 18 etc).
                           
                          Also this will be smallest because we have selected the smallest possilble numbers.
                          Hence ans is 6.
                           
                          On 8/26/06, gaurav agarwal <chota_newton@...> wrote:



                          I came across a few good problems and would like to share it. but I couldn't get the solutions to them. Kindly help me out.
                           
                          Q1 A survey was conducted on the eating habits of a group of 1000 people. Results show that 92 % of the people surveyed eat south Indian food, 91 % eat North Indian food, 82 % eat American food, 78 % eat Chinese food, 79 % eat Italian food and 80 % eat Continental food. What must be the minimum number of people who eat all the 6 types of food, if 7 people do not eat any of the six types of food?
                           
                          (1)  0                (2) 13               (3) 27               (4) 55
                           
                          Q 2 There are 2n integers [0,0,1,1,2,2,3,3……..(n-1),(n-1)]. From these 2n integers, n integers are chosen such that their average is an integer. Find the minimum average of those chosen n integers, given that n=23.
                           
                          (1) 4                 (2) 5                 (3) 6                 (4) 7
                           
                          Q 3 How many integral pairs (x,y) exist such that   x² + 10y² - 4xy + 2x + 8y – 18 = 0 ?
                           
                          (1) two             (2) three           (3) four             (4) six
                           
                          Q 4 The polynomial equation x4 + ax2 + bx – 15 = 0 has 4 real integral solutions. Which among the following may be a possible value of b?
                           
                          (1)  -15                        (2)  18              (3)  -32            (4) None of these
                           
                           
                                                      P(a-b,b)      if  a>= b
                          Q 5      P(a,b) =      
                                   a            if  a < b
                           
                          it is given that  P(a,7) = 4; P(a,11) = 6 and P(a,13) = 3.
                          Find P(a,17), if 'a' is a positive integer between 2000 and 3000.
                           
                          (1) 6                 (2)  8                (3)  11              (4)  12



                          GAURAV AGARWAL
                          ELECTRONICS ENGINEERING
                          FINAL YEAR
                          INDIAN SCHOOL OF MINES


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                          --
                          Kind Regards
                          Sumit Sarda
                          +91 98275 29597
                        • agar_abhi2003
                          Q1 Ans is (d) and not (b).......all of the given is not a perfect square. q4 i think ans is (d) -- none of these Here u have to consider that x,y have a
                          Message 12 of 13 , Nov 17, 2006
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                            Q1> Ans is (d) and not (b).......all of the given is not a perfect
                            square.

                            q4> i think ans is (d) -- none of these
                            Here u have to consider that x,y have a common domain (2,3), and so
                            if x=y in this domain, then x-y=0, also x-y can be nagative.....so
                            lower limit of x-y cannot be said so easily.......and neighter the
                            ratio.
                            Abhishek


                            --- In ascent4cat@yahoogroups.com, aarti jain <aartirjain@...> wrote:
                            >
                            > hey pallavi,
                            > ssup' ...lisn, al dese probs r quite simple...u jus have to use
                            sum basic rules.
                            > solutions:
                            >
                            > 1) ans is (b)
                            > a perfect square can neva end in 2,3,7 and 8
                            >
                            > 2) i dint get ure Q...as in em not actualy clear bout d Q
                            >
                            > 3) u can solve dis sum by takin few eg.
                            > square of a no. grater den 1000
                            > say for eg: 1001
                            > find the square of 1001 wid the formula (1000+1)^2
                            > ie 1000000+2000+1= 1002001
                            > test for divisibility for 3 is: sum of the digits of the no.
                            shud b divisible by 3
                            > ( for eg: 453 : sum of digits is 12. therefore, the no. is
                            divisible by 3
                            > and to find the remainder, divide the sum by 3
                            > for eg: 454 : sum of digits is 13, the no. is not divisible by 3
                            n d remaider is 1...( divide 13 by 3)
                            > here, is dis sum : sum of digits os 1002001 is 4 , so the
                            remainder is 1
                            > next, square of 1002 is 1004004 and dis no. is divisible by 3
                            > square of 1003 is 1006009, it is not divisible by 3 and
                            remainder is 1.... so on n so forth..
                            > so the ans is option (a) 1 always
                            >
                            > 4) u get the upper limit for x+y wen d value for x and y is
                            maximum which is 4 and 3 resp in dis case and the lower limit for x-
                            y is wen d value for x and y is d lowest, which is 2 and 1 resp in
                            dis case.
                            > therefore, x+y/x-y = 4+3/2-1
                            > =7/1
                            > =7
                            > which is ans option (b) 7
                            >
                            > 5)
                            > pallavi aggarwal <pal_agg2003@...> wrote:
                            >
                            > which of the following is not a perfect square?
                            >
                            > a) 1,00,856 b) 3,25,137 c) 9,45,729
                            d) all of these
                            >
                            >
                            >
                            > some birds settled on the branches of a tree. Ffirst, they sat
                            one to a branch and there was one bird too many. Next they sat two
                            to a branch and there was one branch too many. How many branches
                            were there?
                            >
                            > a) 3 b) 4 c) 5 d) 6
                            >
                            >
                            > the square of a number greater than 1000 that is not divisible
                            by 3, wen divided by 3, leaves a remainder of
                            >
                            > a) 1 always b) 2 always c) either 1 or
                            2 d)cant be said
                            >
                            >
                            >
                            > if 2<x<4 and 1<y<3, then find the ratio of the upper limit for
                            x+y and the lower limit of x-y
                            >
                            > a) 6 b) 7 c) 8 d) none of these
                            >
                            >
                            >
                            > please explain all answers with proper methods
                            >
                            >
                            >
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