x and y are two alternate odd nos(Eg.1,5 and 5,9).The difference between x^3+y and y^3+x is always divisible by m.Then what is the maximum value of m?
i)6,ii)12,iii)24,iv)120

• (x^3+y)-(y^3+x)is divisible by m
  acc to the above equation we get
  =>(x^3-y^3)-(x-y) is divisble by m
  =>(x-y)(x^2+y^2+xy)-(x-y)is divisible by m
  =>(x-y)[(x^2+y^2+xy)-1] is divisible by m
  Put y=1,x=5 we get
  (5-1)[(25)+1+5-1]
  4.3.2(5)
  24(5)
  which is divisble by 24
  Now put y=3,x=7 and we get
  => (7-3)[(49+9+21) - 1]
  =>4(78)
  =>24(13)
  which too is divisible by 24
  last case try y=7,x=11
  (11-7)[(121+49+77)-1]
  =>4(246)
  =>4.6(41)
  => hence 24 is the maximum value possible
  
• 11 years agoHelpfull: Yes(42) No(1)
• two numbers can be 2k+1 and 2k+5, maximum value of m is 24
• 11 years agoHelpfull: Yes(9) No(1)
• @JASMINE KHAN
  12 is not the correct answer,because the smallest alternate odd nos are 1 and 5.So putting these value in your equation we will get
  12y^2+48y+60 =12*5^2+48*5+60=600 which is divisible by 24 and 120
  taking 3 and 7
  we get 12*7^2+48*7+60=984 which is also divisible by 24 but not with 120
  So the maximum value should be 24 as it divides the expression with least possible values.
• 11 years agoHelpfull: Yes(2) No(0)
• answer is 24
• 11 years agoHelpfull: Yes(1) No(0)
• oh yes i found my mistake.
  and thanks sir for giving me the right track.
  and thanks to sumit also
• 11 years agoHelpfull: Yes(1) No(0)
• @satyaranjan yes i have taken my elitmus exam. this is my id sumitrawal586@gmail.com u can link with me here and i'l try my level best to help u if i can
• 11 years agoHelpfull: Yes(1) No(0)
• Roopam Jain method is easy than sumit's, gives directly 24 as its multiple
  
• 11 years agoHelpfull: Yes(1) No(0)
• Answer is 24.
• 11 years agoHelpfull: Yes(0) No(2)
• ans=12
  x and y are two alternate odd numbers.Therefore x-y=4
  given,
  (x^3+y)-(y^3+x) divisible by m.........(1)
  solving above
  (x^3-y^3)-4
  put x=y+4
  12y^2+48y+60 and is divisible by 12........(2)
  from (1) & (2)
  m=12
  
• 11 years agoHelpfull: Yes(0) No(5)
• Those who answered 24 ,please explain me the process to get it
• 11 years agoHelpfull: Yes(0) No(0)
• thanks Sumit for your explanation.
• 11 years agoHelpfull: Yes(0) No(0)
• Hello Sumit,that means you have already given the Elitmus Exam,but I want to appear for this.So I want you to give me some tips regarding Elitmus.Thanks in advance.Please show me the way to prepare best for the exam as per your experience.
• 11 years agoHelpfull: Yes(0) No(0)
• 4 . 120 is the ans
• 11 years agoHelpfull: Yes(0) No(2)