a number has only k and k-2 factor off a number n the factor 1 and n is not consider so what is possibel..
a.n+1 is perfect square.
b.n-1 is a odd or prime number.
c. n+1 is a even number
d. all of above

• answer is a
  k (k-2) = n
  hence for option a lets add 1,
  = (k^2-2k) + 1
  = k^2 -2k + 1
  = (k-1)^2
  which is a perfect square
  
  but for k = 28,
  28*26 = 728
  729 is a perfect square
  but n+1=728+1=729 is not even number. Therefore, option c is false so option d can not be true.
• 8 years agoHelpfull: Yes(26) No(4)
• answer is d.
  consider the number n=8 only 2 factor 4 and 2 other than 1 and 8.
  8+1=9 perfect square.
  8-1=7 odd number.
  
  consider 15 =5*3 and k and k-2 follow 5-3=2..
  15+1 =16 perect square...
  15-1=14 even number..
  consider 35=5*7= other than 1 and 35.
  35+1=36.
  35-1=34 even number..
  
• 8 years agoHelpfull: Yes(11) No(17)
• as we can see tha option b and c are opposite to each other, if n-1 is odd then how it is possible to n+1 is even , it must be odd cz alternete numbers, and option a is right as we can see it by adding 1 in both side
  k^2 -2k +1 = n + 1
  (k-1)^2 = n + 1
  
  :)
  
• 7 years agoHelpfull: Yes(8) No(1)
• n+1 is perfect square . ANS a
• 8 years agoHelpfull: Yes(5) No(2)
• answer is d.
  and chinmay joshi 728 has other factors
  eg: 4 and 182
  look the question
  it is mentioned only factors k & k-2 is present oder than 1 and n
  
• 7 years agoHelpfull: Yes(2) No(0)
• Answer is option D we have to check for all possible solution .
• 8 years agoHelpfull: Yes(1) No(4)
• as discussed by RAJAT , ans : a
  n+1 is perfect square because b & c are not always right.
  you have to go with opt : a
• 7 years agoHelpfull: Yes(1) No(1)
• Anser is a) because
  let k=5 then 5*3=15 and 15+1=16 perfect square and 15-1=14 not odd
  let k=7 then 7*5=35 and 35+1=36 perfect square and 35-1=34 not odd
  let k=9 then 9*7=63 and 63+1=64 perfect square
  hence this would work the similar way
  
  Let me know If you think It's not right. I would love to learn other way as well.
• 7 years agoHelpfull: Yes(1) No(1)
• Since it is given that only K, k-2 is the factor of n except ( 1, n)
  therefore
  K( K - 2 ) = n
  K^2 - 2K = n
  
  NOW WE CHECK FOR EVERY VALUE OF 'K'
  K=1 n = -1 NOT POSSIBLE
  
  K=2 n = 2 NOT POSSIBLE
  
  K=3 n=3 NOT POSSIBLE
  
  K=4 n=8 POSSIBLE
  
  K=5 n=15 POSSIBLE
  
  AND SO ON..........
  
  FROM HERE WE SEE
  
  n+1 = 9, 16...............PERFECT SQUARE SO OPTION FIRST SATISFY BUT OPTION 'C' IS WRONG
  n-1 = 8, 14................OPTION 'B' IS ALSO WRONG
  
  HENCE THE ANSWER IS 'A'
• 7 years agoHelpfull: Yes(1) No(1)
• correct answer is a
  chinmay joshi make correct
• 7 years agoHelpfull: Yes(0) No(0)