If P=(102 power x) - (98 power x) and x is a natural number greater than zero. how many values exist at units place of P?

(a) 4 (b)5 (c)3 (d) 8

• (102^x - 98^x)
  
  to calculate first digit we only need firs digit of no.
  to check power
  if x=1
  then |2^1-8^1|=6
  if x=2
  then |2^2-8^2|=|4-64|=4-4=0(only take first digit)
  if x=3
  then |2^3-8^3|= |8-2 |= 6 (only take first digit)
  if x=4
  then 2^4-8^4= 6-6=0
  after x=4 it is repeat
  
  x = 3 ans
• 9 years agoHelpfull: Yes(18) No(0)
• (c) 3
  
  calculate by putting x=1,2,3,4 you can observe that only 0,4,6 are repeated
• 9 years agoHelpfull: Yes(5) No(1)
• 102^x - 98^x
  to calculate unit digit just consider the unit digit 102^x and 98^x individually.
  so 2^1 - 8^1= 2 - 8 =12 - 8= 4
  2^2 - 8^2= 4 - 4 = 0
  2^3 - 8^3= 8 - 2= 6
  2^4 - 8^4= 6 - 6= 0
  2^5 - 8^5= 2 - 8= 4
  2^6 - 8^6= 4 - 4= 0
  2^7 - 8^7= 8 - 2= 6
  thus, cycle of 4 having unit digits, 4,0 6, and 0
  we have to find different values that exists at unit place. As 0 comes two times in the cycle. so there ill be 3 different values say, 4, 0 and 6
  
• 9 years agoHelpfull: Yes(3) No(1)
• thank u kumar
• 9 years agoHelpfull: Yes(0) No(0)
• ans is (c)3
• 9 years agoHelpfull: Yes(0) No(0)
• correct ans is 3
• 9 years agoHelpfull: Yes(0) No(0)