q) x is a positive number. If 9^x+9^(x+1) +9^(x+2)+ 9^(x+3)+9^(x+4)+9^(x+5)=y, is y divisible by 5?
(1) 5 is a factor of x
(2) x is an integer
(1) 5 is a factor of x
(2) x is an integer
y=9^x*(1+9+9^2+..+9^5) or 9^x*(9^6-1/8)
now 9^6/8 will leave reminder 1..hence 9^6-1 is divisible by 8
also last digit of 9^6 is 1..hence last digit of 9^6-1 is 0..i.e 9^6-1 is multiple of 10..hence 9^6-1 is divisible by both 8 and 5
so if we can conclude 9^x is integer y will be divisible by 5
only option b states that
hence ans option B
