Data Sufficiency

What is the remainder when P is divided by 8 if 6 is a factor of P?
1. The digit in the unit's place of P^2 is 4
2. The unit's digit in P^4 is 6

P is a multiple of 6.

So, P can be (6,12,18,24,30...)

Statement 1:

P^2 ends in 4.

From the set, numbers whose square ends in 4 could be (12,18... any number ending in 2 or 8)

12/8 -> remainder 4
18/8 => remainder 2

Insufficient.

Statement 2:

P^4 ends in 6

6^4 - ends in 6
12^4 - ends in 6
18^4 - ends in 6

Insufficient.

Together, even together we can have two possible cases (say 12,18) E IMO

What is the remainder when P is divided by 8 if 6 is a factor of P?

1. The digit in the unit's place of P^2 is 4

if
P = 6, unit's place of P^2 = 6
P = 12, unit's place of P^2 = 4
P = 18, unit's place of P^2 = 4
P = 24, unit's place of P^2 = 6
P = 30, unit's place of P^2 = 0

p =12,18 satisfy the condition and p/8 leaves 4,2 as remainders respectively. Insufficient!

2. The unit's digit in P^4 is 6

if
P = 6, unit's place of P^4 = 6
P = 12, unit's place of P^4 = 6
P = 18, unit's place of P^4 = 6
P = 24, unit's place of P^4 = 6
P = 30, unit's place of P^4 = 0

P =6,12,18,24, satisfy the condition and p/8 leaves 6,4,2,0 as remainders respectively. Insufficient!

From 1 and 2

P =12 or 18 and p/8 leaves 4,2 as remainders respectively. Insufficient! IMO E