If x is the remainder when 361284 is divided by 5 and y is the remainder when 496 is divided by 6, then what the value of (2x - y)?

Answer: Option C

x is the remainder when 3⁶¹²⁸⁴ is divided by 5
So, $$\frac{3^{61284}}{5}=\frac{3^{4\times 15321}}{5}=\frac{3^4}{5}=\frac{81}{5}$$
Remainder = 1
x = 1
y is the remainder when 4⁹⁶ is divided by 6
$$\frac{4^{96}}{6}=\frac{4^{4\times 24}}{6}=\frac{4^4}{6}=\frac{256}{6}$$
Remainder = 4
y = 4
Now, (2x - y)
= 2 - 4
= -2

Alternate solution:
As we know,
Unit digit of 3⁶¹²⁸⁴
⇒ 3⁴
⇒ 1
So we can say if we divide 3⁶¹²⁸⁴ by 5 then we get remainder 1
x = 1
As we know,
4 ÷ 6, then remainder 4
4² ÷ 6, then remainder 4
4³ ÷ 6, then remainder 4
4ⁿ ÷ 6, then remainder 4
When n = natural number
So we can say 4⁹⁶ is divided by 6, then the remainder is 4
y = 4
Now, (2x - y)
⇒ 2 × 1 - 4
⇒ 2 - 4
⇒ -2