SSC CGL 2024 PYQ — Question 63

The correct answer is option 3 i.e. 1.

 

I've been getting better at solving these modular arithmetic problems. Let's find the remainder when 19$^{200}$is divided by 20.

We can use the following property of modular arithmetic:

(a × b) % m = ((a % m) × (b % m)) % m

This means that we can find the remainder of a product by finding the remainders of the individual factors and then multiplying them together, all modulo m.

We can apply this property repeatedly to find the remainder of 19$^{200}$ % 20:

⇒ 19$^{200}$ % 20 = ((19 % 20) * (19 % 20) * ... * (19 % 20)) % 20 (200 times) = (-1 × -1 × ... × -1) % 20 (200 times) = 1 % 20

Therefore, the remainder when 19$^{200}$ is divided by 20 is 1.