UPSC CDS 2 2022 Math Paper

Euclid's division lemma: If a and b are two positive integers, then there exist unique positive integers q and r such that a=bq+r, where 0≤qr<b
Calculation:
Using the above concept
⇒x=6p+2
Again,
⇒y=6q+3
Equation (1) - (2)
⇒(x−y)=6(p−q)−1
⇒‌

(x−y)

6

=‌

6(p−q)−1

6

∴ Remainder =6−1=5