Question

Find the unit digit of $(1253{)}^{1469}-(1258{)}^{1471}$.

• A. $6$
• B. $9$
• C. $3$
• D. $2$

Answer 1

The correct option is B $9$

Cyclicity of 3 and 8 is 4
For $(1253{)}^{1469}$
On dividing 1469 by 4, we are getting 1 as remainder.
So,$(1253{)}^{1469}$ends with $3$

For $(1258{)}^{1471}$
On dividing 1471 by 4, we are getting 3 as remainder.
and $(1258{)}^{1471}$ ends with $2$.
But, $(1253{)}^{1469}<(1258{)}^{1471}$.
So, unit digit is is 9.