CAT 2005 — QA Question 16

30²⁷²⁰ = 3²⁷²⁰ × 10²⁷²⁰

The rightmost non-zero digit of 30²⁷²⁰ will be the digit in the unit’s place of 3²⁷²⁰.

3’s power cycle is 3, 9, 7, 1 and cyclicity is 4. 

i.e. if we get a remainder of 1, 2, 3, or 0 when 2720 is divided by 4, then the digit in the units place will be 3, 9, 7, or 1 respectively.

2720 = 680 × 4, i.e. the remainder is 0 

∴ The digit in the unit’s place of 3²⁷²⁰ is 1. 

∴ The rightmost non-zero digit of 30²⁷²⁰ is 1.

Hence, option (a).