CSAT 2024

Q. What is the rightmost digit preceding the zeros in the value of 30^30?

a) 1
b) 3
c) 7
d) 9
Correct answer: d) 9

Question from UPSC Prelims 2024 CSAT

Explanation : 

Let’s approach this step-by-step:

1) We can break down 30^30 into (3^30) * (10^30).

2) 10^30 will give us 30 zeros at the end of the number.

3) So, we need to find the last digit of 3^30.

4) Let’s look at the pattern of last digits when we raise 3 to different powers:
3^1 = 3
3^2 = 9
3^3 = 27 (last digit 7)
3^4 = 81 (last digit 1)
3^5 = 243 (last digit 3)

5) We see that the pattern of last digits repeats every 4 powers: 3, 9, 7, 1.

6) To find the last digit of 3^30, we can divide 30 by 4:
30 ÷ 4 = 7 remainder 2

7) This means that 3^30 will have the same last digit as 3^2, which is 9.

Therefore, the rightmost digit preceding the zeros in 30^30 is indeed 9.

The correct answer is d) 9.

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