CSAT 2024 Solutions - What is the rightmost digit preceding the zeros in the value of 30^30?

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A. 1

B. 3

C. 7

D. 9

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Answer: D

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To find the rightmost digit preceding the zeros in 30³⁰, we focus on 3³⁰ since

30³⁰ = 3³⁰ × 10³⁰,

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Since 10³⁰ results in a 31-digit number with 30 zeros at the end, the rightmost digit preceding the zeros will be the unit digit of 3³⁰.

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1. Step 1: Last digits of powers of 3

The last digits of powers of 3 repeat in a cycle of 4:

- 3¹ = 3 (last digit is 3)

- 3² = 9 (last digit is 9)

- 3³ = 27 (last digit is 7)

- 3⁴ = 81 (last digit is 1)

The last digits of powers of 3 repeat in a cycle: 3, 9, 7, 1. This cycle has a length of 4.

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2. Step 2: Find the remainder when 30 is divided by 4

Since 30 ÷ 4 = 7 remainder 2

We have, 3³⁰ = 3^(4*7+2)

Therefore, the last digit of 330 corresponds to the second position in the cycle, which is 9.

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3. Conclusion:

The rightmost digit preceding the zeros in 30³⁰ is 9.

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