➗ Quantitative AptitudeStaff Selection Commission

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From the chapter: Arithmetic Foundations — Numbers, Percentage, Ratio & Averages

What is the unit digit of 3⁶⁵ × 6⁵⁹ × 7⁷¹?

Show the answer and why

Answer: C.

Take each factor separately. 3⁶⁵: 65 ÷ 4 leaves remainder 1, so the 1st entry of the cycle (3, 9, 7, 1) → 3. 6⁵⁹: every power of 6 ends in 6. 7⁷¹: 71 ÷ 4 leaves remainder 3, so the 3rd entry of (7, 9, 3, 1) → 3. Now multiply the unit digits only: 3 × 6 = 18 → 8, then 8 × 3 = 24 → unit digit 4.

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