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GATE 2023 XH2 (English) – Question 9

General Aptitude · Quantitative Aptitude: Arithmetic and Number Computation · 2 marks · Multiple choice

The digit in the unit’s place of the product $7^{1000} \times 3^{999}$ is _______.

  1. 7
  2. 1
  3. 3
  4. 9

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Show answer and explanation

Correct answer: (A) 7

Explanation

The units digits of powers of 7 repeat as 7, 9, 3, 1, and $1000 = 4 \times 250$, so $7^{1000}$ ends in 1. The units digits of powers of 3 repeat as 3, 9, 7, 1, and $999 = 4 \times 249 + 3$, so $3^{999}$ ends in 7. The product ends in $1 \times 7 = 7$.