GATE EE 2023 Set 1 — Question 9
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General Aptitude → Quantitative Aptitude → Ratios, Percentages, Powers, Exponents & Logarithms
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Question
The digit in the unit’s place of the product is _______.
Correct answer
(A) 7
Solution
To find the unit digit of the product, we find the unit digit of each term separately using the concept of cyclicity.
1.Unit digit of :
- Cyclicity of 3: . The cycle is (3, 9, 7, 1) with length 4.
- Divide the exponent by 4: gives a remainder of 3.
- The unit digit corresponds to the 3rd position in the cycle, which is 7.
- Cyclicity of 7: . The cycle is (7, 9, 3, 1) with length 4.
- Divide the exponent by 4: gives a remainder of 0 (or 4).
- The unit digit corresponds to the 4th position in the cycle, which is 1.
- .
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