GATE EE 2016 Set 2 — Question 10
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General Aptitude → Quantitative Aptitude → Ratios, Percentages, Powers, Exponents & Logarithms
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Question
The numeral in the units position of is _____.
Correct answer
7 to 7
Solution
To find the units digit of the expression , we determine the units digit of each term individually:
Units digit = (Units digit of ) + (Units digit of Units digit of )
Units digit = .Therefore, the numeral in the units position is 7.
1.Units digit of : Any number ending in 1 raised to any positive integer power will always have a units digit of 1. Thus, the units digit is 1.
2.Units digit of : Any number ending in 6 raised to any positive integer power will always have a units digit of 6. Thus, the units digit is 6.
3.Units digit of : The units digit of powers of 3 follows a cycle of 4: , , (units digit 7), (units digit 1). The exponent is 424. Since with a remainder of 0, the units digit is the same as , which is 1.
Now, combine these results according to the expression:Units digit = (Units digit of ) + (Units digit of Units digit of )
Units digit = .Therefore, the numeral in the units position is 7.
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