GATE 2017 CE (CE1) – Question 8

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

Find the last digit of $(2171)^7+(2172)^9+(2173)^{11}+(2174)^{13}$.

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Correct answer: (B) 4

Explanation

Only the units digits matter. $1^7$ ends in 1. Powers of 2 cycle 2,4,8,6, so $2^9$ ends in 2. Powers of 3 cycle 3,9,7,1, so $3^{11}$ ends in 7. Odd powers of 4 end in 4. Their sum ends in $1+2+7+4=14$, hence the required last digit is 4, B.

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