Question : $3^{50}+9^{26}+27^{18}+9^{28}+9^{29}$ is divisible by which of the following integers?
Option 1: 11
Option 2: 5
Option 3: 7
Option 4: 2
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Correct Answer: 11
Solution : 3 50 + 9 26 + 27 18 + 9 28 + 9 29 = 3 50 + 3 52 + 3 54 + 3 56 + 3 58 = 3 50 (1 + 3 2 + 3 4 + 3 6 + 3 8 ) = 350(1 + 9 + 81 + 729 + 6561) = 350 × 7381 = 350 × (11 2 × 61) So, the given number is divisible by 11. Hence, the correct answer is 11.
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