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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