Quantitative Aptitude Ques 856

Question: If $ n $ is even, then $ (6^{n}-1) $ is divisible by

Options:

A) 37

B) 30

C) 35

D) 6

Show Answer

Answer:

Correct Answer: C

Solution:

  • If $ x $ is even, then let $ n=2x, $ tor some x. Now, $ 6^{n}-1=(6^{2x}-1)=36^{x}-1 $ $ =(36-1)({36^{x-1}}+{36^{x-2}}+…+1) $ $ =(35)({36^{x-1}}+{36^{x-2}}+…+1) $ Hence, the number is divisible by 35.
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