2122 462 842 464 2130 is divisible by which one of the following integers ........

Quantitative Aptitude (CDS) Number System

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2¹²² + 4⁶² + 8⁴² + 4⁶⁴+ 2¹³⁰ is divisible by which one of the following integers?

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Explanation:

As,
2¹²²+4⁶²+8⁴²+4⁶⁴+2¹³⁰
=2¹²²+2^2×62+2^3×42+2^2×64+2¹³⁰
=2¹²²+2¹²⁴+2¹²⁶+2¹²⁸+2¹³⁰
=2¹²²(1+2²+2⁴+2⁶+2⁸)
=2¹²²(1+4+16+64+256)
=2¹²²×341
Here 341 is divisible by 11.
Hence 2¹²²+4⁶²+8⁴²+4⁶⁴+2¹³⁰ will be divisible by 11
Hence option (4)