Question 63

$$(2^{51}+2^{52}+2^{53}+2^{54}+2^{55})$$ is divisible by

Solution

Expression : $$(2^{51}+2^{52}+2^{53}+2^{54}+2^{55})$$

= $$2^{51}(1+2+2^2+2^3+2^4)$$

= $$2^{51}(1+2+4+8+16)$$

= $$2^{51} \times 31$$

Thus, the above expression is divisible by $$31k$$ and the only option that is divisible by 31 = 124

=> Ans - (C)

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