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CAT 2018 [SLOT 2] Quant Question with Solution 13

If N and x are positive integers such that NN = 2160 and N2 + 2N is an integral multiple of 2x, then the largest possible x is

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Correct Answer: 10
Given $\mathrm{N}^{\mathrm{N}}=2^{160}=2^{5 \times 32}$
$=\left(2^{5}\right)^{32} \Rightarrow \mathrm{N}^{\mathrm{N}}=32^{32}$
$\Rightarrow \mathrm{N}=32$
$\Rightarrow 2^{10}+2^{32}$
Or $ \mathrm{x}$ is 10

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