CAT 2018 Quant Questions

Question:
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

It is given that \({N^N}\) = \({2^{160}}\)

We can rewrite the equation as \({N^N}\) = \({({2^5})^{160/5}}\) = \({32^{32}}\)

\( \Rightarrow \) N = 32

\({N^2} + {2^N}\) = \({32^2} + {2^{32}} = {2^{10}} + {2^{32}} = {2^{10}}*(1 + {2^{22}})\)

Hence, we can say that \({N^2} + {2^N}\)can be divided by \({2^{10}}\)

Therefore, x\(_{max}\) = 10

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CAT 2018 Quant Questions
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