Number that can be expressed as sum of powers of '2' as, $2^{7} + 2^{5} + 2^{4} + 2$ is.

150

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170

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180

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190

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Solution

The correct option is C $180$
$170 = 2^{7} + 52$
$= 2^{7} + 2^{5} + 20 (2^{6} > 52 where as 2^{5} < 52)$

$= 2^{7} + 2^{5} + 2^{4} + 4 (2^{5} > 20 where as 2^{4} < 20)$
$= 2^{7} + 2^{5} + 2^{4} + 2^{2}$

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