Fractional part 27831 is 231 431 831 1031 278=23275=82

| Fractional part

\frac{2^{78}}{31}

A. $\frac{2}{31}$

B. $\frac{4}{31}$

C. $\frac{8}{31}$

D. $\frac{10}{31}$

Please scroll down to see the correct answer and solution guide.

Right Answer is: C

SOLUTION

$2^{78} = 2^{3} {.2}^{75} = 8 (2^{5})^{15} = 8 (1 + 31)^{15} = 8 {^{15} C_{0} +^{15} C_{1} 31 + . . . . +^{15} C_{15} (31)^{15}}$
$2^{78} = 8 +$ an integer multiple of 31
$\frac{2^{78}}{31} = \frac{8}{31} +$ an integer

Fractional part 27831 is 231 431 831 1031 278=23275=82

Right Answer is: C

SOLUTION

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