Question

The value of $\left\{\frac{3^{2003}}{28}\right\}$ , where {.} denotes the fractional part, is equal to :

• A. 15/28
• B. 5/28
• C. 19/28
• D. 9/28

Answer 1

The correct option is C

19/28

$3^{2003}=3^2.3^{2001}={9.27}^{667}$ = $9\{28-1{\}}^{667}$

= 9 { ${28}^{667}-{}^{667}{C}_1{28}^{666}+...+667.28-1\}$

= 9 × 28 × integer - 28 + 19.

$\therefore$ Remainder when $3^{2003}$ is divided by 28 is 19.

$\therefore$ $\left\{\frac{3^{2003}}{28}\right\}=\frac{19}{28}$ .