CAT Quant Practice Problems

Question: The remainder when 784 is divided by 342 is
  1. 0
  2. 1
  3. 49
  4. 341

Correct Option:2

$\frac { 7 ^ { 84 } } { 342 } = \frac { \left( 7 ^ { 3 } \right) ^ { 28 } } { \left( 7 ^ { 3 } - 1 \right) } = \frac { \left\{ \left( 7 ^ { 3 } \right) ^ { 28 } - 1 + 1 \right\} } { \left( 7 ^ { 3 } - 1 \right) }$
$= \frac { \left\{ \left( 7 ^ { 3 } \right) ^ { 28 } - 1 \right\} } { \left( 7 ^ { 3 } - 1 \right) } + \frac { 1 } { \left( 7 ^ { 3 } - 1 \right) }$
$\frac { \left\{ \left( 7 ^ { 3 } \right) ^ { 28 } - 1 \right\} } { \left( 7 ^ { 3 } - 1 \right) }$ is always divisible as it is in the form of

$\frac { \left( x ^ { n } - y ^ { n } \right) } { ( x - y ) }$
Hence, the remainder is 1 .


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