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CAT 1998 Question(Finding the remainder for the given condition)

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Q.) A certain number when divided by 899, leaves a remainder 63. Find the remainder when the same number is divided by 29.

A)5
B)4
C)1
D)Cannot be determined

Solution :

A number when divided by 899, leaves a remainder 63 will be of the form 899k+63 , where k is a constant.

When is is divided by 29 ,then

$Rem(\frac { 899k+63 }{ 29 } )=0+Rem(\frac { 63 }{ 29 } )$ (0 because 899k is divisible by 29)

=$Rem(\frac { 63 }{ 29 } )$

=5

Hence, OPTION(A)

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