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# Remainder Obtained When divided

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A number when divide by D leaves a remainder of 7 and when divided by 3D leaves a remainder of 20. what is the remainder left, when twice the number is divided by 3D?
(i)1
(ii)20
(iii)13
(iv)26

[Number System , Remainder Theorem , possible remainder, CAT Questions]

Solution :
A number when divided by D leaves a remainder of r. The possible remainders when the same number is divided by nD are r , (D+r), (2D+r),(3D+r) …[(n-1)D+r]

Let the number be N. Let the remainder left when N is divided by D be represented by $Rem(\frac { N }{ D } )$

$Rem(\frac { N }{ D } )$=7

$Rem(\frac { N }{ 3D } )$=20

So, $Rem(\frac { N }{ 3D } )$ could be either (D+7) or (2D+7).

D+7 =20
=>D=13

2D+7=20
=>D=6.5

But D can’t be less than 7.
=>D=13

$Rem(\frac { 2N }{ 3D } )$ = $Rem(\frac { 40 }{ 39 } )$ = 1

Hence, OPTION(I)