# Find the sum of the remainders obtained when a number n is divided by 9 and 7 successively given that n is the smallest number that leaves remainders of 4,6, and 9 when divided successively by 13, 11 and 15. Option 1) Option 2) Option 3) Option 4) Option 5)

$The\: n \: can\: be\: written \: as,$
$n = 13k + 4$
$n = 11k' + 6$
$n = 15k" + 9$

So, in order to get the number we have to fullfil the above mentioned numbers one by one....
The number with 15 divided 9 as remainder$= 15x+9$
The number with 11 divided 6 as remainder $= 11*(15x+9) + 6$

The number with 13 divided 4 as remainder$= 13*[11*(15x+9) + 6] +4 = 2145x +1369$ (Thus the general form of the required number)

In order to get the lowest put $x= 1 \: thus\: 3514$

sum of the remainders obtained when 3514 is divided by 9 and 7 successively=9

Exams
Articles
Questions