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Question

# The sum of the digits of a number N is 23. The remainder when N is divided by 11 is 7. What is the remainder when N is divided by 33

CAT 2021

A
B
C
D
##### 13
Solution

Correct option is

(B)

sum of the digits = 23

Remainder = when N/9 = 5

Remainder = when N/3 = 2 ( a no. of the form 9m+5 divided by 3 leaves remainder 2)

so , N = 11m + 7 ; N = 3n+2

11m + 7 = Possible numbers are = 7 , 18 , 29 , 40 , 51

3n+ 2 = Possible nos are = 2, 5 , 8 , 11 , 14 , 17 , 20 , 23 ,26 , 29

now the number that is of the form 11m +7 ; and 3n+ 2 should be of the form = 33 K +29

becuase starting with 29 , every 11th no. is of the form 11m+ 7

and every 3rd no. is of the form 3n+ 2

so , starting from 29 , every 33rd no. should be on both lists ( 33= 11*3)

OR any no. of the form ; 33K +29 will be of the form

11m+7 ; and 3n+2 ( m , n, k are natural nos)

so , remainder when N/ 33 = 29

hence B is the correct option