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

CORRECT ANSWER WRONG ANSWER

CORRECT ANSWER WRONG ANSWER

CORRECT ANSWER WRONG ANSWER

CORRECT ANSWER WRONG ANSWER

Solution

Correct option is

(B)

Explanatory Answer

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