 0
Oct. 9, 2020, 3:25 p.m.
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?

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?

1. 7
2. 29
3. 16
4. 13

I dont know where to start such questions

quant
numbers 0
Oct. 9, 2020, 3:26 p.m.

Sum of digits = 23
Remainder when N is divided by 9
N/9 = 5 {Remainder on division by 9 for any number is equal to the remainder of dividing the sum of the digits of the number by 9}

Remainder of N/3 = 2 {A number of the form 9k + 5 divided by 3 leaves a remainder 2}
N = 11k + 7
N = 3m + 2
11k + 7 => Possible numbers are 7, 18, 29, 40, 51
3m + 2 => Possible numbers are 2, 5, 8, 11, 14, 17, 20, 23, 26, 29

The number that is of the form 11k + 7 and 3m + 2 should be of the form 33b + 29. How did we arrive at this result?

The first natural number that satisfies both properties is 29.
Now, starting with 29, every 11th number is of the form 11k + 7, and every 3rd number is of the form 3m + 2.
So, starting from 29, every 33rd number should be on both lists (33 is the LCM of 11 and 3).
Or, any number of the form 33b + 29 will be both of the form 11K + 7 and 3m + 2, where b, k, m are natural numbers.

The remainder when the said number is divided by 33 is 29.

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