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?
7
29
16
13

Answer 1

18 is the remainder

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Answer 2

Answer: 29

Step-by-step explanation:

As per the divisibility rule of 3, since the sum of the digits of N is 23, the remainder when N is divided by 3 is 2. (same as remainder obtained when 23 is divided by 3)

Let’s say R is the remainder when N is divided by 33.

=> N=33n+R ————-(I)

Now R must satisfy the following two conditions

R must leave a remainder 7 when divided by 11 ——— (A)

R must leave a remainder 2 when divided by 3 ———-(B)

From (A), we can assume that R=11x+7

Now 11x+7 should leave a remainder 2 when divided by 3

=> 2x+1 should leave a remainder 2 when divided by 3

=> x=2,5,8,11,……..

=> x=3k+2 , where k=0,1,2,3…….

So the remainder R=11x+7=11(3k+2)+7=33k+29

From (I) we have , N=33n+R=33n+33k+29=33(n+k)+29

It is evident that R will leave a remainder of 29 when divided by 33

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