What is the remainder when the number [123123...123] of 300 digits is divided by 99? Choose one answer. a. 36 b. 27 c. 18 d. 33 the right answer is 33.. i don find any connection to this so cud u pls guide towrads the right answer...
123123 is divisible by 11 to be divisible by 99 the number shd be also divisible by 9 the minimum digits shd be 123123123123123123 ie 6 -> 123 so for 100 such numbers the reminder wld be same 4 ->123 and thats 33.
The solution is as confusing as the question
First there are many kind of divisibility problems to know all the tricks refer to the number system notes and try to solve all the questions in number system Question Bank. The above question is one of the kind where a set numbers are repeated few times and you are asked to find the reminder. Keep in mind following two points while solving this typeof questions 1. You have to divide the large number in to two parts where the first number has reminder zero and the other has some. 2. If the number you are diving is large then find out its factors and use the divisibility rules for those factors for example when you are asked to chk the divisibility of a number by 56 ( 7 x 8)- you have to chk that the number shd be divisible by both 7 and 8. ========================================================== Here we have to find out the reminder of the number 123123...(300 digits) when divided by 99 123123..(300 digits) is same as repeating 123 for 100 times. we have to find the part of the above number which is divisible by 99 and the reminder of the other part is the reminder of the whole number. Now to chk divisibility by 99 we 'll chk that the number shd be divisible by both 9 and 11. 123123 is divisible by 11 sum of 123 is 6. So to be divisible by 9 we have to take at least 6 of such parts (3 of such parts ll be divisible by 9 but not by 11) i.e 123(repeated 6 times/ 18 digits)has a sum 36 and is divisible by 9. and its also divisible by 11 so 123(repeated 6 times/ 18 digits)is divisible by 99 and thus 123(repeated 12 times/ 36 digits)is divisible by 99 123(repeated 18 times/ 54 digits)is divisible by 99 .... .. like so 123(repeated 96 times)is divisible by 99 Thus we have to find the reminder of 123(repeated 4 times) and thats is 33 which is the reminder of the whole number
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123123....123 is divisible by 11 but not by 9. We find the quotient on division by 11 and then find remainder when this quotient is divided by 9. Multiplying by 11, we get our answer. 123123 on dividing by 11 gives 11193. Therefore 123123....123 [the 300 digit no.] on division by 11 gives 111930111930.......11193 [the 299 digit no.] The sum of the digits of this no. is (1+1+1+9+3) * 50 = 15*50= 750 750 on division by 9 gives 3 as remainder. Thus remainder when 123123.....123 is divided by 99 is 3 * 11 = 33.
another nice method