Question

23. The least number which should be subtracted from 10000 so that 33 divides the difference
exactly is
(1 Point)
10
1
100
33
pls tell the answer
and ensure that the answer is correct​

Answer 1

The least number that should be subtracted from 10000 so that 33 divides the difference is 1

Therefore, option (2) is correct.

Step-by-step explanation:

If 10000 is divisible by 33 then it must be divisible by 3 and 11

We know that a number is divisible by 3 when the sum of the digits is divisible by 3

And a number is divisible by 11 if difference of the sum of the digits at odd places and sum of the digits at even places is divisible by 11

if we subtract 1 from 10000 we get 9999, which is divisible by 3

Sum of digits at odd places = 9+9  = 18

Sum of digits at even places = 9+9 = 18

18 - 18 = 0, which is divisible by 11

Therefore, number 9999 is divisible by both 11 and 3

Thus, the number 9999 is divisible by 33

Therefore, the least number that should be subtracted from 10000 so that 33 divides the difference is 1

Hope this answer is helpful.

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Answer 2

Given :  A number subtracted from 10000 so that 33 divides the difference

To find : The least number

Solution:

a  = bq  + r

10000 = 33q  + r

=> 33q = 10000 - r

Hence r has to be subtracted from 10000

0 < r < 33

             303

33   _|  10000  |_

             99

           ____

              10

                0

              ____

                  100

                    99

                  _____

                       1

10000 = 33 * 303   + 1

1 is the least number which should be subtracted from 10000 so that 33 Divides the Difference exactly  

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