So the learning from this problem can be summarized below :
If a number "N" is divided by "D" and leaves a remainder "R" , then if that same number "N" is divided by "k*D" where "k" is a positive integer , then the number of remainders that are possible are R , D+R , 2D+R , .... , (k-1)D + R.
So if the question was that what is the remainder when the number was divided by 288 , we can approach it in a mechanical way.
The possible remainders are 23 , 36+23 , 72+23 , .... , 252+23 . We can straightaway reject answer choices that are not in this list.
Sample question : A number N divided by D gives a remainder of 7 , the same number divided by 5D gives a remainder of 24. Find D [N and D are both positive integers].Ans: The possible remainder for the 2nd case are 7 , D+7 , 2D+7 , 3D+7 , 4D+7.
So 7<> 24, case closed for 1st possibility ,
D+7 = 24 or D=17 (ok)
2D+7= 24, not ok as D cannot be fraction.
3D + 7=24, not ok as D cannot be fraction
4D+ 7 = 24, not possible as D cannot be fraction.
So possible values of D is only 17. So 17 must be present among the answer choices.
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