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let the number =n let the quotient =q n/10000=q ,remainder 57 therefore n = 10000q +57 when q=1 ; n=10057 10057/1000 = 10 r 57 when q=2 ; n=20057 20057/1000 = 20 r 57 hence ans is 57
Important: Many integer properties questions can be solved by identifying a value that satisfies the given information
Also important: If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc. For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.
Given: The remainder is 57 when a number is divided by 10,000 This means the number in question COULD be 57 (or 10,057 or 20,057 or 30,057 or....) As you can imagine it's much easier to work with the smallest possible value of 57
What is the remainder when the same number is divided by 1,000? When 57 is divided by 1,000, the remainder is 57
Answer: 57
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