When 10000 is divided by 13 , the remainder is 3 . Which one of the following numbers also gives a remainder of 3 when divided by 13 ?
(A) 9997
(B) 10003
(C) 10013
(D) 10010
(E) 10016
Solution 1

When 10000 is divided by 13 with the help of a calculator, we get $10000 \div 13=769.230 \ldots$. Since $769 \times 13=9997$ and $10000-9997=3$, then we have a quotient of 769 and a remainder of 3 .

That is, $10000=769 \times 13+3$.

This is called a division statement.

Similarly, we may determine the remainder when each of the five possible answers (the dividend) is divided by 13 (the divisor).

We summarize this work in the table below.

| Answer | Division Statement | Remainder |
| :---: | :---: | :---: |
| (A) | $9997=769 \times 13+0$ | 0 |
| (B) | $10003=769 \times 13+6$ | 6 |
| (C) | $10013=770 \times 13+3$ | 3 |
| (D) | $10010=769 \times 13+0$ | 0 |
| (E) | $10016=770 \times 13+6$ | 6 |

Of the five possible answers, only 10013 gives a remainder of 3 when divided by 13 .

## Solution 2

When 10000 is divided by 13 , the remainder is 3 .

Thus, adding any multiple of 13 to 10000 will give the same remainder, 3 , upon division by 13 . Of the five choices given, the only answer that differs from 10000 by a multiple of 13 is 10013 . When 10013 is divided by 13, the remainder is also 3 .

ANSwer: (C)