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# Discussion

When a number is divided by 17, the remainder is 9. When the same number is divided by 23, the remainder is 4. Find the number?

• A.20
• B.349
• C.329
• D.60

$$x = 17p + 9$$ and $$x = 23q + 4$$
i.e. $$17p + 9 = 23q + 4$$
Therefore, $$q = \frac{(17p + 5)}{23}$$
Least value of p for which q is a whole number is $$p = 20$$
$$x = 17p + 9$$
$$= 17 \times 20 + 9$$
$$= 349$$

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