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When a number is divided by 13, the remainder is 11. When the same number is divided by 17, then remainder is 9. What is the number?

339
349
369
Data inadequate

Correct Answer: 349

Explanation:

x = 13 p + 11 and x = 17 q + 9

∴ 13p + 11 = 17q + 9

⟹ 17q - 13p = 2

⟹ q =	2 + 13p
	17

The least value of p for which q =	2 + 13p	is a whole number is p = 26
	17

∴ x = (13 x 26 + 11)

= (338 + 11)

= 349

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