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 ?

Question:
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 ?

[A].

339

[B].

349

[C].

369

[D].

Data inadequate

Answer: Option B

Explanation:

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