x is a positive integer of T less than 500. When x is divided by 7, the remainder is 1; when x is divided by 3, the remainder is 2. How many x are there? Choose the correct choice from the following answers:
A) 21	B) 22	C) 23	D) 24	E) 25

Rationale: took me more than 2 mins to solve . that ' s how i did it . x is between 1 - 499 included . smallest number that can be written as 7 n + 1 ( 7 * 0 + 1 ) is 1 largest number that can be written as 7 n + 1 is ( 7 * 71 + 1 ) is 498 so there are total 72 numbers that can be written as 7 n + 1 because x can also be written as 3 m + 2 , we have to see how many numbers that can be written as 7 n + 1 also can be written as 3 m + 2 7 * 0 + 1 can not be written in the form 3 m + 2 7 * 1 + 1 can be written in the form 3 m + 2 7 * 2 + 1 can not be written in the form 3 m + 2 7 * 3 + 1 can not be written in the form 3 m + 2 7 * 4 + 1 can be written in the form 3 m + 2 here we see a sequence that one out of every 4 numbers can be written as 3 m + 1 72 / 4 = 24 numbers can be written as 3 m + 1 d is the answer
Answer: D