x is a positive integer of F 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?
Select the correct option.
A) 21  B) 22  C) 23  D) 24  E) 25
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 7n+1 (7*0+1) is 1   Largest number that can be written as 7n+1 is (7*71 +1) is 498   So there are total 72 numbers that can be written as 7n+1   Because x can also be written as 3m+2, we have to see how many numbers that can be written as 7n+1 also can be written as 3m+2   7*0+1 can not be written in the form 3m+2   7*1+1 can be written in the form 3m+2   7*2+1 can not be written in the form 3m+2   7*3+1 can not be written in the form 3m+2   7*4+1 can be written in the form 3m+2   Here we see a sequence that one out of every 4 numbers can be written as 3m+1   72/4= 24 numbers can be written as 3m+1   24 is the answer
<result>D</result>
x is a positive integer of F 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?