There are between 300 and 310 cards in a collection of cards. If they are counted out 3 at a time, there are 2 left over, but if they are counted out 4 at a time, there is 1 left over. How many cards are in the collection? Pick:  A) 301  B) 303  C) 306  D) 307  E) 309
Let number of cards = x   If the cards are counted 3 at a time , there are 2 left over-   x= 3p+2   x can take values 306 , 309   If the cards are counted 4 at a time , there is 1 left over   x= 4q+1   x can take values 301 , 309   Therefore , x = 309   Answer 309
<result>E</result>
There are between 300 and 310 cards in a collection of cards. If they are counted out 3 at a time, there are 2 left over, but if they are counted out 4 at a time, there is 1 left over. How many cards are in the collection?