There are between 500 and 510 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? Choose the correct choice from the following choices.
A) 501
B) 503
C) 506
D) 507
E) 510
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 503 , 506 , 510   If the cards are counted 4 at a time , there is 1 left over   x= 4q+1   x can take values 501 , 506   Therefore , x = 506   Answer 506
<result>C</result>
There are between 500 and 510 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?