When positive integer k is divided by 5, the remainder is 2. When k is divided by 6, the remainder is 5. If k is less than 42, what is the remainder when k is divided by 7?
Choose the correct choice.
A) 5
B) 3
C) 6
D) 7
E) 10
Cant think of a straight approach but here is how I solved it:   K is divided by 5 and remainder is 2. This means k = 5n + 2 (n is an integer)   so the possible values of K = {2, 7, 12, 17, 22, 27, 32, 37} (less than 42)   Secondly, if K is divided by 6, the remainder is 5 =&gt; k= 6m + 5   so the possible value set for k = {5, 11, 17, 23, 29,35,41} (less than 42)   17 is the only common number in both the sets. Hence k = 17   Answer : 3
<result>B</result>
When positive integer k is divided by 5, the remainder is 2. When k is divided by 6, the remainder is 5. If k is less than 42, what is the remainder when k is divided by 7?