The number n yields a remainder p when divided by 12 and a remainder q when divided by 7. If p = q + 7, then which one of the following could be the value of n ? Choose the correct choice from the following:
A) 45  B) 34  C) 72  D) 85  E) 100
I solved this question in the following way:   Q&lt;7 so Q can be from 0 to 6 and P&lt;12 so P can be from 0 to 11, BUT the constraint is P=Q +7 so this will mean that P can be in the range from 7 to 11.   n=12k + P or n= 12k + 7 to 11 and look at the answer as, place different values for k, 34 will give 34 which is 12*2 + 10, the other answers are out of the range
<result>B</result>
The number n yields a remainder p when divided by 12 and a remainder q when divided by 7. If p = q + 7, then which one of the following could be the value of n ?