Question

Two numbers a and b, when divided by 7 and 6 respectively, leave remainders p and q respectively. What is the maximum value of p + q ?

• A. 11
• B. 12
• C. 6
• D. 5

Answer 1

The correct option is A

11

According to Euclid division lemma:
There exist integers m and n such that a = 7m + p and b = 6n + q.

For $0\le p<7\Rightarrow$ Maximum value of p will be 6.

For $0\le q<6\Rightarrow$ Maximum value of q will be 5.

Therefore, the maximum value of p + q will be 11.