**Q: When the positive integer b is divided by 5, the remainder is 1. When b is divided by 7, the remainder is also 1. If b is less than 100, what is the largest possible value for b?**

Answer: 71

Explanation: *b* is an integer that is one more than a multiple of both 5 and 7. The smallest such value is 35 +1 = 36. But, we need the largest one less than 100. The next common multiple of 5 and 7 is 70 (do 35 x 2), and the next one is 105 (35 x 3). Use 70, and add 1. 71.