Solution to the Problem:
The answer is 99 raisins.
The original number is at least 50 and no more than 100.
After you divide the raisins into groups of 5, there are 4 left over.
So the starting number must be four more than a multiple of 5.
Within the given range, this is true only of 54, 59, 64, 69, 74, 79, 84, 89, 94, and 99.
After you eat 4 raisins, 50, 55, 60, 65, 70, 75, 80, 85, 90, or 95 raisins remain.
After you divide these raisins into groups of 4, there are 3 left over.
So the number of raisins must be 3 more than a multiple of 4.
This is true only of 55 (originally 59), 75 (originally 79), and
95 (originally 99).
After you eat the 3 raisins, 52, 72, or 92 remain.
After you divide these raisins into groups of 3, there are 2 left over.
So the number of raisins must be 2 more than a multiple of 3.
This is true only of 92 (originally 99).
92 - 2 = 90, which is evenly divisible by 2, meeting the final requirement.
Click here to see Dr. Hari Kishan's mathematical explanation