Problema Solution
Taha received his locker combination for his new locker. He noticed that each of the three integers of the combination is a prime, the sum of the three integers is 50, and the three integers are in decreasing order. What is the value of the last digit of Taha's locker?
Answer provided by our tutors
let x, y and z be the three prime integers and x>=y>=z
the sum of 3 integers is 50:
x + y + z = 50
z + z + z <= x + y + z = 50
3z <= 50
3z <= 50/3
z < 17
if z is odd integer then 50 - z is also an odd integer which is in contradiction with the fact that the sum of the 2 other prime integers must be an even number.
Thus we conclude that z is even prime number that is z = 2.
the value of the last digit of Taha's locker is 2.