1. Frank has two integers that add up to 26. Kees adds two more integers and gets 41. Pieter adds two more integers and gets 58. At least how many of the six added numbers are even?
A) 0
B) 1
C) 2
D) 3
E) 4
A1. C) 2 The two numbers Frank has are either both even or both odd; otherwise, their sum would not be even. The two numbers Kees has add up to $41-26=15$, so one of his numbers must be even and the other odd, because otherwise the sum would not be odd. Pieter's numbers add up to $58-41=17$, so one of his numbers must also be even. Therefore, the minimum number of even numbers is 2, and this occurs, for example, if Frank has the numbers 11 and 15, Kees has the numbers 7 and 8, and Pieter has the numbers 4 and 13.