2012 AMC 12B Problem 5
Problem 5 of 25EasierNumber Theory
Two integers have a sum of When two more integers are added to the first two integers the sum is Finally when two more integers are added to the sum of the previous four integers the sum is What is the minimum number of even integers among the integers?
Answer choices
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Solution
The three successive pairs have sums and
A pair sums to an even number when its two integers share parity, and to an odd number when exactly one is even. Only the middle pair sums to an odd number, so it must contain at least one even integer.
The other two pairs can be all odd, so as few as even integer is possible, for example
Thus, the correct answer is A.