2012 AMC 12B Problem 5
Attempt Problem 5 of the 2012 AMC 12B below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2012 AMC 12B solutions, or check the answer key.
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5.
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: A
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.
Problem 5 in Other Years
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