Find the largest pair of consecutive even integers whose sum is less than 85.
40 + 42
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To find the largest pair of consecutive even integers whose sum is less than 85, we can start by examining the possible pairs of consecutive even integers:
2 and 4: The sum is 2 + 4 = 6, which is less than 85.
4 and 6: The sum is 4 + 6 = 10, which is less than 85.
6 and 8: The sum is 6 + 8 = 14, which is less than 85.
We continue checking the pairs until we find a sum that is no longer less than 85.
8 and 10: The sum is 8 + 10 = 18, which is less than 85.
10 and 12: The sum is 10 + 12 = 22, which is less than 85.
12 and 14: The sum is 12 + 14 = 26, which is less than 85.
14 and 16: The sum is 14 + 16 = 30, which is less than 85.
16 and 18: The sum is 16 + 18 = 34, which is less than 85.
18 and 20: The sum is 18 + 20 = 38, which is less than 85.
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We continue this process until we reach a pair where the sum exceeds 85:
30 and 32: The sum is 30 + 32 = 62, which is less than 85.
32 and 34: The sum is 32 + 34 = 66, which is less than 85.
34 and 36: The sum is 34 + 36 = 70, which is less than 85.
36 and 38: The sum is 36 + 38 = 74, which is less than 85.
38 and 40: The sum is 38 + 40 = 78, which is less than 85.
40 and 42: The sum is 40 + 42 = 82, which is less than 85.
42 and 44: The sum is 42 + 44 = 86, which is greater than 85.
Thus, the largest pair of consecutive even integers whose sum is less than 85 is 40 and 42.