If the sum of two consecutive integers is 57, what are the integers?

If the sum of two consecutive integers is 57, what are the integers?

• A. 27 and 28
• B. 29 and 30
• C. 26 and 31
• D. 28 and 29

Answer: (D)

Consecutive integers differ by 1, so if the smaller is x, the next one is x + 1. Their sum is x + (x + 1) = 2x + 1, which is always odd. Since the sum is 57, set 2x + 1 = 57. Subtracting 1 gives 2x = 56, so x = 28. The two numbers are 28 and 29, and 28 + 29 indeed equals 57. (For comparison, 27 and 28 add to 55, 29 and 30 add to 59, and 26 and 31 aren’t consecutive, so only 28 and 29 work.)

Consecutive integers differ by 1, so if the smaller is x, the next one is x + 1. Their sum is x + (x + 1) = 2x + 1, which is always odd. Since the sum is 57, set 2x + 1 = 57. Subtracting 1 gives 2x = 56, so x = 28. The two numbers are 28 and 29, and 28 + 29 indeed equals 57. (For comparison, 27 and 28 add to 55, 29 and 30 add to 59, and 26 and 31 aren’t consecutive, so only 28 and 29 work.)