The sum of three consecutive integers is 72. What is the greatest of the three integers?
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Answer & Explanation
Correct answer
C
Write the three consecutive integers as n, n + 1, and n + 2, so their sum is 3n + 3 = 72. Subtract 3 to get 3n = 69, then divide by 3 to get n = 23, making the greatest integer 25. So the answer is C. Faster still, the middle integer is the average, 72 ÷ 3 = 24, so the three are 23, 24, 25. Check: 23 + 24 + 25 = 72.
Choice A reports the smallest integer, the wrong end of the run. Choice B reports the middle integer, the average rather than the greatest. Choice D treats the run as consecutive even integers with a gap of 2, and E halves the total as if there were only two pieces.