Problem of the Day


Consider a set of 729 consecutive integers whose smallest element is x. If the arithmetic mean of this set of numbers is 1,072, what is the value of x?

A. 672
B. 708
C. 780
D. 828
E. 1,236

Reveal Answer

Answer

B. 708

See the Solution

Solution

[latexpage]

The key to solving this problem is recognizing that the arithmetic mean of a set of consecutive integers is the same as its median. In other words, 1,072 is precisely in the middle of the 729 consecutive integers. The remaining 728 integers will be divided equally above and below 1,072. Half of 728 is 364, so the smallest element will be $1,072-364=708$.


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