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  3. If the average(arithmetic mean)of 7 consecutive numbers is 16, what is the sum of the least and greatest of the 7 integers?

If the average(arithmetic mean)of 7 consecutive numbers is 16, what is the sum of the least and greatest of the 7 integers?

admin2013-05-19  12
问题 If the average(arithmetic mean)of 7 consecutive numbers is 16, what is the sum of the least and greatest of the 7 integers?
选项 A、13
B、14
C、16
D、19
E、32
答案E
解析 The correct answer is E. To solve this problem, first set the least of the seven values to x. When the least of the seven numbers is x, the remaining numbers are x+1, x+2, x+3, x+4, x+5, and x+6, because the numbers are consecutive. Because the average of the seven numbers is 16, then[x+(x+l)+(x+2)+(x+3)+(x+4)+(x+5)+(x+6)]divided by 7 = 16. Solve for x:
(7x + 21)/7= 16
7x+21 = 112
7x=91
x=13
The smallest number, x, is 13, and the largest number is x+6. Therefore the largest number is equal to 13+6, or 19, and the sum of these two numbers is 13 + 19, or 32.
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