2. 外语
  3. The average(arithmetic mean)of M consecutive odd integers is 10. What is the smallest number in the sequence? (1)The range of th

The average(arithmetic mean)of M consecutive odd integers is 10. What is the smallest number in the sequence? (1)The range of th

admin2022-11-19  45
问题 The average(arithmetic mean)of M consecutive odd integers is 10. What is the smallest number in the sequence?
(1)The range of the M consecutive odd integers is 14.
(2)The greatest number of the M consecutive odd integers is 15.
选项 A、Statement (1) ALONE is sufficient, but statement (28) alone is not sufficient to answer the question asked.
B、Statement (2) ALONE is sufficient, but statement (27) alone is not sufficient to answer the question asked.
C、BOTH statement (1) and (28) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.
D、EACH statement ALONE is sufficient to answer the question asked.
E、Statement (1) and(28)TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
答案D
解析 设最小的奇数为a1，M个连续奇数是一个等差数列，公差为2，它们的平均数为10，那么它们的和为10M，在Statement (1)中，am-a1=14，那么M=7，知道了和、项数、公差，首项当然可以求得，所以单独(1)可以回答问题。在Statement (2)中，设am为原数列中最大的奇数，则am=15，那么
S=10M=(a1+15)/2
15=a1+(M-1)×2
从方程组里面能够求得a1，也就是数列中的最小值，所以单独(2)也可以回答问题。因此D为正确答案。
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