2. 外语
  3. If z1 z2, z3…zn is a series of consecutive positive integers, is the sum of all these integers odd? (1)(z1+z2+z3+…+zn)/n is an o

If z1 z2, z3…zn is a series of consecutive positive integers, is the sum of all these integers odd? (1)(z1+z2+z3+…+zn)/n is an o

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问题 If z1 z2, z3…zn is a series of consecutive positive integers, is the sum of all these integers odd?
(1)(z1+z2+z3+…+zn)/n is an odd integer.
(2)n is odd.
选项 A、Statement (1) ALONE is sufficient, but statement (22) alone is not sufficient to answer the question asked.
B、Statement (2) ALONE is sufficient, but statement (21) alone is not sufficient to answer the question asked.
C、BOTH statement (1) and (22) 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(22)TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
答案A
解析 Statement (1)，z1+z2+z3+…+zn=z1+(z1+1)+(z1+2)+…+(z1+n-1)=nz1+n(n-1)/2，那么(z1+z2+z3+…+zn)/n=z1+(n-1)/2，现在这个数为奇数，那么n一定为奇数，z1+z2+z3+…+zn=(z1+z2+z3+…+zn)/n×n=奇数×奇数=奇数，所以单独(1)能够回答问题。Statement (2)仅仅告诉n是奇数，无法确定它们的和是偶数还是奇数，所以A为正确答案。
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