The following data sufficiency problems consist of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of counterclockwise), you must indicate whether.
If a is an integer, is b an integer ？（）
(1) The average (arithmetic mean) of a and b is an integer.
(2) The average (arithmetic mean) of a, b, and b+4 is a.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
参考答案：D
解析：
alone is sufficient; the statement can be restated as (a+b)/2 is an integer; no non-integer divided by an integer--in this case, 2--is going to yield an integer, so a+b must be an integer, and therefore b must be an integer. (2) alone is sufficient; the statement can be restated as a+2b+4=3a, so b+2=a; we know that a is an integer, and any integer plus 2 is an integer, so b must be an integer.