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The following data sufficiency problems consist of a question and two statements
The following data sufficiency problems consist of a question and two statements
游客
2025-02-27
9
管理
问题
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
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. [br] 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.
选项
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.
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