2. 外语
  3. If denotes a mathematical operation, does x y = y x for all x and y ? (1) For all x and y, x y = 2(x2 + y2). (2) For all y,

If denotes a mathematical operation, does x y = y x for all x and y ? (1) For all x and y, x y = 2(x2 + y2). (2) For all y,

admin2022-10-18  34
问题 If denotes a mathematical operation, does x y = y x for all x and y ?
(1) For all x and y, x y = 2(x2 + y2).
(2) For all y, 0 y = 2y2.
选项 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.
答案A
解析 (1)     For all x and y, x y = 2(x2 + y2) is equal to y x = 2(y2 + x2); SUFFICIENT.
(2)     If x y = 2(x2 + y2) for all x and y, then 0 y = 2y2 for all y and x y = y x for all x and y. However, if x y = 2(x3 + y2) for all x and y, then 0 y = 2y2 for all y, but 1 277 2 = 2(13) + 2(22) = 10 and 2 1 = 2(23) + 2(12) = 18; NOT sufficient.
The correct answer is A;
statement 1 alone is sufficient.
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