2. 外语
  3. Alan and Sue have each been saving one dollar a day and will continue to do so for the next month. If Sue began saving several d

Alan and Sue have each been saving one dollar a day and will continue to do so for the next month. If Sue began saving several d

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问题 Alan and Sue have each been saving one dollar a day and will continue to do so for the next month. If Sue began saving several days before Alan, in how many days from today will Alan have saved one-half as much as Sue?
(1) As of today, Alan has saved 7 dollars and Sue has saved 27 dollars.
(2) Three days from today, Alan will have saved one-third as much as Sue.
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 Let A be the amount Alan has saved as of today. Let S be the amount Sue had already saved when Alan started saving. Then, as of today, Sue has saved S + A dollars. Determine d，the number of days from today that Alan will have saved half as much as Sue. That is, determine d，where A + d = (S + A + d)/2 or, after algebraic manipulation, determine d such that d= S-A.
(1)     It is given that A = 7 and S = 27, so d= 20; SUFFICIENT.
(2)     It is given that three days from today, Alan will have saved one-third as much as Sue, from which it follows that A + 3 = (S + A + 3)/3 or, after algebraic manipulation, S = 2A + 6. Then, d=S-A=(2A+6)-A = A+6. Since the value of A can vary, the value of d cannot be determined; NOT sufficient.
The correct answer is A;
statement 1 alone is sufficient.
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