题目信息
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?
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.
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正确答案：
A:Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Algebra First-degree equations
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) or, after algebraic manipulation, determine d such that d = S − A.
It is given that A = 7 and S = 27, so d = 20; SUFFICIENT. 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) 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.
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) or, after algebraic manipulation, determine d such that d = S − A.It is given that A = 7 and S = 27, so d = 20; SUFFICIENT. 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) 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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