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  3. At a certain university recreation center, a member can receive a 30-minute massage, a 60-minute massage, or a 90-minute massage

At a certain university recreation center, a member can receive a 30-minute massage, a 60-minute massage, or a 90-minute massage

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问题 At a certain university recreation center, a member can receive a 30-minute massage, a 60-minute massage, or a 90-minute massage, and is charged $0. 50 per minute for each massage. A member receiving a massage is charged the same fixed amount for each additional service, such as nutrition advice or a fitness evaluation. At this center, what is the total charge to a member for a 60-minute massage and 3 additional services?
(1) At this recreation center, Jordan, a member, had a massage and 3 additional services for a total charge of $37. 50.
(2) At this recreation center, Ryan, a member, had a massage and 2 additional services for a total charge of $60. 00.
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C
解析 Let x be the charge, in dollars, of each additional service. Determine the value of (60)(0.5) + 3x, or equivalently, determine the value of x.
(1) The table below shows the value of x for each of the three possible massages that Jordan had.
Massage            Total charge              x
30-minute          15 + 3x = 37.50          7.50
60-minute          30 + 3x = 37.50          2.50
90-minute          45 + 3x = 37.50         -2.50
From the table it follows that there are two possible values of x, namely x = 7.5 and x = 2.5; NOT sufficient.
(2) The table below shows the value of x for each of the three possible massages that Ryan had.
Massage           Total charge         x
30-minute        15 + 2x = 60         22.50
60-minute        30 + 2x = 60         15.00
90-minute        45 + 2x = 60          7.50
From the table it follows that there are three possible values of x, namely x = 22.5, x = 15, and x = 7.5; NOT sufficient.
Given (1) and (2), it follows that x = 7.5.
The correct answer is C;
both statements together are sufficient.
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