2. 外语
  3. Tami purchased several identically priced metal frames and several identically priced wooden frames for a total pretax price of

Tami purchased several identically priced metal frames and several identically priced wooden frames for a total pretax price of

admin2022-10-18  64
问题 Tami purchased several identically priced metal frames and several identically priced wooden frames for a total pretax price of $144. What was the total pretax price of the metal frames that Tami purchased?
(1) The price of each metal frame was 60% greater than the price of each wooden frame.
(2) Tami purchased twice as many wooden frames as metal frames.
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 m and w, respectively, be the number of metal frames and wooden frames that Tami purchased, and let M and W, respectively, be their individual prices in dollars. We are given that mM+ wW=144. What is the value of mM?
(1)    Given that M= 1.6W= 8W/5, or W= 5W/8, we have mM+ w (5W/8) =144. Although it might seem there is not enough information to determine the value of mM, keep in mind that we are only seeking the value of the product mM, and not the individual values of m and M. Also, there are several implicit constraints involved, such as each of M and W must be a positive number less than 144 and each of m and w must be a positive integer. To see that more than one value of mM is possible, it will be convenient to specify a particular value for w, for example,
w= 16. Then mM+w(5W/8)=144
becomes mM= 144 - 10M, and non-sufficiency is now straightforward. If w = 16 and M= 4, then mM= 104. However, if w = 16 and M= 8, then mM= 64; NOT sufficient.
(2)    Given that w = 2m, we have mM+ (2m)W= 144, or mM= 144 - 2mW. If m = 10 and W= 4, then mM= 64. However, if m = 10 and W= 5, then mM= 44; NOT sufficient.
Given (1) and (2), we have W= 5M/8 and w = 2m.
Therefore, mM+ wW= 144 becomes
mM+{2m)(5M/8)=144，or(1+5/4)mM=144，and hence the value of mM can be determined.
The correct answer is C;
both statements together are sufficient.
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