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  3. A large flower arrangement contains 3 types of flowers: carnations, lilies, and

A large flower arrangement contains 3 types of flowers: carnations, lilies, and

游客2024-01-13  26
问题 A large flower arrangement contains 3 types of flowers: carnations, lilies, and roses. Of all the flowers in the arrangement, 1/2 are carnations, 1/3 are lilies, and 1/6 are roses. The total price of which of the 3 types of flowers in the arrangement is the greatest?
(1) The prices per flower for carnations, lilies, and roses are in the ratio 1:3:4, respectively.
(2) The price of one rose is $0. 75 more than the price of one carnation, and the price of one rose is $0. 25 more than the price of one lily.
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 T be the total number of flowers, and let $C, $L，and $R be the cost, respectively, of one carnation, one lily, and one rose.
(1) We are given that L = 3C (because C:L is 1:3) and R = AC (because C:R is 1:4). The table below shows the total price for each type of flower.

From the table it is clear that lilies have the greatest total cost; SUFFICIENT.
(2)    We are given that R = 0.75 + C and R = 0.25 + L. To simplify matters, we can use these equations to express each of the variables C, L, and R in terms of a single fixed variable, for example, C= R- 3/4 and L = R-1/4. This will allow us to replace all appearances of C, L, and R with appearances of R only, thereby reducing by two the number of variables that have to be dealt with. The table below shows, for two values of T and R， the total price for each type of flower.

From the table it is clear that the type of flower having the greatest total cost can vary; NOT sufficient.
The correct answer is A;
statement 1 alone is sufficient.
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