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Mathematics>Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer.

To make an orange dye, 3 parts of red dye are mixed with 2 parts of yellow dye. To make a green dye, 2 parts of blue dye are mixed with 1 part of yellow dye. If equal amounts of green and orange are mixed, what fraction of the new mixture is yellow dye?

(A) 3/16
(B) 1/4
(C) 11/30
(D) 3/8
(E) 7/12

答案和解析

答案：C

解析：

Suppose that x quarts of the final mixture of dye will be made. Since it is to be made from equal amounts of orange and green dye, it will consist of (1/2)x quarts of orange dye and (1/2)x quarts of green dye. Since the orange dye has 2 parts yellow dye for each 5 parts total dye, 2/5 of it is yellow dye. Similarly, 1/3 of the green dye is yellow dye. The amount of yellow in the final mixture is given by

((2/5)(1/2)x) + ((1/3)(1/2)x) = ((1/5)x ) + ((1/6)x)

= (11/30)x quarts

So 11/30 of the final mixture is yellow dye.

Note: Although "quartsh" were used to express the amount of the final mixture, it could have been pints or any other unit of liquid measure.