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  3. All trainees in a certain aviator training program must take both a written test

All trainees in a certain aviator training program must take both a written test

游客2025-02-27  46
问题 All trainees in a certain aviator training program must take both a written test and a flight test. If 70 percent of the trainees passed the written test, and 80 percent of the trainees passed the flight test, what percent of the trainees passed both tests?
(1) 10 percent of the trainees did not pass either test.
(2) 20 percent of the trainees passed only the flight test.
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 D
解析 Let x be the percent of the trainees who passed both tests. The following Venn diagram represents the information that is given as well as information that can be derived from what is given. Note that x - 50 in the diagram can be found by using the requirement that the sum of the four values in the diagram is 100. What is the value of x?

(1)     Given that x - 50 = 10, it follows that x = 60; SUFFICIENT.
(2)     Given that 80 - x = 20, it follows that x = 60; SUFFICIENT.
This second way of expressing the quantitative relations for a two-circle Venn diagram can be modified to give a similar way of expressing the quantitative relations for a three-circle Venn diagram:
Total = (sum of 1-way) - (sum of 2-way) + (sum of 3-way) + None.
Although Venn diagrams involving more than three circles will not likely be needed for the GMAT, we recommend researching the inclusion-exclusion principle if the reader is interested in further extensions of these ideas.
The correct answer is D;
each statement alone is sufficient.
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