题目信息
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?
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.
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已选答案：
正确答案：
D:EACH statement ALONE is sufficient.
Algebra Sets
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 ?
Given that x – 50 = 10, it follows that x = 60; SUFFICIENT. Given that 80 – x = 20, it follows that x = 60; SUFFICIENT.
Tip A useful way to summarize the quantitative relations for a two-circle Venn diagram is Total = A + B − Both + Neither, where A is the number of elements in Circle A, B is the number of elements in Circle B, “Both” is the number of elements in the intersection of the circles, and “Neither” is the number of elements that do not belong to either of the circles. If we think of A and B as the numbers of elements in the two 1-way intersections (i.e., Circle A alone and Circle B alone) and “Both” as the number of elements in the single 2-way intersection (i.e., Circle A intersects Circle B), then this equation can be written as Total = (sum of 1-way) − (sum of 2-way) + None.
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.
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 ?
Given that x – 50 = 10, it follows that x = 60; SUFFICIENT. Given that 80 – x = 20, it follows that x = 60; SUFFICIENT.
Tip A useful way to summarize the quantitative relations for a two-circle Venn diagram is Total = A + B − Both + Neither, where A is the number of elements in Circle A, B is the number of elements in Circle B, “Both” is the number of elements in the intersection of the circles, and “Neither” is the number of elements that do not belong to either of the circles. If we think of A and B as the numbers of elements in the two 1-way intersections (i.e., Circle A alone and Circle B alone) and “Both” as the number of elements in the single 2-way intersection (i.e., Circle A intersects Circle B), then this equation can be written as Total = (sum of 1-way) − (sum of 2-way) + None.
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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