Multiple choice

Directions: The following problem contains a question and two statements giving certain data. You have to decide whether the data given in the statements is sufficient for answering the question and then mark the option accordingly. 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) 10 percent of the trainees did not pass either test. (B) 20 percent of the trainees passed only the flight test.

  1. Statement (A) alone is sufficient but statement (B) alone is not sufficient.

  2. Statement (B) alone is sufficient but statement (A) alone is not sufficient.

  3. Both (A) and (B) together are sufficient but none of them alone is sufficient.

  4. Both statements independently are sufficient.

  5. Both (A) and (B) together are not sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let W=70, F=80. Total = 100. (A) 10% pass neither, so 90% pass at least one. W+F - Both = 90 => 70+80 - Both = 90 => Both = 60. (B) 20% pass only flight, so 80 - Both = 20 => Both = 60. Both are sufficient.

AI explanation

Using the set theory formula Total = Written + Flight - Both + Neither, you can analyze the statements. For statement (A), assuming a total of 100 trainees, 100 = 70 + 80 - Both + 10, which solves to show that 60 percent of trainees passed both tests. For statement (B), the number of trainees who passed only the flight test equals the total flight test passers minus the trainees who passed both, meaning 20% = 80% - Both, which also solves to show that 60 percent passed both. Both statements independently provide sufficient data to answer the question, so both statements independently are sufficient.

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