Multiple choice

Amtrak train covers a certain distance from Quebec to Alabama in 3 hours at a certain speed. What would be the speed to cover the same distance in 2 hours? (1) Speed of the train to cover the same distance in 3 hours is more than 50 miles per hour. (2) The difference in speed of the train when covering the distance in the stated durations is 30 miles per hour.

  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  4. EACH statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let d be the distance and v be the speed. We know d/3 = v. We want to find the speed v' = d/2. Statement 1 gives v > 50, which is not enough to find v'. Statement 2 gives v' - v = 30. Since v' = 1.5v, we have 1.5v - v = 30, so 0.5v = 30, v = 60. Thus, v' = 90. Statement 2 is sufficient.

AI explanation

Let the new speed for the two-hour trip be s miles per hour, making the original three-hour speed (2/3)s. Statement 2 gives the speed difference as s - (2/3)s = 30, which simplifies to s/3 = 30 and yields s = 90 miles per hour. Because the distance remains constant, finding the new speed requires only the ratio of the times and the difference in speeds, which statement 2 completely provides. Therefore, statement 2 alone is sufficient to answer the question.

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