Multiple choice

Lily and Rose are running around a circular track in opposite directions. After how much time do they meet, if they start simultaneously from the same point? (1) Their speeds are 6.0 miles/hour and 4.5 miles/hour, respectively. (2) If the diameter of the track is exactly double the present diameter, it takes 4 minutes for them to meet.

  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

Relative speed = 6.0 + 4.5 = 10.5 mph. Time to meet = Distance / Relative Speed. Statement 1 gives speeds but no distance. Statement 2 gives a relationship between diameter and time, which allows calculating the distance (circumference). Thus, statement 2 is sufficient.

AI explanation

Statement 2 states that doubling the diameter makes their meeting time 4 minutes. Since their relative speed is constant, doubling the circumference doubles the meeting time, meaning the original meeting time is 2 minutes. Statement 1 only provides their speeds of 6 and 4.5 miles per hour but lacks the track length, which is needed to find the meeting time. Thus, statement 2 alone is sufficient.

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