Multiple choice

James and Olivia started simultaneously from P and Q (respectively) towards Q and P (respectively). At what distance from P do they meet, if the distance between P and Q is 140 mi? (1) The ratio of their speeds is 3 : 4. (2) The speed of Olivia is 10 mi/h more than that of James.

  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.
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A Correct answer
Explanation

Statement 1 provides the ratio of speeds, which is sufficient to find the meeting point relative to the total distance. Statement 2 provides the difference in speeds, but without the total time or individual speeds, the meeting point cannot be determined.

AI explanation

When two objects travel towards each other, the ratio of the distances they cover from their respective starting points to the meeting point is exactly the same as the ratio of their speeds. Using statement (1) alone, the ratio of their speeds is 3 : 4, which means James covers 3 parts of the total distance and Olivia covers 4 parts. Given the total distance of 140 miles, James meets Olivia at a distance of 140 multiplied by 3/7, which equals 60 miles from P. Statement (2) only gives a speed difference but no actual values, so it cannot provide the exact distance; therefore, statement (1) alone is sufficient, but statement (2) alone is not.

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