Multiple choice

What is the distance between Harry's home and his office? (1) Harry's average speed on his commute to work this Monday was 30 miles per hour. (2) If Harry's average speed on his commute to work this Monday had been twice as fast, his trip would have been 15 minutes shorter.

  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
C Correct answer
Explanation

Let d be distance, v be speed, t be time. (1) v = 30. We have d = 30t. Two variables, not sufficient. (2) If speed is 2v, time is t - 15/60. d = 2v(t - 0.25). We have two equations: d = vt and d = 2v(t - 0.25). Substituting v = 30, we get d = 30t and d = 60(t - 0.25). 30t = 60t - 15 => 30t = 15 => t = 0.5. Then d = 15. Both statements are needed.

AI explanation

Let the distance be D miles and the actual time be T hours, making the actual speed D divided by T equal to 30 miles per hour from statement 1. Statement 2 provides the equation T minus D divided by 60 equals 15 minutes, which is 1/4 of an hour. If you substitute D equals 30T into the second equation, you get T minus 30T divided by 60 equals 1/4, which solves to T equals 1/2 hour. Since neither statement alone can provide the actual distance without the other, both statements together are necessary to find the distance of 15 miles.

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