Multiple choice

Directions: In this problem, a question is given followed by three statements numbered I, II and III. Read the statements carefully and decide which of them is/are sufficient/required to answer the question. What is the time taken by Lisa to complete a 10-kilometre race? Statements: A. If Lisa increases her speed by 20%, she will finish the race 5 minutes earlier. B. If Lisa decreases her speed by 15%, she will finish the race 6 minutes later. C. Lisa's speed is 8 km/hr.

  1. Only C is sufficient.

  2. Only B and C are sufficient.

  3. Only A and C are sufficient.

  4. Each of the statements A, B and C alone is sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let speed be v and time be t. Distance = 10. v*t = 10. Statement A: 1.2v * (t - 5/60) = 10. Statement B: 0.85v * (t + 6/60) = 10. Statement C: v = 8. Each statement provides enough info to solve for t.

AI explanation

Using the basic formula relating time, distance, and speed, each statement independently allows you to solve for the initial speed. In statement A, if Lisa increases her speed by 20%, her new speed is 1.2 times her original speed, making her new time 1/1.2 of her original time; the resulting 5-minute difference yields an original time of 30 minutes. Statement B uses the same logic for a 15% decrease, where the new time becomes 1/0.85 of the original time, and the 6-minute difference again results in exactly 30 minutes. Statement C provides the speed of 8 km/hr directly, which gives a time of 10 divided by 8 hours, or 1.25 hours, confirming the result is exactly 1 hour and 15 minutes. Therefore, each of the statements A, B and C alone is sufficient.

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