Multiple choice

Directions: The following problem has a question and two statements which are labeled (A) and (B). Use the data given in (A) and (B) to decide whether the given statements are sufficient to answer the question. Then mark answer: What is the speed of a car? (A) When it travels 10 km/hr slower it takes 5 hours longer to cover 100 kms. (B) When it travels 5 km/hr faster, it takes one hour less to cover 100 kms.

  1. If you can get the answer from any one of the statements.

  2. If you can get the answer from either of the statements individually.

  3. If you can get the answer from (A) and (B) together, although neither statement by itself suffices.

  4. If you cannot get the answer from statements (A) and (B) together, but need even more data.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let speed be v. (A) 100/(v-10) - 100/v = 5. (B) 100/v - 100/(v+5) = 1. Both equations are solvable for v. Thus, either statement is sufficient.

AI explanation

Let the actual speed of the car be x km/hr. Using statement A, the difference in time gives the equation (100 / (x - 10)) - (100 / x) = 5, which simplifies to the quadratic equation x^2 - 10x - 200 = 0 and yields x = 20 km/hr. Using statement B, the equation is (100 / x) - (100 / (x + 5)) = 1, which simplifies to x^2 + 5x - 500 = 0 and also yields a unique speed of 20 km/hr. Therefore, the car's speed can be determined from either statement individually.

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